• Contents
  • Topics
  • About
  • Acknowledgments
    • Credits
      • Documentation
      • Software
      • Testing
      • Technical Support
    • Acknowledgments
  • What’s New in SAS/STAT 12.1
    • Overview
      • New Procedures
      • Highlights of Enhancements
      • Highlights of Enhancements in SAS/STAT 9.3
      • New Macros
    • Enhancements
      • CALIS Procedure
      • EFFECTPLOT Statement
      • FMM Procedure
      • FREQ Procedure
      • GLIMMIX Procedure
      • LIFEREG Procedure
      • LIFETEST Procedure
      • LOESS Procedure
      • LOGISTIC Procedure
      • MCMC Procedure
      • MULTTEST Procedure
      • NLIN Procedure
      • NPAR1WAY Procedure
      • ODS Graphics
      • PHREG Procedure
      • POWER Procedure
      • PROBIT Procedure
      • QUANTREG Procedure
      • REG Procedure
      • ROBUSTREG Procedure
      • SEQDESIGN Procedure
      • SEQTEST Procedure
      • SURVEYFREQ Procedure
      • SURVEYMEANS Procedure
      • SURVEYPHREG Procedure
      • SURVEYREG Procedure
      • SURVEYSELECT Procedure
    • What’s Changed
      • LIFETEST Procedure
      • FREQ Procedure
      • MCMC Procedure
      • MULTTEST Procedure
      • SURVEYSELECT Procedure
      • GLIMMIX, GLM, HPMIXED, and MIXED Procedures
    • References
  • Getting Started/Overview
    • Overview of SAS/STAT Software
    • Experimental Software
    • About This Book
      • Chapter Organization
      • Typographical Conventions
      • Options Used in Examples
    • Where to Turn for More Information
      • Accessing the SAS/STAT Sample Library
      • Sashelp Data Sets
      • Online Documentation
      • SAS Technical Support Services
    • Related SAS Software
      • SAS/IML Software
      • Base SAS Software
      • ODS Graphics
      • SAS/ETS Software
      • SAS/GRAPH Software
      • SAS/INSIGHT Software
      • SAS/OR Software
      • SAS/QC Software
      • SAS/IML Studio
  • Introductions
    • Introduction to Statistical Modeling with SAS/STAT Software
      • Overview: Statistical Modeling
        • Statistical Models
        • Classes of Statistical Models
          • Linear and Nonlinear Models
          • Regression Models and Models with Classification Effects
          • Univariate and Multivariate Models
          • Fixed, Random, and Mixed Models
          • Generalized Linear Models
          • Latent Variable Models
          • Bayesian Models
        • Classical Estimation Principles
          • Least Squares
          • Likelihood
          • Inference Principles for Survey Data
      • Statistical Background
        • Hypothesis Testing and Power
        • Important Linear Algebra Concepts
        • Expectations of Random Variables and Vectors
        • Mean Squared Error
        • Linear Model Theory
          • Finding the Least Squares Estimators
          • Analysis of Variance
          • Estimating the Error Variance
          • Maximum Likelihood Estimation
          • Estimable Functions
          • Test of Hypotheses
          • Residual Analysis
          • Sweep Operator
      • References
    • Introduction to Regression Procedures
      • Overview: Regression Procedures
        • Introduction
        • Introductory Example: Linear Regression
        • Linear Regression: The REG Procedure
        • Response Surface Regression: The RSREG Procedure
        • Partial Least Squares Regression: The PLS Procedure
        • Generalized Linear Regression
          • Logistic Regression
          • Other Generalized Linear Models
        • Regression for Ill-Conditioned Data: The ORTHOREG Procedure
        • Quantile Regression: The QUANTREG Procedure
        • Nonlinear Regression
        • Nonparametric Regression
          • Local Regression: The LOESS Procedure
          • Smooth Function Approximation: The TPSPLINE Procedure
          • Generalized Additive Models: The GAM Procedure
        • Robust Regression: The ROBUSTREG Procedure
        • Regression with Transformations: The TRANSREG Procedure
        • Interactive Features in the CATMOD, GLM, and REG Procedures
      • Statistical Background in Linear Regression
        • Linear Regression Models
        • Parameter Estimates and Associated Statistics
        • Predicted and Residual Values
        • Testing Linear Hypotheses
        • Multivariate Tests
        • Comments on Interpreting Regression Statistics
      • References
    • Introduction to Analysis of Variance Procedures
      • Overview: Analysis of Variance Procedures
        • Procedures That Perform Sum of Squares Analysis of Variance
        • Procedures That Perform General Analysis of Variance
      • Statistical Details for Analysis of Variance
        • From Sums of Squares to Linear Hypotheses
        • Tests of Effects Based on Expected Mean Squares
      • Analysis of Variance for Fixed-Effect Models
        • PROC GLM for General Linear Models
        • PROC ANOVA for Balanced Designs
        • Comparing Group Means
        • PROC TTEST for Comparing Two Groups
      • Analysis of Variance for Categorical Data and Generalized Linear Models
      • Nonparametric Analysis of Variance
      • Constructing Analysis of Variance Designs
      • For More Information
      • References
    • Introduction to Mixed Modeling Procedures
      • Overview: Mixed Modeling Procedures
      • Types of Mixed Models
        • Linear, Generalized Linear, and Nonlinear Mixed Models
          • Linear Mixed Model
          • Generalized Linear Mixed Model
          • Nonlinear Mixed Model
        • Models for Clustered and Hierarchical Data
        • Models with Subjects and Groups
      • Linear Mixed Models
        • Comparing the MIXED and GLM Procedures
        • Comparing the MIXED and HPMIXED Procedures
      • Generalized Linear Mixed Models
        • Comparing the GENMOD and GLIMMIX Procedures
      • Nonlinear Mixed Models: The NLMIXED Procedure
      • References
    • Introduction to Bayesian Analysis Procedures
      • Overview
      • Introduction
      • Background in Bayesian Statistics
        • Prior Distributions
        • Bayesian Inference
        • Bayesian Analysis: Advantages and Disadvantages
        • Markov Chain Monte Carlo Method
        • Assessing Markov Chain Convergence
        • Summary Statistics
      • A Bayesian Reading List
        • Textbooks
        • Tutorial and Review Papers on MCMC
      • References
    • Introduction to Categorical Data Analysis Procedures
      • Overview: Categorical Data Analysis Procedures
      • Introduction
      • Sampling Frameworks and Distribution Assumptions
        • Simple Random Sampling: One Population
        • Stratified Simple Random Sampling: Multiple Populations
        • Observational Data: Analyzing the Entire Population
        • Randomized Experiments
        • Relaxation of Sampling Assumptions
      • Comparison of PROC FREQ and the Modeling Procedures
      • Comparison of Modeling Procedures
        • Logistic Regression
      • References
    • Introduction to Multivariate Procedures
      • Overview: Multivariate Procedures
      • Comparison of the PRINCOMP and FACTOR Procedures
      • Comparison of the PRINCOMP and PRINQUAL Procedures
      • Comparison of the PRINCOMP and CORRESP Procedures
      • Comparison of the PRINQUAL and CORRESP Procedures
      • Comparison of the TRANSREG and PRINQUAL Procedures
      • References
    • Introduction to Discriminant Procedures
      • Overview: Discriminant Procedures
      • Background: Discriminant Procedures
      • Example: Contrasting Univariate and Multivariate Analyses
      • References
    • Introduction to Clustering Procedures
      • Overview: Clustering Procedures
      • Clustering Variables
      • Clustering Observations
      • Characteristics of Methods for Clustering Observations
        • Well-Separated Clusters
        • Poorly Separated Clusters
        • Multinormal Clusters of Unequal Size and Dispersion
        • Elongated Multinormal Clusters
        • Nonconvex Clusters
      • The Number of Clusters
      • References
    • Introduction to Scoring, Standardization, and Ranking Procedures
      • Overview: Scoring, Standardization, and Ranking Procedures
    • Introduction to Survival Analysis Procedures
      • Overview
      • Survival Analysis Procedures
        • The LIFEREG Procedure
        • The LIFETEST Procedure
        • The PHREG Procedure
        • The SURVEYPHREG Procedure
      • Survival Analysis with SAS/STAT Procedures
      • Bayesian Survival Analysis with SAS/STAT Procedures
      • References
    • Introduction to Survey Sampling and Analysis Procedures
      • Overview: Survey Sampling and Analysis Procedures
      • The Survey Procedures
        • PROC SURVEYSELECT
        • PROC SURVEYMEANS
        • PROC SURVEYFREQ
        • PROC SURVEYREG
        • PROC SURVEYLOGISTIC
        • PROC SURVEYPHREG
      • Survey Design Specification
        • Population
        • Stratification
        • Clustering
        • Multistage Sampling
        • Sampling Weights
        • Population Totals and Sampling Rates
      • Variance Estimation
      • Example: Survey Sampling and Analysis Procedures
        • Sample Selection
        • Survey Data Analysis
      • References
    • The Four Types of Estimable Functions
      • Overview
      • Estimability
        • General Form of an Estimable Function
        • Introduction to Reduction Notation
        • Examples
      • Estimable Functions
        • Type I SS and Estimable Functions
        • Type II SS and Estimable Functions
        • Type III and IV SS and Estimable Functions
      • References
    • Introduction to Nonparametric Analysis
      • Overview: Nonparametric Analysis
        • Testing for Normality
        • Comparing Distributions
      • One-Sample Tests
      • Two-Sample Tests
        • Comparing Two Independent Samples
        • Comparing Two Related Samples
      • Tests for k Samples
        • Comparing k Independent Samples
        • Comparing k Dependent Samples
      • Measures of Correlation and Associated Tests
      • Obtaining Ranks
      • Kernel Density Estimation
      • References
    • Introduction to Structural Equation Modeling with Latent Variables
      • Overview of Structural Equation Modeling with Latent Variables
      • Testing Covariance Patterns
        • Testing Built-In Covariance Patterns in PROC CALIS
        • Direct and Implied Covariance Patterns
      • Regression with Measurement Errors
        • Simple Linear Regression
        • Errors-in-Variables Regression
        • Regression with Measurement Errors in X and Y
      • Model Identification
        • Illustration of Model Identification: Spleen Data
      • Path Diagrams and Path Analysis
        • A Simplified Path Diagram for the Spleen Data
      • Some Measurement Models
        • H4: Full Measurement Model for Lord Data
        • H3: Congeneric (One-Factor) Model for Lord Data
        • H2: Two-Factor Model with Parallel Tests for Lord Data
        • H1: One-Factor Model with Parallel Tests for Lord Data
      • The FACTOR and RAM Modeling Languages
        • Specifying the Full Measurement Model (H4) by the FACTOR Modeling Language: Lord Data
        • Specifying the Parallel Tests Model (H2) by the FACTOR Modeling Language: Lord Data
        • Specifying the Parallel Tests Model (H2) by the RAM Modeling Language: Lord Data
      • A Combined Measurement-Structural Model
        • Career Aspiration: Analysis 1
        • Career Aspiration: Analysis 2
        • Career Aspiration: Analysis 3
      • Fitting LISREL Models by the LISMOD Modeling Language
        • The Measurement Model for y
        • The Measurement Model for x
        • The Structural Model
        • Fit Summary of the LISMOD Model for Career Aspiration Analysis 3
      • Some Important PROC CALIS Features
        • Modeling Languages for Specifying Models
        • Estimation Methods
        • Statistical Inference
        • Multiple-Group Analysis
        • Goodness-of-Fit Statistics
        • Customizable Fit Summary Table
        • Standardized Solution
        • Testing Parametric Functions
        • Effect Analysis
        • Model Modifications
        • Optimization Methods
        • Other Commonly Used Options
      • Comparison of the CALIS and FACTOR Procedures for Exploratory Factor Analysis
      • Comparison of the CALIS and SYSLIN Procedures
      • References
    • Introduction to Power and Sample Size Analysis
      • Overview
        • Coverage of Statistical Analyses
      • Statistical Background
        • Hypothesis Testing, Power, and Confidence Interval Precision
          • Standard Hypothesis Tests
          • Equivalence and Noninferiority
          • Confidence Interval Precision
        • Computing Power and Sample Size
      • Power and Study Planning
        • Components of Study Planning
        • Effect Size
        • Uncertainty and Sensitivity Analysis
      • SAS/STAT Tools for Power and Sample Size Analysis
        • Basic Graphs (POWER, GLMPOWER, Power and Sample Size Application)
        • Highly Customized Graphs (POWER, GLMPOWER)
        • Formatted Tables (%POWTABLE Macro)
        • Narratives and Graphical User Interface (Power and Sample Size Application)
        • Customized Power Formulas (DATA Step)
        • Empirical Power Simulation (DATA Step, SAS/STAT Software)
      • References
  • Shared Concepts and Topics
    • Levelization of Classification Variables
    • Parameterization of Model Effects
      • GLM Parameterization of Classification Variables and Effects
        • Intercept
        • Regression Effects
        • Main Effects
        • Interaction Effects
        • Nested Effects
        • Continuous-Nesting-Class Effects
        • Continuous-by-Class Effects
        • General Effects
      • Other Parameterizations
    • CODE Statement
      • Syntax: CODE Statement
    • EFFECT Statement
      • Collection Effects
      • Lag Effects
      • Multimember Effects
      • Polynomial Effects
      • Spline Effects
      • Splines and Spline Bases
        • Truncated Power Function Basis
        • B-Spline Basis
        • Natural Cubic Spline Basis
    • EFFECTPLOT Statement
      • Syntax: EFFECTPLOT Statement
        • Dictionary of Options
      • ODS Graphics: EFFECTPLOT Statement
      • Examples: EFFECTPLOT Statement
        • A Saddle Surface
        • Unbalanced Two-Way ANOVA
        • Logistic Regression
    • ESTIMATE Statement
      • Syntax: ESTIMATE Statement
      • Positional and Nonpositional Syntax for Coefficients in Linear Functions
      • Joint Hypothesis Tests with Complex Alternatives, the Chi-Bar-Square Statistic
      • ODS Table Names: ESTIMATE Statement
      • ODS Graphics: ESTIMATE Statement
    • LSMEANS Statement
      • Syntax: LSMEANS Statement
      • ODS Table Names: LSMEANS Statement
      • ODS Graphics: LSMEANS Statement
    • LSMESTIMATE Statement
      • Syntax: LSMESTIMATE Statement
      • ODS Table Names: LSMESTIMATE Statement
      • ODS Graphics: LSMESTIMATE Statement
    • NLOPTIONS Statement
      • Syntax: NLOPTIONS Statement
      • Choosing an Optimization Algorithm
        • First- or Second-Order Algorithms
        • Algorithm Descriptions
    • SLICE Statement
      • Syntax: SLICE Statement
      • ODS Table Names: SLICE Statement
    • STORE Statement
      • Syntax: STORE Statement
    • TEST Statement
      • Syntax: TEST Statement
      • ODS Table Names: TEST Statement
    • Programming Statements
    • References
  • Using the Output Delivery System
    • Overview: Using the Output Delivery System
      • Output Defaults
        • HTML Output in the SAS Windowing Environment
        • LISTING Output in the SAS Windowing Environment
        • Assumptions about ODS Defaults in this Chapter
        • The HTMLBLUE Style
      • Default Open Destination
        • Setting the Default Destination in the Results Tab
        • Setting the Default Destination in the SAS Registry
        • Setting the Default Destination in SAS System Options
        • Setting the Destination in ODS Statements
      • Output Objects and ODS Destinations
      • The ODS Statement
      • Paths and Selection
      • RUN-Group Processing
      • The SAS Results Window
      • The ODS PATH Statement
      • The Master Template Store
      • Controlling Output Appearance with Templates
      • ODS and the NOPRINT Option
    • Examples: Using the Output Delivery System
      • Creating HTML Output with ODS
      • Selecting ODS Tables for Display
      • Excluding ODS Tables from Display
      • Creating an Output Data Set from an ODS Table
      • Creating an Output Data Set: Subsetting the Data
      • RUN-Group Processing
      • ODS Output Data Sets and Using PROC TEMPLATE to Customize Output
      • HTML Output with Hyperlinks between Tables
      • HTML Output with Graphics and Hyperlinks
      • Correlation and Covariance Matrices
    • References
  • Statistical Graphics Using ODS
    • Statistical Graphics Using ODS
      • Introduction
        • Chapter Reading Guide
        • Assumptions about ODS Defaults in This Chapter
      • Getting Started with ODS Statistical Graphics
        • Default Plots for Simple Linear Regression with PROC REG
        • Survival Estimate Plot with PROC LIFETEST
        • Contour and Surface Plots with PROC KDE
        • Contour Plots with PROC KRIGE2D
        • Partial Least Squares Plots with PROC PLS
        • Box-Cox Transformation Plot with PROC TRANSREG
        • LS-Means Diffogram with PROC GLIMMIX
        • Principal Component Analysis Plots with PROC PRINCOMP
        • Grouped Scatter Plot with PROC SGPLOT
      • A Primer on ODS Statistical Graphics
        • Enabling and Disabling ODS Graphics
        • Graph Styles
        • ODS Destinations
        • Accessing Individual Graphs
        • Specifying the Size and Resolution of Graphs
        • Modifying Your Graphs
        • Procedures That Support ODS Graphics
        • Procedures That Support ODS Graphics and Traditional Graphics
      • Syntax
        • ODS GRAPHICS Statement
        • ODS Destination Statements
        • PLOTS= Option
      • Selecting and Viewing Graphs
        • Specifying an ODS Destination for Graphics
        • Viewing Your Graphs in the SAS Windowing Environment
        • Determining Graph Names and Labels
        • Selecting and Excluding Graphs
      • Graphics Image Files
        • Image File Types
        • Scalable Vector Graphics
        • Naming Graphics Image Files
        • Saving Graphics Image Files
        • Creating Graphs in Multiple Destinations
      • Graph Size and Resolution
      • ODS Graphics Editor
        • Enabling the Creation of Editable Graphs
        • Editing a Graph with the ODS Graphics Editor
      • The Default Template Stores and the Template Search Path
      • Styles
        • An Overview of Styles
        • Style Elements and Attributes
        • Style Templates and Colors
        • Some Common Style Elements
        • Style Comparisons
        • Modifying the HTMLBLUE Style
        • Style Template Modification Macro
        • Creating an All-Color Style
        • Changing the Default Markers and Lines
        • Changing the Default Style
      • Statistical Graphics Procedures
        • The SGPLOT Procedure
        • The SGSCATTER Procedure
        • The SGPANEL Procedure
        • The SGRENDER Procedure
      • Examples of ODS Statistical Graphics
        • Creating Graphs with Tool Tips in HTML
        • Creating Graphs for a Presentation
        • Creating Graphs in PostScript Files
        • Displaying Graphs Using the DOCUMENT Procedure
        • Customizing the Style for Box Plots
      • References
    • ODS Graphics Template Modification
      • Graph Templates
        • The Graph Template Language
        • Locating Templates
        • Displaying Templates
        • Editing Templates
        • Saving Customized Templates
        • Using Customized Templates
        • Reverting to the Default Templates
        • Graph Template Modification Macro
      • Examples of ODS Graphics Template Modification
        • Customizing Graphs Through Template Changes
          • Modifying Graph Titles and Axis Labels
          • Modifying Colors, Line Styles, and Markers
          • Modifying Tick Marks and Grid Lines
          • Modifying the Style to Show Grid Lines
        • Adding Equations and Special Characters to Fit Plots
          • Simple Linear Regression
          • Cubic Fit Function
          • Unicode and Special Characters
        • Customizing Survival Plots
          • Modifying the Plot Title
          • Modifying the Axes
          • Creating a Template That Is Easy to Modify
          • Modifying the Plot Title in the Revised Template
          • Modifying the Legend and Inset Table
          • Modifying the Layout and Adding a New Inset Table
          • Changing Line Styles
          • Changing Fonts
          • Changing How Censored Data Are Displayed
          • Displaying Survival Summary Statistics
        • Customizing Panels
        • Customizing Axes and Reference Lines
        • Adding Text to Every Graph
          • Adding a Date and Project Stamp to a Few Graphs
          • Adding Data Set Information to a Graph
          • Adding a Date and Project Stamp to All Graphs
        • PROC TEMPLATE Statement Order and Primary Plots
      • References
  • Procedures
    • The ACECLUS Procedure
      • Overview: ACECLUS Procedure
        • Background
      • Getting Started: ACECLUS Procedure
      • Syntax: ACECLUS Procedure
        • PROC ACECLUS Statement
        • BY Statement
        • FREQ Statement
        • VAR Statement
        • WEIGHT Statement
      • Details: ACECLUS Procedure
        • Missing Values
        • Output Data Sets
        • Computational Resources
        • Displayed Output
        • ODS Table Names
      • Example: ACECLUS Procedure
        • Transformation and Cluster Analysis of Fisher Iris Data
      • References
    • The ADAPTIVEREG Procedure
      • Overview: ADAPTIVEREG Procedure
      • Getting Started: ADAPTIVEREG Procedure
      • Syntax: ADAPTIVEREG Procedure
        • PROC ADAPTIVEREG Statement
        • BY Statement
        • CLASS Statement
        • FREQ Statement
        • MODEL Statement
        • OUTPUT Statement
        • PARTITION Statement
        • SCORE Statement
        • WEIGHT Statement
      • Details: ADAPTIVEREG Procedure
        • Fitting Algorithms
        • Missing Values
        • ANOVA Decomposition
        • Computational Resources
        • ODS Table Names
        • ODS Graphics
      • Examples: ADAPTIVEREG Procedure
        • Surface Fitting with Many Noisy Variables
        • Fitting Data with Mixture Structures
        • Predicting E-Mail Spam
        • Nonparametric Poisson Model for Mackerel Egg Density
      • References
    • The ANOVA Procedure
      • Overview: ANOVA Procedure
      • Getting Started: ANOVA Procedure
        • One-Way Layout with Means Comparisons
        • Randomized Complete Block with One Factor
      • Syntax: ANOVA Procedure
        • PROC ANOVA Statement
        • ABSORB Statement
        • BY Statement
        • CLASS Statement
        • FREQ Statement
        • MANOVA Statement
        • MEANS Statement
        • MODEL Statement
        • REPEATED Statement
        • TEST Statement
      • Details: ANOVA Procedure
        • Specification of Effects
        • Using PROC ANOVA Interactively
        • Missing Values
        • Output Data Set
        • Computational Method
        • Displayed Output
        • ODS Table Names
        • ODS Graphics
      • Examples: ANOVA Procedure
        • Randomized Complete Block With Factorial Treatment Structure
        • Alternative Multiple Comparison Procedures
        • Split Plot
        • Latin Square Split Plot
        • Strip-Split Plot
      • References
    • The BOXPLOT Procedure
      • Overview: BOXPLOT Procedure
        • Traditional Graphics and ODS Graphics
      • Getting Started: BOXPLOT Procedure
        • Creating Box Plots from Raw Data
        • Creating Box Plots from Summary Data
        • Saving Summary Data with Outliers
      • Syntax: BOXPLOT Procedure
        • PROC BOXPLOT Statement
        • BY Statement
        • ID Statement
        • INSET Statement
        • INSETGROUP Statement
        • PLOT Statement
      • Details: BOXPLOT Procedure
        • Summary Statistics Represented by Box Plots
        • Output Data Sets
        • Input Data Sets
        • Styles of Box Plots
        • Percentile Definitions
        • Missing Values
        • Continuous Group Variables
        • Positioning Insets
        • Displaying Blocks of Data
        • Clipping Extreme Values
        • ODS Graphics
      • Examples: BOXPLOT Procedure
        • Displaying Summary Statistics in a Box Plot
        • Using Box Plots to Compare Groups
        • Creating Various Styles of Box-and-Whiskers Plots
        • Creating Notched Box-and-Whiskers Plots
        • Creating Box-and-Whiskers Plots with Varying Widths
        • Creating Box-and-Whiskers Plots Using ODS Graphics
      • References
    • The CALIS Procedure
      • Overview: CALIS Procedure
        • Structural Equation Modeling Application
        • Changes and Enhancements
        • Compatibility with the CALIS Procedure in SAS/STAT 9.2 or Earlier
        • Compatibility with the TCALIS Procedure in SAS/STAT 9.2
        • A Guide to the PROC CALIS Documentation
      • Getting Started: CALIS Procedure
        • A Structural Equation Example
        • A Factor Model Example
        • Direct Covariance Structures Analysis
        • Which Modeling Language?
      • Syntax: CALIS Procedure
        • Classes of Statements in PROC CALIS
        • Single-Group Analysis Syntax
        • Multiple-Group Multiple-Model Analysis Syntax
        • PROC CALIS Statement
        • BOUNDS Statement
        • BY Statement
        • COSAN Statement
        • COV Statement
        • DETERM Statement
        • EFFPART Statement
        • FACTOR Statement
        • FITINDEX Statement
        • FREQ Statement
        • GROUP Statement
        • LINCON Statement
        • LINEQS Statement
        • LISMOD Statement
        • LMTESTS Statement
        • MATRIX Statement
        • MEAN Statement
        • MODEL Statement
        • MSTRUCT Statement
        • NLINCON Statement
        • NLOPTIONS Statement
        • OUTFILES Statement
        • PARAMETERS Statement
        • PARTIAL Statement
        • PATH Statement
        • PCOV Statement
        • PVAR Statement
        • RAM Statement
        • REFMODEL Statement
        • RENAMEPARM Statement
        • SAS Programming Statements
        • SIMTESTS Statement
        • STD Statement
        • STRUCTEQ Statement
        • TESTFUNC Statement
        • VAR Statement
        • VARIANCE Statement
        • VARNAMES Statement
        • WEIGHT Statement
      • Details: CALIS Procedure
        • Input Data Sets
        • Output Data Sets
        • Default Analysis Type and Default Parameterization
        • The COSAN Model
        • The FACTOR Model
        • The LINEQS Model
        • The LISMOD Model and Submodels
        • The MSTRUCT Model
        • The PATH Model
        • The RAM Model
        • Naming Variables and Parameters
        • Setting Constraints on Parameters
        • Automatic Variable Selection
        • Estimation Criteria
        • Relationships among Estimation Criteria
        • Gradient, Hessian, Information Matrix, and Approximate Standard Errors
        • Counting the Degrees of Freedom
        • Assessment of Fit
        • Case-Level Residuals, Outliers, Leverage Observations, and Residual Diagnostics
        • Total, Direct, and Indirect Effects
        • Standardized Solutions
        • Modification Indices
        • Missing Values and the Analysis of Missing Patterns
        • Measures of Multivariate Kurtosis
        • Initial Estimates
        • Use of Optimization Techniques
        • Computational Problems
        • Displayed Output
        • ODS Table Names
        • ODS Graphics
      • Examples: CALIS Procedure
        • Estimating Covariances and Correlations
        • Estimating Covariances and Means Simultaneously
        • Testing Uncorrelatedness of Variables
        • Testing Covariance Patterns
        • Testing Some Standard Covariance Pattern Hypotheses
        • Linear Regression Model
        • Multivariate Regression Models
        • Measurement Error Models
        • Testing Specific Measurement Error Models
        • Measurement Error Models with Multiple Predictors
        • Measurement Error Models Specified As Linear Equations
        • Confirmatory Factor Models
        • Confirmatory Factor Models: Some Variations
        • Residual Diagnostics and Robust Estimation
        • The Full Information Maximum Likelihood Method
        • Comparing the ML and FIML Estimation
        • Path Analysis: Stability of Alienation
        • Simultaneous Equations with Mean Structures and Reciprocal Paths
        • Fitting Direct Covariance Structures
        • Confirmatory Factor Analysis: Cognitive Abilities
        • Testing Equality of Two Covariance Matrices Using a Multiple-Group Analysis
        • Testing Equality of Covariance and Mean Matrices between Independent Groups
        • Illustrating Various General Modeling Languages
        • Testing Competing Path Models for the Career Aspiration Data
        • Fitting a Latent Growth Curve Model
        • Higher-Order and Hierarchical Factor Models
        • Linear Relations among Factor Loadings
        • Multiple-Group Model for Purchasing Behavior
        • Fitting the RAM and EQS Models by the COSAN Modeling Language
        • Second-Order Confirmatory Factor Analysis
        • Linear Relations among Factor Loadings: COSAN Model Specification
        • Ordinal Relations among Factor Loadings
        • Longitudinal Factor Analysis
      • References
    • The CANCORR Procedure
      • Overview: CANCORR Procedure
        • Background
      • Getting Started: CANCORR Procedure
      • Syntax: CANCORR Procedure
        • PROC CANCORR Statement
        • BY Statement
        • FREQ Statement
        • PARTIAL Statement
        • VAR Statement
        • WEIGHT Statement
        • WITH Statement
      • Details: CANCORR Procedure
        • Missing Values
        • Formulas
        • Output Data Sets
        • Computational Resources
        • Displayed Output
        • ODS Table Names
      • Example: CANCORR Procedure
        • Canonical Correlation Analysis of Fitness Club Data
      • References
    • The CANDISC Procedure
      • Overview: CANDISC Procedure
      • Getting Started: CANDISC Procedure
      • Syntax: CANDISC Procedure
        • PROC CANDISC Statement
        • BY Statement
        • CLASS Statement
        • FREQ Statement
        • VAR Statement
        • WEIGHT Statement
      • Details: CANDISC Procedure
        • Missing Values
        • Computational Details
        • Input Data Set
        • Output Data Sets
        • Computational Resources
        • Displayed Output
        • ODS Table Names
      • Example: CANDISC Procedure
        • Analysis of Iris Data With PROC CANDISC
      • References
    • The CATMOD Procedure
      • Overview: CATMOD Procedure
        • Types of Input Data
        • Types of Statistical Analyses
        • Background: The Underlying Model
        • Linear Models Contrasted with Log-Linear Models
        • Using PROC CATMOD Interactively
      • Getting Started: CATMOD Procedure
        • Weighted Least Squares Analysis of Mean Response
        • Generalized Logits Model
      • Syntax: CATMOD Procedure
        • PROC CATMOD Statement
        • BY Statement
        • CONTRAST Statement
        • DIRECT Statement
        • FACTORS Statement
        • LOGLIN Statement
        • MODEL Statement
        • POPULATION Statement
        • REPEATED Statement
        • RESPONSE Statement
        • RESTRICT Statement
        • WEIGHT Statement
      • Details: CATMOD Procedure
        • Missing Values
        • Input Data Sets
        • Ordering of Populations and Responses
        • Specification of Effects
        • Output Data Sets
        • Logistic Analysis
        • Log-Linear Model Analysis
        • Repeated Measures Analysis
        • Generation of the Design Matrix
        • Cautions
        • Computational Method
        • Computational Formulas
        • Memory and Time Requirements
        • Displayed Output
        • ODS Table Names
      • Examples: CATMOD Procedure
        • Linear Response Function, r=2 Responses
        • Mean Score Response Function, r=3 Responses
        • Logistic Regression, Standard Response Function
        • Log-Linear Model, Three Dependent Variables
        • Log-Linear Model, Structural and Sampling Zeros
        • Repeated Measures, 2 Response Levels, 3 Populations
        • Repeated Measures, 4 Response Levels, 1 Population
        • Repeated Measures, Logistic Analysis of Growth Curve
        • Repeated Measures, Two Repeated Measurement Factors
        • Direct Input of Response Functions and Covariance Matrix
        • Predicted Probabilities
      • References
    • The CLUSTER Procedure
      • Overview: CLUSTER Procedure
      • Getting Started: CLUSTER Procedure
      • Syntax: CLUSTER Procedure
        • PROC CLUSTER Statement
        • BY Statement
        • COPY Statement
        • FREQ Statement
        • ID Statement
        • RMSSTD Statement
        • VAR Statement
      • Details: CLUSTER Procedure
        • Clustering Methods
        • Miscellaneous Formulas
        • Ultrametrics
        • Algorithms
        • Computational Resources
        • Missing Values
        • Ties
        • Size, Shape, and Correlation
        • Output Data Set
        • Displayed Output
        • ODS Table Names
        • ODS Graphics
      • Examples: CLUSTER Procedure
        • Cluster Analysis of Flying Mileages between 10 American Cities
        • Crude Birth and Death Rates
        • Cluster Analysis of Fisher’s Iris Data
        • Evaluating the Effects of Ties
      • References
    • The CORRESP Procedure
      • Overview: CORRESP Procedure
        • Background
      • Getting Started: CORRESP Procedure
      • Syntax: CORRESP Procedure
        • PROC CORRESP Statement
        • BY Statement
        • ID Statement
        • SUPPLEMENTARY Statement
        • TABLES Statement
        • VAR Statement
        • WEIGHT Statement
      • Details: CORRESP Procedure
        • Input Data Set
        • Using the TABLES Statement
        • Using the VAR Statement
        • Missing and Invalid Data
        • Coding, Fuzzy Coding, and Doubling
        • Creating a Data Set Containing the Crosstabulation
        • Output Data Sets
        • Computational Resources
        • Algorithm and Notation
        • Displayed Output
        • ODS Table Names
        • ODS Graphics
      • Examples: CORRESP Procedure
        • Simple and Multiple Correspondence Analysis of Automobiles and Their Owners
        • Simple Correspondence Analysis of U.S. Population
      • References
    • The DISCRIM Procedure
      • Overview: DISCRIM Procedure
      • Getting Started: DISCRIM Procedure
      • Syntax: DISCRIM Procedure
        • PROC DISCRIM Statement
        • BY Statement
        • CLASS Statement
        • FREQ Statement
        • ID Statement
        • PRIORS Statement
        • TESTCLASS Statement
        • TESTFREQ Statement
        • TESTID Statement
        • VAR Statement
        • WEIGHT Statement
      • Details: DISCRIM Procedure
        • Missing Values
        • Background
        • Posterior Probability Error-Rate Estimates
        • Saving and Using Calibration Information
        • Input Data Sets
        • Output Data Sets
        • Computational Resources
        • Displayed Output
        • ODS Table Names
      • Examples: DISCRIM Procedure
        • Univariate Density Estimates and Posterior Probabilities
        • Bivariate Density Estimates and Posterior Probabilities
        • Normal-Theory Discriminant Analysis of Iris Data
        • Linear Discriminant Analysis of Remote-Sensing Data on Crops
      • References
    • The DISTANCE Procedure
      • Overview: DISTANCE Procedure
        • Levels of Measurement
        • Symmetric versus Asymmetric Nominal Variables
        • Standardization
      • Getting Started: DISTANCE Procedure
        • Creating a Distance Matrix as Input for a Subsequent Cluster Analysis
      • Syntax: DISTANCE Procedure
        • PROC DISTANCE Statement
        • VAR Statement
        • ID Statement
        • COPY Statement
        • BY Statement
        • FREQ Statement
        • WEIGHT Statement
      • Details: DISTANCE Procedure
        • Proximity Measures
        • Missing Values
        • Formatted versus Unformatted Values
        • Output Data Sets
      • Examples: DISTANCE Procedure
        • Divorce Grounds – the Jaccard Coefficient
        • Financial Data – Stock Dividends
      • References
    • The FACTOR Procedure
      • Overview: FACTOR Procedure
        • Background
        • Outline of Use
      • Getting Started: FACTOR Procedure
      • Syntax: FACTOR Procedure
        • PROC FACTOR Statement
        • BY Statement
        • FREQ Statement
        • PARTIAL Statement
        • PRIORS Statement
        • VAR Statement
        • WEIGHT Statement
      • Details: FACTOR Procedure
        • Input Data Set
        • Output Data Sets
        • Confidence Intervals and the Salience of Factor Loadings
        • Simplicity Functions for Rotations
        • Missing Values
        • Cautions
        • Factor Scores
        • Variable Weights and Variance Explained
        • Heywood Cases and Other Anomalies about Communality Estimates
        • Time Requirements
        • Displayed Output
        • ODS Table Names
        • ODS Graphics
      • Examples: FACTOR Procedure
        • Principal Component Analysis
        • Principal Factor Analysis
        • Maximum Likelihood Factor Analysis
        • Using Confidence Intervals to Locate Salient Factor Loadings
      • References
    • The FASTCLUS Procedure
      • Overview: FASTCLUS Procedure
        • Background
      • Getting Started: FASTCLUS Procedure
      • Syntax: FASTCLUS Procedure
        • PROC FASTCLUS Statement
        • BY Statement
        • FREQ Statement
        • ID Statement
        • VAR Statement
        • WEIGHT Statement
      • Details: FASTCLUS Procedure
        • Updates in the FASTCLUS Procedure
        • Missing Values
        • Output Data Sets
        • Computational Resources
        • Using PROC FASTCLUS
        • Displayed Output
        • ODS Table Names
      • Examples: FASTCLUS Procedure
        • Fisher’s Iris Data
        • Outliers
      • References
    • The FMM Procedure
      • Overview: FMM Procedure
        • Basic Features
        • Assumptions
        • Notation for the Finite Mixture Model
          • Homogeneous Mixtures
          • Special Mixtures
        • PROC FMM Contrasted with Other SAS Procedures
      • Getting Started: FMM Procedure
        • Mixture Modeling for Binomial Overdispersion: “Student,” Pearson, Beer, and Yeast
        • Modeling Zero-Inflation: Is it Better to Fish Poorly or Not to Have Fished At All?
        • Looking for Multiple Modes: Are Galaxies Clustered?
          • Comparison with Roeder’s Method
      • Syntax: FMM Procedure
        • PROC FMM Statement
        • BAYES Statement
        • BY Statement
        • CLASS Statement
        • FREQ Statement
        • ID Statement
        • MODEL Statement
          • Response Variable Options
          • Model Options
        • OUTPUT Statement
        • PERFORMANCE Statement
        • PROBMODEL Statement
        • RESTRICT Statement
        • WEIGHT Statement
      • Details: FMM Procedure
        • A Gentle Introduction to Finite Mixture Models
          • The Form of the Finite Mixture Model
          • Mixture Models Contrasted with Mixing and Mixed Models: Untangling the Terminology Web
          • Overdispersion
        • Log-Likelihood Functions for Response Distributions
        • Bayesian Analysis
          • Conjugate Sampling
          • Metropolis-Hastings Algorithm
          • Latent Variables via Data Augmentation
          • Prior Distributions
        • Parameterization of Model Effects
        • Default Output
          • Model Information
          • Class Level Information
          • Number of Observations
          • Response Profile
          • Default Output for Maximum Likelihood
          • Default Output for Bayes Estimation
        • ODS Table Names
        • ODS Graphics
      • Examples: FMM Procedure
        • Modeling Mixing Probabilities: All Mice Are Created Equal, but Some Are More Equal
        • The Usefulness of Custom Starting Values: When Do Cows Eat?
        • Enforcing Homogeneity Constraints: Count and Dispersion—It Is All Over!
      • References
    • The FREQ Procedure
      • Overview: FREQ Procedure
      • Getting Started: FREQ Procedure
        • Frequency Tables and Statistics
        • Agreement Study
      • Syntax: FREQ Procedure
        • PROC FREQ Statement
        • BY Statement
        • EXACT Statement
        • OUTPUT Statement
        • TABLES Statement
        • TEST Statement
        • WEIGHT Statement
      • Details: FREQ Procedure
        • Inputting Frequency Counts
        • Grouping with Formats
        • Missing Values
        • In-Database Computation
        • Statistical Computations
          • Definitions and Notation
          • Chi-Square Tests and Statistics
          • Measures of Association
          • Binomial Proportion
          • Risks and Risk Differences
          • Odds Ratio and Relative Risks for 2 x 2 Tables
          • Cochran-Armitage Test for Trend
          • Jonckheere-Terpstra Test
          • Tests and Measures of Agreement
          • Cochran-Mantel-Haenszel Statistics
          • Gail-Simon Test for Qualitative Interactions
          • Exact Statistics
        • Computational Resources
        • Output Data Sets
        • Displayed Output
        • ODS Table Names
        • ODS Graphics
      • Examples: FREQ Procedure
        • Output Data Set of Frequencies
        • Frequency Dot Plots
        • Chi-Square Goodness-of-Fit Tests
        • Binomial Proportions
        • Analysis of a 2x2 Contingency Table
        • Output Data Set of Chi-Square Statistics
        • Cochran-Mantel-Haenszel Statistics
        • Cochran-Armitage Trend Test
        • Friedman’s Chi-Square Test
        • Cochran’s Q Test
      • References
    • The GAM Procedure
      • Overview: GAM Procedure
      • Getting Started: GAM Procedure
      • Syntax: GAM Procedure
        • PROC GAM Statement
        • BY Statement
        • CLASS Statement
        • FREQ Statement
        • MODEL Statement
        • OUTPUT Statement
        • SCORE Statement
      • Details: GAM Procedure
        • Missing Values
        • Nonparametric Regression
        • Additive Models and Generalized Additive Models
        • Forms of Additive Models
        • Estimates from PROC GAM
        • Backfitting and Local Scoring Algorithms
        • Smoothers
        • Selection of Smoothing Parameters
        • Confidence Intervals for Smoothers
        • Distribution Family and Canonical Link
        • Dispersion Parameter
        • Computational Resources
        • ODS Table Names
        • ODS Graphics
      • Examples: GAM Procedure
        • Generalized Additive Model with Binary Data
        • Poisson Regression Analysis of Component Reliability
        • Comparing PROC GAM with PROC LOESS
      • References
    • The GENMOD Procedure
      • Overview: GENMOD Procedure
        • What Is a Generalized Linear Model?
        • Examples of Generalized Linear Models
        • The GENMOD Procedure
      • Getting Started: GENMOD Procedure
        • Poisson Regression
        • Bayesian Analysis of a Linear Regression Model
        • Generalized Estimating Equations
      • Syntax: GENMOD Procedure
        • PROC GENMOD Statement
        • ASSESS Statement
        • BAYES Statement
        • BY Statement
        • CLASS Statement
        • CODE Statement
        • CONTRAST Statement
        • DEVIANCE Statement
        • EFFECTPLOT Statement
        • ESTIMATE Statement
        • EXACT Statement
        • EXACTOPTIONS Statement
        • FREQ Statement
        • FWDLINK Statement
        • INVLINK Statement
        • LSMEANS Statement
        • LSMESTIMATE Statement
        • MODEL Statement
        • OUTPUT Statement
        • Programming Statements
        • REPEATED Statement
        • SLICE Statement
        • STORE Statement
        • STRATA Statement
        • VARIANCE Statement
        • WEIGHT Statement
        • ZEROMODEL Statement
      • Details: GENMOD Procedure
        • Generalized Linear Models Theory
        • Specification of Effects
        • Parameterization Used in PROC GENMOD
        • Type 1 Analysis
        • Type 3 Analysis
        • Confidence Intervals for Parameters
        • F Statistics
        • Lagrange Multiplier Statistics
        • Predicted Values of the Mean
        • Residuals
        • Multinomial Models
        • Zero-Inflated Models
        • Generalized Estimating Equations
        • Assessment of Models Based on Aggregates of Residuals
        • Case Deletion Diagnostic Statistics
        • Bayesian Analysis
        • Exact Logistic and Exact Poisson Regression
        • Missing Values
        • Displayed Output for Classical Analysis
        • Displayed Output for Bayesian Analysis
        • Displayed Output for Exact Analysis
        • ODS Table Names
        • ODS Graphics
      • Examples: GENMOD Procedure
        • Logistic Regression
        • Normal Regression, Log Link
        • Gamma Distribution Applied to Life Data
        • Ordinal Model for Multinomial Data
        • GEE for Binary Data with Logit Link Function
        • Log Odds Ratios and the ALR Algorithm
        • Log-Linear Model for Count Data
        • Model Assessment of Multiple Regression Using Aggregates of Residuals
        • Assessment of a Marginal Model for Dependent Data
        • Bayesian Analysis of a Poisson Regression Model
        • Exact Poisson Regression
      • References
    • The GLIMMIX Procedure
      • Overview: GLIMMIX Procedure
        • Basic Features
        • Assumptions
        • Notation for the Generalized Linear Mixed Model
          • The Basic Model
          • G-Side and R-Side Random Effects and Covariance Structures
          • Relationship with Generalized Linear Models
        • PROC GLIMMIX Contrasted with Other SAS Procedures
      • Getting Started: GLIMMIX Procedure
        • Logistic Regressions with Random Intercepts
      • Syntax: GLIMMIX Procedure
        • PROC GLIMMIX Statement
        • BY Statement
        • CLASS Statement
        • CODE Statement
        • CONTRAST Statement
        • COVTEST Statement
        • EFFECT Statement
        • ESTIMATE Statement
        • FREQ Statement
        • ID Statement
        • LSMEANS Statement
        • LSMESTIMATE Statement
        • MODEL Statement
          • Response Variable Options
          • Model Options
        • NLOPTIONS Statement
        • OUTPUT Statement
        • PARMS Statement
        • RANDOM Statement
        • SLICE Statement
        • STORE Statement
        • WEIGHT Statement
        • Programming Statements
        • User-Defined Link or Variance Function
          • Implied Variance Functions
          • Automatic Variables
      • Details: GLIMMIX Procedure
        • Generalized Linear Models Theory
          • Maximum Likelihood
          • Scale and Dispersion Parameters
          • Quasi-likelihood for Independent Data
          • Effects of Adding Overdispersion
        • Generalized Linear Mixed Models Theory
          • Model or Integral Approximation
          • Pseudo-likelihood Estimation Based on Linearization
          • Maximum Likelihood Estimation Based on Laplace Approximation
          • Maximum Likelihood Estimation Based on Adaptive Quadrature
          • Aspects Common to Adaptive Quadrature and Laplace Approximation
          • Notes on Bias of Estimators
        • GLM Mode or GLMM Mode
        • Statistical Inference for Covariance Parameters
          • The Likelihood Ratio Test
          • One- and Two-Sided Testing, Mixture Distributions
          • Handling the Degenerate Distribution
          • Wald Versus Likelihood Ratio Tests
          • Confidence Bounds Based on Likelihoods
        • Degrees of Freedom Methods
          • Between-Within Degrees of Freedom Approximation
          • Containment Degrees of Freedom Approximation
          • Satterthwaite Degrees of Freedom Approximation
          • Kenward-Roger Degrees of Freedom Approximation
        • Empirical Covariance (“Sandwich”) Estimators
          • Residual-Based Estimators
          • Design-Adjusted MBN Estimator
        • Exploring and Comparing Covariance Matrices
        • Processing by Subjects
        • Radial Smoothing Based on Mixed Models
          • From Penalized Splines to Mixed Models
          • Knot Selection
        • Odds and Odds Ratio Estimation
          • The Odds Ratio Estimates Table
          • Odds or Odds Ratio
          • Odds Ratios in Multinomial Models
        • Parameterization of Generalized Linear Mixed Models
          • Intercept
          • Interaction Effects
          • Nested Effects
          • Implications of the Non-Full-Rank Parameterization
          • Missing Level Combinations
          • Notes on the EFFECT Statement
          • Positional and Nonpositional Syntax for Contrast Coefficients
        • Response-Level Ordering and Referencing
        • Comparing the GLIMMIX and MIXED Procedures
        • Singly or Doubly Iterative Fitting
        • Default Estimation Techniques
        • Default Output
          • Model Information
          • Class Level Information
          • Number of Observations
          • Response Profile
          • Dimensions
          • Optimization Information
          • Iteration History
          • Convergence Status
          • Fit Statistics
          • Covariance Parameter Estimates
          • Type III Tests of Fixed Effects
        • Notes on Output Statistics
        • ODS Table Names
        • ODS Graphics
          • ODS Graph Names
          • Diagnostic Plots
          • Graphics for LS-Mean Comparisons
      • Examples: GLIMMIX Procedure
        • Binomial Counts in Randomized Blocks
        • Mating Experiment with Crossed Random Effects
        • Smoothing Disease Rates; Standardized Mortality Ratios
        • Quasi-likelihood Estimation for Proportions with Unknown Distribution
        • Joint Modeling of Binary and Count Data
        • Radial Smoothing of Repeated Measures Data
        • Isotonic Contrasts for Ordered Alternatives
        • Adjusted Covariance Matrices of Fixed Effects
        • Testing Equality of Covariance and Correlation Matrices
        • Multiple Trends Correspond to Multiple Extrema in Profile Likelihoods
        • Maximum Likelihood in Proportional Odds Model with Random Effects
        • Fitting a Marginal (GEE-Type) Model
        • Response Surface Comparisons with Multiplicity Adjustments
        • Generalized Poisson Mixed Model for Overdispersed Count Data
        • Comparing Multiple B-Splines
        • Diallel Experiment with Multimember Random Effects
        • Linear Inference Based on Summary Data
      • References
    • The GLM Procedure
      • Overview: GLM Procedure
        • PROC GLM Features
        • PROC GLM Contrasted with Other SAS Procedures
      • Getting Started: GLM Procedure
        • PROC GLM for Unbalanced ANOVA
        • PROC GLM for Quadratic Least Squares Regression
      • Syntax: GLM Procedure
        • PROC GLM Statement
        • ABSORB Statement
        • BY Statement
        • CLASS Statement
        • CODE Statement
        • CONTRAST Statement
        • ESTIMATE Statement
        • FREQ Statement
        • ID Statement
        • LSMEANS Statement
        • MANOVA Statement
        • MEANS Statement
        • MODEL Statement
        • OUTPUT Statement
        • RANDOM Statement
        • REPEATED Statement
        • STORE Statement
        • TEST Statement
        • WEIGHT Statement
      • Details: GLM Procedure
        • Statistical Assumptions for Using PROC GLM
        • Specification of Effects
        • Using PROC GLM Interactively
        • Parameterization of PROC GLM Models
        • Hypothesis Testing in PROC GLM
        • Effect Size Measures for F Tests in GLM
        • Absorption
        • Specification of ESTIMATE Expressions
        • Comparing Groups
          • Means versus LS-Means
          • Multiple Comparisons
          • Simple Effects
          • Homogeneity of Variance in One-Way Models
          • Weighted Means
          • Construction of Least Squares Means
        • Multivariate Analysis of Variance
        • Repeated Measures Analysis of Variance
        • Random-Effects Analysis
        • Missing Values
        • Computational Resources
        • Computational Method
        • Output Data Sets
        • Displayed Output
        • ODS Table Names
        • ODS Graphics
      • Examples: GLM Procedure
        • Randomized Complete Blocks with Means Comparisons and Contrasts
        • Regression with Mileage Data
        • Unbalanced ANOVA for Two-Way Design with Interaction
        • Analysis of Covariance
        • Three-Way Analysis of Variance with Contrasts
        • Multivariate Analysis of Variance
        • Repeated Measures Analysis of Variance
        • Mixed Model Analysis of Variance with the RANDOM Statement
        • Analyzing a Doubly Multivariate Repeated Measures Design
        • Testing for Equal Group Variances
        • Analysis of a Screening Design
      • References
    • The GLMMOD Procedure
      • Overview: GLMMOD Procedure
      • Getting Started: GLMMOD Procedure
        • A One-Way Design
      • Syntax: GLMMOD Procedure
        • PROC GLMMOD Statement
        • BY Statement
        • CLASS Statement
        • FREQ and WEIGHT Statements
        • MODEL Statement
      • Details: GLMMOD Procedure
        • Displayed Output
        • Missing Values
        • OUTPARM= Data Set
        • OUTDESIGN= Data Set
        • ODS Table Names
      • Examples: GLMMOD Procedure
        • A Two-Way Design
        • Factorial Screening
      • References
    • The GLMPOWER Procedure
      • Overview: GLMPOWER Procedure
      • Getting Started: GLMPOWER Procedure
        • Simple Two-Way ANOVA
        • Incorporating Contrasts, Unbalanced Designs, and Multiple Means Scenarios
      • Syntax: GLMPOWER Procedure
        • PROC GLMPOWER Statement
        • BY Statement
        • CLASS Statement
        • CONTRAST Statement
        • MODEL Statement
        • PLOT Statement
        • POWER Statement
        • WEIGHT Statement
      • Details: GLMPOWER Procedure
        • Specifying Value Lists in the POWER Statement
          • Number-Lists
        • Sample Size Adjustment Options
        • Error and Information Output
        • Displayed Output
        • ODS Table Names
        • Computational Methods and Formulas
          • Contrasts in Fixed-Effect Univariate Models
          • Adjustments for Covariates
        • ODS Graphics
        • ODS Styles Suitable for Use with PROC GLMPOWER
      • Examples: GLMPOWER Procedure
        • One-Way ANOVA
        • Two-Way ANOVA with Covariate
      • References
    • The GLMSELECT Procedure
      • Overview: GLMSELECT Procedure
        • Features
      • Getting Started: GLMSELECT Procedure
      • Syntax: GLMSELECT Procedure
        • PROC GLMSELECT Statement
        • BY Statement
        • CLASS Statement
        • CODE Statement
        • EFFECT Statement
        • FREQ Statement
        • MODEL Statement
        • MODELAVERAGE Statement
        • OUTPUT Statement
        • PARTITION Statement
        • PERFORMANCE Statement
        • SCORE Statement
        • STORE Statement
        • WEIGHT Statement
      • Details: GLMSELECT Procedure
        • Model-Selection Methods
          • Full Model Fitted (NONE)
          • Forward Selection (FORWARD)
          • Backward Elimination (BACKWARD)
          • Stepwise Selection(STEPWISE)
          • Least Angle Regression (LAR)
          • Lasso Selection (LASSO)
          • Adaptive Lasso Selection
        • Model Selection Issues
        • Criteria Used in Model Selection Methods
        • CLASS Variable Parameterization and the SPLIT Option
        • Macro Variables Containing Selected Models
        • Using the STORE Statement
        • Building the SSCP Matrix
        • Model Averaging
        • Using Validation and Test Data
        • Cross Validation
        • Displayed Output
        • ODS Table Names
        • ODS Graphics
      • Examples: GLMSELECT Procedure
        • Modeling Baseball Salaries Using Performance Statistics
        • Using Validation and Cross Validation
        • Scatter Plot Smoothing by Selecting Spline Functions
        • Multimember Effects and the Design Matrix
        • Model Averaging
      • References
    • The HPMIXED Procedure
      • Overview: HPMIXED Procedure
        • Basic Features
        • Assumptions and Notation
        • Computational Approach
        • The HPMIXED Procedure Contrasted with the MIXED Procedure
      • Getting Started: HPMIXED Procedure
        • Mixed Model with Large Number of Fixed and Random Effects
      • Syntax: HPMIXED Procedure
        • PROC HPMIXED Statement
        • BY Statement
        • CLASS Statement
        • CONTRAST Statement
        • EFFECT Statement
        • ESTIMATE Statement
        • ID Statement
        • LSMEANS Statement
        • MODEL Statement
        • NLOPTIONS Statement
        • OUTPUT Statement
        • PARMS Statement
        • RANDOM Statement
        • REPEATED Statement
        • TEST Statement
        • WEIGHT Statement
      • Details: HPMIXED Procedure
        • Model Assumptions
        • Computing and Maximizing the Likelihood
        • Computing Starting Values by EM-REML
        • Sparse Matrix Techniques
        • Hypothesis Tests for Fixed Effects
        • Default Output
        • ODS Table Names
      • Examples: HPMIXED Procedure
        • Ranking Many Random-Effect Coefficients
        • Comparing Results from PROC HPMIXED and PROC MIXED
        • Using PROC GLIMMIX for Further Analysis of PROC HPMIXED Fit
        • Mixed Model Analysis of Microarray Data
        • Repeated Measures
      • References
    • The INBREED Procedure
      • Overview: INBREED Procedure
      • Getting Started: INBREED Procedure
        • The Format of the Input Data Set
        • Performing the Analysis
      • Syntax: INBREED Procedure
        • PROC INBREED Statement
        • BY Statement
        • CLASS Statement
        • GENDER Statement
        • MATINGS Statement
        • VAR Statement
      • Details: INBREED Procedure
        • Missing Values
        • DATA= Data Set
        • Computational Details
        • OUTCOV= Data Set
        • Displayed Output
        • ODS Table Names
      • Examples: INBREED Procedure
        • Monoecious Population Analysis
        • Pedigree Analysis
        • Pedigree Analysis with BY Groups
      • References
    • The KDE Procedure
      • Overview: KDE Procedure
      • Getting Started: KDE Procedure
      • Syntax: KDE Procedure
        • PROC KDE Statement
        • BIVAR Statement
        • UNIVAR Statement
        • BY Statement
        • FREQ Statement
        • WEIGHT Statement
      • Details: KDE Procedure
        • Computational Overview
        • Kernel Density Estimates
        • Binning
        • Convolutions
        • Fast Fourier Transform
        • Bandwidth Selection
        • ODS Table Names
        • ODS Graphics
      • Examples: KDE Procedure
        • Computing a Basic Kernel Density Estimate
        • Changing the Bandwidth
        • Changing the Bandwidth (Bivariate)
        • Requesting Additional Output Tables
        • Univariate KDE Graphics
        • Bivariate KDE Graphics
      • References
    • The KRIGE2D Procedure
      • Overview: KRIGE2D Procedure
        • Introduction to Spatial Prediction
      • Getting Started: KRIGE2D Procedure
        • Spatial Prediction Using Kriging, Contour Plots
      • Syntax: KRIGE2D Procedure
        • PROC KRIGE2D Statement
        • BY Statement
        • COORDINATES Statement
        • GRID Statement
        • ID Statement
        • PREDICT Statement
        • MODEL Statement
        • RESTORE Statement
      • Details: KRIGE2D Procedure
        • Theoretical Semivariogram Models
        • The Nugget Effect
        • Anisotropic Models
          • Geometric Anisotropy
          • Zonal Anisotropy
          • Anisotropic Nugget Effect
        • Details of Ordinary Kriging
          • Introduction
          • Spatial Random Fields
          • Ordinary Kriging
        • Computational Resources
        • Output Data Sets
        • Displayed Output
        • ODS Table Names
        • ODS Graphics
      • Examples: KRIGE2D Procedure
        • Spatial Prediction of Pollutant Concentration
        • Investigating the Effect of Model Specification on Spatial Prediction
        • Data Quality and Prediction with Missing Values
      • References
    • The LATTICE Procedure
      • Overview: LATTICE Procedure
      • Getting Started: LATTICE Procedure
      • Syntax: LATTICE Procedure
        • PROC LATTICE Statement
        • BY Statement
        • VAR Statement
      • Details: LATTICE Procedure
        • Input Data Set
        • Missing Values
        • Displayed Output
        • ODS Table Names
      • Example: LATTICE Procedure
        • Analysis of Variance through PROC LATTICE
      • References
    • The LIFEREG Procedure
      • Overview: LIFEREG Procedure
      • Getting Started: LIFEREG Procedure
        • Modeling Right-Censored Failure Time Data
        • Bayesian Analysis of Right-Censored Data
      • Syntax: LIFEREG Procedure
        • PROC LIFEREG Statement
        • BAYES Statement
        • BY Statement
        • CLASS Statement
        • EFFECTPLOT Statement
        • ESTIMATE Statement
        • INSET Statement
        • LSMEANS Statement
        • LSMESTIMATE Statement
        • MODEL Statement
        • OUTPUT Statement
        • PROBPLOT Statement
        • SLICE Statement
        • STORE Statement
        • TEST Statement
        • WEIGHT Statement
      • Details: LIFEREG Procedure
        • Missing Values
        • Model Specification
        • Computational Method
        • Supported Distributions
        • Predicted Values
        • Confidence Intervals
        • Fit Statistics
        • Probability Plotting
        • INEST= Data Set
        • OUTEST= Data Set
        • XDATA= Data Set
        • Computational Resources
        • Bayesian Analysis
        • Displayed Output for Classical Analysis
        • Displayed Output for Bayesian Analysis
        • ODS Table Names
        • ODS Graphics
      • Examples: LIFEREG Procedure
        • Motorette Failure
        • Computing Predicted Values for a Tobit Model
        • Overcoming Convergence Problems by Specifying Initial Values
        • Analysis of Arbitrarily Censored Data with Interaction Effects
        • Probability Plotting—Right Censoring
        • Probability Plotting—Arbitrary Censoring
        • Bayesian Analysis of Clinical Trial Data
        • Model Postfitting Analysis
      • References
    • The LIFETEST Procedure
      • Overview: LIFETEST Procedure
      • Getting Started: LIFETEST Procedure
      • Syntax: LIFETEST Procedure
        • PROC LIFETEST Statement
        • BY Statement
        • FREQ Statement
        • ID Statement
        • STRATA Statement
        • TEST Statement
        • TIME Statement
        • WEIGHT Statement
      • Details: LIFETEST Procedure
        • Missing Values
        • Computational Formulas
        • Computer Resources
        • Output Data Sets
          • OUTSURV= Data Set
          • OUTTEST= Data Set
        • Displayed Output
        • ODS Table Names
        • ODS Graphics
        • Modifying the ODS Template for Survival Plots
      • Examples: LIFETEST Procedure
        • Product-Limit Estimates and Tests of Association
        • Enhanced Survival Plot and Multiple-Comparison Adjustments
        • Life-Table Estimates for Males with Angina Pectoris
      • References
    • The LOESS Procedure
      • Overview: LOESS Procedure
        • Local Regression and the Loess Method
      • Getting Started: LOESS Procedure
        • Scatter Plot Smoothing
      • Syntax: LOESS Procedure
        • PROC LOESS Statement
        • BY Statement
        • ID Statement
        • MODEL Statement
        • OUTPUT Statement
        • SCORE Statement
        • WEIGHT Statement
      • Details: LOESS Procedure
        • Missing Values
        • Output Data Sets
        • Data Scaling
        • Direct versus Interpolated Fitting
        • k-d Trees and Blending
        • Local Weighting
        • Iterative Reweighting
        • Specifying the Local Polynomials
        • Smoothing Matrix
        • Model Degrees of Freedom
        • Statistical Inference and Lookup Degrees of Freedom
        • Automatic Smoothing Parameter Selection
        • Sparse and Approximate Degrees of Freedom Computation
        • Scoring Data Sets
        • ODS Table Names
        • ODS Graphics
      • Examples: LOESS Procedure
        • Engine Exhaust Emissions
        • Sulfate Deposits in the U.S. for 1990
        • Catalyst Experiment
        • El Niño Southern Oscillation
      • References
    • The LOGISTIC Procedure
      • Overview: LOGISTIC Procedure
      • Getting Started: LOGISTIC Procedure
      • Syntax: LOGISTIC Procedure
        • PROC LOGISTIC Statement
        • BY Statement
        • CLASS Statement
        • CODE Statement
        • CONTRAST Statement
        • EFFECT Statement
        • EFFECTPLOT Statement
        • ESTIMATE Statement
        • EXACT Statement
        • EXACTOPTIONS Statement
        • FREQ Statement
        • ID Statement
        • LSMEANS Statement
        • LSMESTIMATE Statement
        • MODEL Statement
        • NLOPTIONS Statement
        • ODDSRATIO Statement
        • OUTPUT Statement
        • ROC Statement
        • ROCCONTRAST Statement
        • SCORE Statement
        • SLICE Statement
        • STORE Statement
        • STRATA Statement
        • TEST Statement
        • UNITS Statement
        • WEIGHT Statement
      • Details: LOGISTIC Procedure
        • Missing Values
        • Response Level Ordering
        • Link Functions and the Corresponding Distributions
        • Determining Observations for Likelihood Contributions
        • Iterative Algorithms for Model Fitting
        • Convergence Criteria
        • Existence of Maximum Likelihood Estimates
        • Effect-Selection Methods
        • Model Fitting Information
        • Generalized Coefficient of Determination
        • Score Statistics and Tests
        • Confidence Intervals for Parameters
        • Odds Ratio Estimation
        • Rank Correlation of Observed Responses and Predicted Probabilities
        • Linear Predictor, Predicted Probability, and Confidence Limits
        • Classification Table
        • Overdispersion
        • The Hosmer-Lemeshow Goodness-of-Fit Test
        • Receiver Operating Characteristic Curves
        • Testing Linear Hypotheses about the Regression Coefficients
        • Regression Diagnostics
        • Scoring Data Sets
        • Conditional Logistic Regression
        • Exact Conditional Logistic Regression
        • Input and Output Data Sets
        • Computational Resources
        • Displayed Output
        • ODS Table Names
        • ODS Graphics
      • Examples: LOGISTIC Procedure
        • Stepwise Logistic Regression and Predicted Values
        • Logistic Modeling with Categorical Predictors
        • Ordinal Logistic Regression
        • Nominal Response Data: Generalized Logits Model
        • Stratified Sampling
        • Logistic Regression Diagnostics
        • ROC Curve, Customized Odds Ratios, Goodness-of-Fit Statistics, R-Square, and Confidence Limits
        • Comparing Receiver Operating Characteristic Curves
        • Goodness-of-Fit Tests and Subpopulations
        • Overdispersion
        • Conditional Logistic Regression for Matched Pairs Data
        • Firth’s Penalized Likelihood Compared with Other Approaches
        • Complementary Log-Log Model for Infection Rates
        • Complementary Log-Log Model for Interval-Censored Survival Times
        • Scoring Data Sets
        • Using the LSMEANS Statement
        • Partial Proportional Odds Model
      • References
    • The MCMC Procedure
      • Overview: MCMC Procedure
        • PROC MCMC Compared with Other SAS Procedures
      • Getting Started: MCMC Procedure
        • Simple Linear Regression
        • The Behrens-Fisher Problem
        • Random-Effects Model
      • Syntax: MCMC Procedure
        • PROC MCMC Statement
        • ARRAY Statement
        • BEGINCNST/ENDCNST Statement
        • BEGINNODATA/ENDNODATA Statements
        • BY Statement
        • MODEL Statement
        • PARMS Statement
        • PREDDIST Statement
        • PRIOR/HYPERPRIOR Statement
        • Programming Statements
        • RANDOM Statement
        • UDS Statement
      • Details: MCMC Procedure
        • How PROC MCMC Works
        • Blocking of Parameters
        • Sampling Methods
        • Tuning the Proposal Distribution
        • Direct Sampling
        • Conjugate Sampling
        • Initial Values of the Markov Chains
        • Assignments of Parameters
        • Standard Distributions
        • Usage of Multivariate Distributions
        • Specifying a New Distribution
        • Using Density Functions in the Programming Statements
        • Truncation and Censoring
        • Some Useful SAS Functions
        • Matrix Functions in PROC MCMC
        • Create Design Matrix
        • Modeling Joint Likelihood
        • Regenerating Diagnostics Plots
        • Caterpillar Plot
        • Autocall Macros for Postprocessing
        • Gamma and Inverse-Gamma Distributions
        • Posterior Predictive Distribution
        • Handling of Missing Data
        • Functions of Random-Effects Parameters
        • Floating Point Errors and Overflows
        • Handling Error Messages
        • Computational Resources
        • Displayed Output
        • ODS Table Names
        • ODS Graphics
      • Examples: MCMC Procedure
        • Simulating Samples From a Known Density
        • Box-Cox Transformation
        • Logistic Regression Model with a Diffuse Prior
        • Logistic Regression Model with Jeffreys’ Prior
        • Poisson Regression
        • Nonlinear Poisson Regression Models
        • Logistic Regression Random-Effects Model
        • Nonlinear Poisson Regression Multilevel Random-Effects Model
        • Multivariate Normal Random-Effects Model
        • Missing at Random Analysis
        • Nonignorably Missing Data (MNAR) Analysis
        • Change Point Models
        • Exponential and Weibull Survival Analysis
        • Time Independent Cox Model
        • Time Dependent Cox Model
        • Piecewise Exponential Frailty Model
        • Normal Regression with Interval Censoring
        • Constrained Analysis
        • Implement a New Sampling Algorithm
        • Using a Transformation to Improve Mixing
        • Gelman-Rubin Diagnostics
      • References
    • The MDS Procedure
      • Overview: MDS Procedure
      • Getting Started: MDS Procedure
      • Syntax: MDS Procedure
        • PROC MDS Statement
        • BY Statement
        • ID Statement
        • INVAR Statement
        • MATRIX Statement
        • VAR Statement
        • WEIGHT Statement
      • Details: MDS Procedure
        • Formulas
        • OUT= Data Set
        • OUTFIT= Data Set
        • OUTRES= Data Set
        • INITIAL= Data Set
        • Missing Values
        • Normalization of the Estimates
        • Comparison with Earlier Procedures
        • Displayed Output
        • ODS Table Names
        • ODS Graphics
      • Example: MDS Procedure
        • Jacobowitz Body Parts Data from Children and Adults
      • References
    • The MI Procedure
      • Overview: MI Procedure
      • Getting Started: MI Procedure
      • Syntax: MI Procedure
        • PROC MI Statement
        • BY Statement
        • CLASS Statement
        • EM Statement
        • FCS Statement
        • FREQ Statement
        • MCMC Statement
        • MONOTONE Statement
        • TRANSFORM Statement
        • VAR Statement
      • Details: MI Procedure
        • Descriptive Statistics
        • EM Algorithm for Data with Missing Values
        • Statistical Assumptions for Multiple Imputation
        • Missing Data Patterns
        • Imputation Methods
        • Monotone Methods for Data Sets with Monotone Missing Patterns
        • Monotone and FCS Regression Methods
        • Monotone and FCS Predictive Mean Matching Methods
        • Monotone Propensity Score Method
        • Monotone and FCS Discriminant Function Methods
        • Monotone and FCS Logistic Regression Methods
        • FCS Methods for Data Sets with Arbitrary Missing Patterns
        • Checking Convergence in FCS Methods
        • MCMC Method for Arbitrary Missing Multivariate Normal Data
        • Producing Monotone Missingness with the MCMC Method
        • MCMC Method Specifications
        • Checking Convergence in MCMC
        • Input Data Sets
        • Output Data Sets
        • Combining Inferences from Multiply Imputed Data Sets
        • Multiple Imputation Efficiency
        • Imputer’s Model Versus Analyst’s Model
        • Parameter Simulation versus Multiple Imputation
        • Summary of Issues in Multiple Imputation
        • ODS Table Names
        • ODS Graphics
      • Examples: MI Procedure
        • EM Algorithm for MLE
        • Monotone Propensity Score Method
        • Monotone Regression Method
        • Monotone Logistic Regression Method for CLASS Variables
        • Monotone Discriminant Function Method for CLASS Variables
        • FCS Method for Continuous Variables
        • FCS Method for CLASS Variables
        • FCS Method with Trace Plot
        • MCMC Method
        • Producing Monotone Missingness with MCMC
        • Checking Convergence in MCMC
        • Saving and Using Parameters for MCMC
        • Transforming to Normality
        • Multistage Imputation
      • References
    • The MIANALYZE Procedure
      • Overview: MIANALYZE Procedure
      • Getting Started: MIANALYZE Procedure
      • Syntax: MIANALYZE Procedure
        • PROC MIANALYZE Statement
        • BY Statement
        • CLASS Statement
        • MODELEFFECTS Statement
        • STDERR Statement
        • TEST Statement
      • Details: MIANALYZE Procedure
        • Input Data Sets
        • Combining Inferences from Imputed Data Sets
        • Multiple Imputation Efficiency
        • Multivariate Inferences
        • Testing Linear Hypotheses about the Parameters
        • Examples of the Complete-Data Inferences
        • ODS Table Names
      • Examples: MIANALYZE Procedure
        • Reading Means and Standard Errors from Variables in a DATA= Data Set
        • Reading Means and Covariance Matrices from a DATA= COV Data Set
        • Reading Regression Results from a DATA= EST Data Set
        • Reading Mixed Model Results from PARMS= and COVB= Data Sets
        • Reading Generalized Linear Model Results
        • Reading GLM Results from PARMS= and XPXI= Data Sets
        • Reading Logistic Model Results from PARMS= and COVB= Data Sets
        • Reading Mixed Model Results with Classification Variables
        • Using a TEST statement
        • Combining Correlation Coefficients
      • References
    • The MIXED Procedure
      • Overview: MIXED Procedure
        • Basic Features
        • Notation for the Mixed Model
        • PROC MIXED Contrasted with Other SAS Procedures
      • Getting Started: MIXED Procedure
        • Clustered Data Example
      • Syntax: MIXED Procedure
        • PROC MIXED Statement
        • BY Statement
        • CLASS Statement
        • CODE Statement
        • CONTRAST Statement
        • ESTIMATE Statement
        • ID Statement
        • LSMEANS Statement
        • LSMESTIMATE Statement
        • MODEL Statement
        • PARMS Statement
        • PERFORMANCE Statement
        • PRIOR Statement
        • RANDOM Statement
        • REPEATED Statement
        • SLICE Statement
        • STORE Statement
        • WEIGHT Statement
      • Details: MIXED Procedure
        • Mixed Models Theory
        • Parameterization of Mixed Models
        • Residuals and Influence Diagnostics
        • Default Output
        • ODS Table Names
        • ODS Graphics
        • Computational Issues
      • Examples: MIXED Procedure
        • Split-Plot Design
        • Repeated Measures
        • Plotting the Likelihood
        • Known G and R
        • Random Coefficients
        • Line-Source Sprinkler Irrigation
        • Influence in Heterogeneous Variance Model
        • Influence Analysis for Repeated Measures Data
        • Examining Individual Test Components
        • Isotonic Contrasts for Ordered Mean Values
      • References
    • The MODECLUS Procedure
      • Overview: MODECLUS Procedure
      • Getting Started: MODECLUS Procedure
      • Syntax: MODECLUS Procedure
        • PROC MODECLUS Statement
        • BY Statement
        • FREQ Statement
        • ID Statement
        • VAR Statement
      • Details: MODECLUS Procedure
        • Density Estimation
        • Clustering Methods
        • Significance Tests
        • Computational Resources
        • Missing Values
        • Output Data Sets
        • Displayed Output
        • ODS Table Names
      • Examples: MODECLUS Procedure
        • Cluster Analysis of Samples from Univariate Distributions
        • Cluster Analysis of Flying Mileages between Ten American Cities
        • Cluster Analysis with Significance Tests
        • Cluster Analysis: Hertzsprung-Russell Plot
        • Using the TRACE Option When METHOD=6
      • References
    • The MULTTEST Procedure
      • Overview: MULTTEST Procedure
      • Getting Started: MULTTEST Procedure
        • Drug Example
      • Syntax: MULTTEST Procedure
        • PROC MULTTEST Statement
        • BY Statement
        • CLASS Statement
        • CONTRAST Statement
        • FREQ Statement
        • ID Statement
        • STRATA Statement
        • TEST Statement
      • Details: MULTTEST Procedure
        • Statistical Tests
        • p-Value Adjustments
        • Missing Values
        • Computational Resources
        • Output Data Sets
        • Displayed Output
        • ODS Table Names
        • ODS Graphics
      • Examples: MULTTEST Procedure
        • Cochran-Armitage Test with Permutation Resampling
        • Freeman-Tukey and t Tests with Bootstrap Resampling
        • Peto Mortality-Prevalence Test
        • Fisher Test with Permutation Resampling
        • Inputting Raw p-Values
        • Adaptive Adjustments and ODS Graphics
      • References
    • The NESTED Procedure
      • Overview: NESTED Procedure
        • Contrasted with Other SAS Procedures
      • Getting Started: NESTED Procedure
        • Reliability of Automobile Models
      • Syntax: NESTED Procedure
        • PROC NESTED Statement
        • BY Statement
        • CLASS Statement
        • VAR Statement
      • Details: NESTED Procedure
        • Missing Values
        • Unbalanced Data
        • General Random-Effects Model
        • Analysis of Covariation
        • Error Terms in F Tests
        • Computational Method
        • Displayed Output
        • ODS Table Names
      • Example: NESTED Procedure
        • Variability of Calcium Concentration in Turnip Greens
      • References
    • The NLIN Procedure
      • Overview: NLIN Procedure
      • Getting Started: NLIN Procedure
        • Nonlinear or Linear Model
        • Notation for Nonlinear Regression Models
        • Estimating the Parameters in the Nonlinear Model
      • Syntax: NLIN Procedure
        • PROC NLIN Statement
        • BOUNDS Statement
        • BY Statement
        • CONTROL Statement
        • DER Statement
        • ID Statement
        • MODEL Statement
        • OUTPUT Statement
        • PARAMETERS Statement
        • PROFILE Statement
        • RETAIN Statement
        • Other Programming Statements
      • Details: NLIN Procedure
        • Automatic Derivatives
        • Measures of Nonlinearity and Diagnostics
        • Missing Values
        • Special Variables
        • Troubleshooting
        • Computational Methods
        • Output Data Sets
        • Confidence Intervals
        • Covariance Matrix of Parameter Estimates
        • Convergence Measures
        • Displayed Output
        • Incompatibilities with SAS 6.11 and Earlier Versions of PROC NLIN
        • ODS Table Names
        • ODS Graphics
      • Examples: NLIN Procedure
        • Segmented Model
        • Iteratively Reweighted Least Squares
        • Probit Model with Likelihood Function
        • Affecting Curvature through Parameterization
        • Comparing Nonlinear Trends among Groups
        • ODS Graphics and Diagnostics
        • Parameter Profiling
      • References
    • The NLMIXED Procedure
      • Overview: NLMIXED Procedure
        • Introduction
        • Literature on Nonlinear Mixed Models
        • PROC NLMIXED Compared with Other SAS Procedures and Macros
      • Getting Started: NLMIXED Procedure
        • Nonlinear Growth Curves with Gaussian Data
        • Logistic-Normal Model with Binomial Data
      • Syntax: NLMIXED Procedure
        • PROC NLMIXED Statement
        • ARRAY Statement
        • BOUNDS Statement
        • BY Statement
        • CONTRAST Statement
        • ESTIMATE Statement
        • ID Statement
        • MODEL Statement
        • PARMS Statement
        • PREDICT Statement
        • RANDOM Statement
        • REPLICATE Statement
        • Programming Statements
      • Details: NLMIXED Procedure
        • Modeling Assumptions and Notation
        • Integral Approximations
        • Built-in Log-Likelihood Functions
        • Optimization Algorithms
        • Finite-Difference Approximations of Derivatives
        • Hessian Scaling
        • Active Set Methods
        • Line-Search Methods
        • Restricting the Step Length
        • Computational Problems
        • Covariance Matrix
        • Prediction
        • Computational Resources
        • Displayed Output
        • ODS Table Names
      • Examples: NLMIXED Procedure
        • One-Compartment Model with Pharmacokinetic Data
        • Probit-Normal Model with Binomial Data
        • Probit-Normal Model with Ordinal Data
        • Poisson-Normal Model with Count Data
        • Failure Time and Frailty Model
      • References
    • The NPAR1WAY Procedure
      • Overview: NPAR1WAY Procedure
      • Getting Started: NPAR1WAY Procedure
      • Syntax: NPAR1WAY Procedure
        • PROC NPAR1WAY Statement
        • BY Statement
        • CLASS Statement
        • EXACT Statement
        • FREQ Statement
        • OUTPUT Statement
        • VAR Statement
      • Details: NPAR1WAY Procedure
        • Missing Values
        • Tied Values
        • Statistical Computations
          • Simple Linear Rank Tests for Two-Sample Data
          • One-Way ANOVA Tests
          • Scores for Linear Rank and One-Way ANOVA Tests
          • Hodges-Lehmann Estimation of Location Shift
          • Fligner-Policello Test
          • Multiple Comparisons Based on Pairwise Rankings
          • Tests Based on the Empirical Distribution Function
          • Exact Tests
        • Contents of the Output Data Set
        • Displayed Output
        • ODS Table Names
        • ODS Graphics
      • Examples: NPAR1WAY Procedure
        • Two-Sample Location Tests and Plots
        • EDF Statistics and EDF Plot
        • Exact Wilcoxon Two-Sample Test
        • Hodges-Lehmann Estimation
        • Exact Savage Multisample Test
      • References
    • The ORTHOREG Procedure
      • Overview: ORTHOREG Procedure
      • Getting Started: ORTHOREG Procedure
        • Longley Data
      • Syntax: ORTHOREG Procedure
        • PROC ORTHOREG Statement
        • BY Statement
        • CLASS Statement
        • EFFECT Statement
        • EFFECTPLOT Statement
        • ESTIMATE Statement
        • LSMEANS Statement
        • LSMESTIMATE Statement
        • MODEL Statement
        • SLICE Statement
        • STORE Statement
        • TEST Statement
        • WEIGHT Statement
      • Details: ORTHOREG Procedure
        • Missing Values
        • Output Data Set
        • Displayed Output
        • ODS Table Names
        • ODS Graphics
      • Examples: ORTHOREG Procedure
        • Precise Analysis of Variance
        • Wampler Data
        • Fitting Polynomials
      • References
    • The PHREG Procedure
      • Overview: PHREG Procedure
      • Getting Started: PHREG Procedure
        • Classical Method of Maximum Likelihood
        • Bayesian Analysis
      • Syntax: PHREG Procedure
        • PROC PHREG Statement
        • ASSESS Statement
        • BASELINE Statement
        • BAYES Statement
        • BY Statement
        • CLASS Statement
        • CONTRAST Statement
        • EFFECT Statement
        • ESTIMATE Statement
        • FREQ Statement
        • HAZARDRATIO Statement
        • ID Statement
        • LSMEANS Statement
        • LSMESTIMATE Statement
        • MODEL Statement
        • OUTPUT Statement
        • Programming Statements
        • RANDOM Statement
        • STRATA Statement
        • SLICE Statement
        • STORE Statement
        • TEST Statement
        • WEIGHT Statement
      • Details: PHREG Procedure
        • Failure Time Distribution
        • Time and CLASS Variables Usage
        • Partial Likelihood Function for the Cox Model
        • Counting Process Style of Input
        • Left-Truncation of Failure Times
        • The Multiplicative Hazards Model
        • The Frailty Model
        • Hazard Ratios
        • Proportional Rates/Means Models for Recurrent Events
        • Newton-Raphson Method
        • Firth’s Modification for Maximum Likelihood Estimation
        • Robust Sandwich Variance Estimate
        • Testing the Global Null Hypothesis
        • Type 3 Tests
        • Confidence Limits for a Hazard Ratio
        • Using the TEST Statement to Test Linear Hypotheses
        • Analysis of Multivariate Failure Time Data
        • Model Fit Statistics
        • Residuals
        • Diagnostics Based on Weighted Residuals
        • Influence of Observations on Overall Fit of the Model
        • Survivor Function Estimators
        • Effect Selection Methods
        • Assessment of the Proportional Hazards Model
        • The Penalized Partial Likelihood Approach for Fitting Frailty Models
        • Specifics for Bayesian Analysis
        • Computational Resources
        • Input and Output Data Sets
        • Displayed Output
        • ODS Table Names
        • ODS Graphics
      • Examples: PHREG Procedure
        • Stepwise Regression
        • Best Subset Selection
        • Modeling with Categorical Predictors
        • Firth’s Correction for Monotone Likelihood
        • Conditional Logistic Regression for m:n Matching
        • Model Using Time-Dependent Explanatory Variables
        • Time-Dependent Repeated Measurements of a Covariate
        • Survival Curves
        • Analysis of Residuals
        • Analysis of Recurrent Events Data
        • Analysis of Clustered Data
        • Model Assessment Using Cumulative Sums of Martingale Residuals
        • Bayesian Analysis of the Cox Model
        • Bayesian Analysis of Piecewise Exponential Model
      • References
    • The PLAN Procedure
      • Overview: PLAN Procedure
      • Getting Started: PLAN Procedure
        • Three Replications with Four Factors
        • Randomly Assigning Subjects to Treatments
      • Syntax: PLAN Procedure
        • PROC PLAN Statement
        • FACTORS Statement
        • OUTPUT Statement
        • TREATMENTS Statement
      • Details: PLAN Procedure
        • Using PROC PLAN Interactively
        • Output Data Sets
        • Specifying Factor Structures
        • Randomizing Designs
        • Displayed Output
        • ODS Table Names
      • Examples: PLAN Procedure
        • A Split-Plot Design
        • A Hierarchical Design
        • An Incomplete Block Design
        • A Latin Square Design
        • A Generalized Cyclic Incomplete Block Design
        • Permutations and Combinations
        • Crossover Designs
      • References
    • The PLM Procedure
      • Overview: PLM Procedure
        • Basic Features
        • PROC PLM Contrasted with Other SAS Procedures
      • Getting Started: PLM Procedure
      • Syntax: PLM Procedure
        • PROC PLM Statement
        • CODE Statement
        • EFFECTPLOT Statement
        • ESTIMATE Statement
        • FILTER Statement
        • LSMEANS Statement
        • LSMESTIMATE Statement
        • SCORE Statement
        • SHOW Statement
        • SLICE Statement
        • TEST Statement
        • WHERE Statement
      • Details: PLM Procedure
        • BY Processing and the PLM Procedure
        • Analysis Based on Posterior Estimates
        • User-Defined Formats and the PLM Procedure
        • ODS Table Names
        • ODS Graphics
      • Examples: PLM Procedure
        • Scoring with PROC PLM
        • Working with Item Stores
        • Group Comparisons in an Ordinal Model
        • Posterior Inference for Binomial Data
        • BY-Group Processing
        • Comparing Multiple B-Splines
        • Linear Inference with Arbitrary Estimates
      • References
    • The PLS Procedure
      • Overview: PLS Procedure
        • Basic Features
      • Getting Started: PLS Procedure
        • Spectrometric Calibration
      • Syntax: PLS Procedure
        • PROC PLS Statement
        • BY Statement
        • CLASS Statement
        • EFFECT Statement
        • ID Statement
        • MODEL Statement
        • OUTPUT Statement
      • Details: PLS Procedure
        • Regression Methods
        • Cross Validation
        • Centering and Scaling
        • Missing Values
        • Displayed Output
        • ODS Table Names
        • ODS Graphics
      • Examples: PLS Procedure
        • Examining Model Details
        • Examining Outliers
        • Choosing a PLS Model by Test Set Validation
        • Partial Least Squares Spline Smoothing
      • References
    • The POWER Procedure
      • Overview: POWER Procedure
      • Getting Started: POWER Procedure
        • Computing Power for a One-Sample t Test
        • Determining Required Sample Size for a Two-Sample t Test
      • Syntax: POWER Procedure
        • PROC POWER Statement
        • LOGISTIC Statement
        • MULTREG Statement
        • ONECORR Statement
        • ONESAMPLEFREQ Statement
        • ONESAMPLEMEANS Statement
        • ONEWAYANOVA Statement
        • PAIREDFREQ Statement
        • PAIREDMEANS Statement
        • PLOT Statement
        • TWOSAMPLEFREQ Statement
        • TWOSAMPLEMEANS Statement
        • TWOSAMPLESURVIVAL Statement
        • TWOSAMPLEWILCOXON Statement
      • Details: POWER Procedure
        • Overview of Power Concepts
        • Summary of Analyses
        • Specifying Value Lists in Analysis Statements
          • Keyword-Lists
          • Number-Lists
          • Grouped-Number-Lists
          • Name-Lists
          • Grouped-Name-Lists
        • Sample Size Adjustment Options
        • Error and Information Output
        • Displayed Output
        • ODS Table Names
        • Computational Resources
          • Memory
          • CPU Time
        • Computational Methods and Formulas
          • Common Notation
          • Analyses in the LOGISTIC Statement
          • Analyses in the MULTREG Statement
          • Analyses in the ONECORR Statement
          • Analyses in the ONESAMPLEFREQ Statement
          • Analyses in the ONESAMPLEMEANS Statement
          • Analyses in the ONEWAYANOVA Statement
          • Analyses in the PAIREDFREQ Statement
          • Analyses in the PAIREDMEANS Statement
          • Analyses in the TWOSAMPLEFREQ Statement
          • Analyses in the TWOSAMPLEMEANS Statement
          • Analyses in the TWOSAMPLESURVIVAL Statement
          • Analyses in the TWOSAMPLEWILCOXON Statement
        • ODS Graphics
        • ODS Styles Suitable for Use with PROC POWER
      • Examples: POWER Procedure
        • One-Way ANOVA
        • The Sawtooth Power Function in Proportion Analyses
        • Simple AB/BA Crossover Designs
        • Noninferiority Test with Lognormal Data
        • Multiple Regression and Correlation
        • Comparing Two Survival Curves
        • Confidence Interval Precision
        • Customizing Plots
          • Assigning Analysis Parameters to Axes
          • Fine-Tuning a Sample Size Axis
          • Adding Reference Lines
          • Linking Plot Features to Analysis Parameters
          • Choosing Key (Legend) Styles
          • Modifying Symbol Locations
        • Binary Logistic Regression with Independent Predictors
        • Wilcoxon-Mann-Whitney Test
      • References
    • The Power and Sample Size Application
      • Overview: PSS Application
        • SAS Power and Sample Size
      • Getting Started: PSS Application
        • Overview
        • The Basic Steps
        • A Simple Example
      • How to Use: PSS Application
        • Overview
        • SAS Connections
        • Setting Preferences
        • Creating and Editing PSS Projects
        • Importing and Exporting Projects
      • Details: PSS Application
        • Software Requirements
        • Installation
        • Configuration
      • Example: Two-Sample t Test
        • Overview
        • Test of Two Independent Means for Equal Variances
        • Test of Two Independent Means for Unequal Variances
        • Test of Mean Ratios
        • Additional Topics
      • Example: Analysis of Variance
        • Overview
        • The Example
        • Additional Topics
      • Example: Two-Sample Survival Rank Tests
        • Overview
        • The Example
        • Additional Topics
    • The PRINCOMP Procedure
      • Overview: PRINCOMP Procedure
      • Getting Started: PRINCOMP Procedure
      • Syntax: PRINCOMP Procedure
        • PROC PRINCOMP Statement
        • BY Statement
        • FREQ Statement
        • ID Statement
        • PARTIAL Statement
        • VAR Statement
        • WEIGHT Statement
      • Details: PRINCOMP Procedure
        • Missing Values
        • Output Data Sets
        • Computational Resources
        • Displayed Output
        • ODS Table Names
        • ODS Graphics
      • Examples: PRINCOMP Procedure
        • Temperatures
        • Basketball Data
        • Job Ratings
      • References
    • The PRINQUAL Procedure
      • Overview: PRINQUAL Procedure
      • Getting Started: PRINQUAL Procedure
      • Syntax: PRINQUAL Procedure
        • PROC PRINQUAL Statement
        • BY Statement
        • FREQ Statement
        • ID Statement
        • TRANSFORM Statement
        • WEIGHT Statement
      • Details: PRINQUAL Procedure
        • The Three Methods of Variable Transformation
        • Understanding How PROC PRINQUAL Works
        • Splines
        • Missing Values
        • Controlling the Number of Iterations
        • Performing a Principal Component Analysis of Transformed Data
        • Using the MAC Method
        • Output Data Set
        • Avoiding Constant Transformations
        • Constant Variables
        • Character OPSCORE Variables
        • REITERATE Option Usage
        • Passive Observations
        • Computational Resources
        • Displayed Output
        • ODS Table Names
        • ODS Graphics
      • Examples: PRINQUAL Procedure
        • Multidimensional Preference Analysis of Automobile Data
        • Principal Components of Basketball Rankings
      • References
    • The PROBIT Procedure
      • Overview: PROBIT Procedure
      • Getting Started: PROBIT Procedure
        • Estimating the Natural Response Threshold Parameter
      • Syntax: PROBIT Procedure
        • PROC PROBIT Statement
        • BY Statement
        • CDFPLOT Statement
        • CLASS Statement
        • EFFECTPLOT Statement
        • ESTIMATE Statement
        • INSET Statement
        • IPPPLOT Statement
        • LPREDPLOT Statement
        • LSMEANS Statement
        • LSMESTIMATE Statement
        • MODEL Statement
        • OUTPUT Statement
        • PREDPPLOT Statement
        • SLICE Statement
        • STORE Statement
        • TEST Statement
        • WEIGHT Statement
      • Details: PROBIT Procedure
        • Missing Values
        • Response Level Ordering
        • Computational Method
        • Distributions
        • INEST= SAS-data-set
        • Model Specification
        • Lack-of-Fit Tests
        • Rescaling the Covariance Matrix
        • Tolerance Distribution
        • Inverse Confidence Limits
        • OUTEST= SAS-data-set
        • XDATA= SAS-data-set
        • Traditional High-Resolution Graphics
        • Displayed Output
        • ODS Table Names
        • ODS Graphics
      • Examples: PROBIT Procedure
        • Dosage Levels
        • Multilevel Response
        • Logistic Regression
        • An Epidemiology Study
        • Model Postfitting Analysis
      • References
    • The QUANTLIFE Procedure
      • Overview: QUANTLIFE Procedure
        • Features
        • Quantile Regression
      • Getting Started: QUANTLIFE Procedure
      • Syntax: QUANTLIFE Procedure
        • PROC QUANTLIFE Statement
        • BASELINE Statement
        • BY Statement
        • CLASS Statement
        • EFFECT Statement
        • MODEL Statement
        • OUTPUT Statement
        • TEST Statement
        • WEIGHT Statement
      • Details: QUANTLIFE Procedure
        • Notation for Censored Quantile Regression
        • Kaplan-Meier-Type Estimator for Censored Quantile Regression
        • Nelson-Aalen-Type Estimator for Censored Quantile Regression
        • Confidence Interval
        • Output Data Sets
        • ODS Table Names
        • ODS Graphics
      • Examples: QUANTLIFE Procedure
        • Primary Biliary Cirrhosis Study
        • Drug Abuse Study
      • References
    • The QUANTREG Procedure
      • Overview: QUANTREG Procedure
        • Features
        • Quantile Regression
      • Getting Started: QUANTREG Procedure
        • Analysis of Fish-Habitat Relationships
        • Growth Charts for Body Mass Index
      • Syntax: QUANTREG Procedure
        • PROC QUANTREG Statement
        • BY Statement
        • CLASS Statement
        • EFFECT Statement
        • ESTIMATE Statement
        • ID Statement
        • MODEL Statement
        • OUTPUT Statement
        • PERFORMANCE Statement
        • TEST Statement
        • WEIGHT Statement
      • Details: QUANTREG Procedure
        • Quantile Regression as an Optimization Problem
        • Optimization Algorithms
        • Confidence Interval
        • Covariance-Correlation
        • Linear Test
        • Leverage Point and Outlier Detection
        • INEST= Data Set
        • OUTEST= Data Set
        • Computational Resources
        • ODS Table Names
        • ODS Graphics
      • Examples: QUANTREG Procedure
        • Comparison of Algorithms
        • Quantile Regression for Econometric Growth Data
        • Quantile Regression Analysis of Birth-Weight Data
        • Nonparametric Quantile Regression for Ozone Levels
        • Quantile Polynomial Regression for Salary Data
      • References
    • The QUANTSELECT Procedure
      • Overview: QUANTSELECT Procedure
        • Features
      • Getting Started: QUANTSELECT Procedure
      • Syntax: QUANTSELECT Procedure
        • PROC QUANTSELECT Statement
        • BY Statement
        • CLASS Statement
        • EFFECT Statement
        • MODEL Statement
        • OUTPUT Statement
        • PARTITION Statement
        • WEIGHT Statement
      • Details: QUANTSELECT Procedure
        • Effect Selection Methods
          • Full Model Fitted (NONE)
          • Forward Selection (FORWARD)
          • Backward Elimination (BACKWARD)
          • Stepwise Selection (STEPWISE)
          • LASSO Method (LASSO)
        • Criteria Used in Model Selection Methods
        • Macro Variables That Contain Selected Models
        • Using Validation and Test Data
        • Displayed Output
        • ODS Table Names
        • ODS Graphics
      • Example: QUANTSELECT Procedure
        • Simulated Data Example
      • References
    • The REG Procedure
      • Overview: REG Procedure
      • Getting Started: REG Procedure
        • Simple Linear Regression
        • Polynomial Regression
        • Using PROC REG Interactively
      • Syntax: REG Procedure
        • PROC REG Statement
        • ADD Statement
        • BY Statement
        • CODE Statement
        • DELETE Statement
        • FREQ Statement
        • ID Statement
        • MODEL Statement
        • MTEST Statement
        • OUTPUT Statement
        • PAINT Statement
        • PLOT Statement
        • PRINT Statement
        • REFIT Statement
        • RESTRICT Statement
        • REWEIGHT Statement
        • STORE Statement
        • TEST Statement
        • VAR Statement
        • WEIGHT Statement
      • Details: REG Procedure
        • Missing Values
        • Input Data Sets
        • Output Data Sets
        • Interactive Analysis
        • Model-Selection Methods
        • Criteria Used in Model-Selection Methods
        • Limitations in Model-Selection Methods
        • Parameter Estimates and Associated Statistics
        • Predicted and Residual Values
        • Models of Less Than Full Rank
        • Collinearity Diagnostics
        • Model Fit and Diagnostic Statistics
        • Influence Statistics
        • Reweighting Observations in an Analysis
        • Testing for Heteroscedasticity
        • Testing for Lack of Fit
        • Multivariate Tests
        • Autocorrelation in Time Series Data
        • Computations for Ridge Regression and IPC Analysis
        • Construction of Q-Q and P-P Plots
        • Computational Methods
        • Computer Resources in Regression Analysis
        • Displayed Output
        • ODS Table Names
        • ODS Graphics
      • Examples: REG Procedure
        • Modeling Salaries of Major League Baseball Players
        • Aerobic Fitness Prediction
        • Predicting Weight by Height and Age
        • Regression with Quantitative and Qualitative Variables
        • Ridge Regression for Acetylene Data
        • Chemical Reaction Response
      • References
    • The ROBUSTREG Procedure
      • Overview: ROBUSTREG Procedure
        • Features
      • Getting Started: ROBUSTREG Procedure
        • M Estimation
        • LTS Estimation
      • Syntax: ROBUSTREG Procedure
        • PROC ROBUSTREG Statement
        • BY Statement
        • CLASS Statement
        • EFFECT Statement
        • ID Statement
        • MODEL Statement
        • OUTPUT Statement
        • PERFORMANCE Statement
        • TEST Statement
        • WEIGHT Statement
      • Details: ROBUSTREG Procedure
        • M Estimation
        • High-Breakdown-Value Estimation
        • MM Estimation
        • Robust Distance
        • Leverage Point and Outlier Detection
        • Implementation of the WEIGHT Statement
        • INEST= Data Set
        • OUTEST= Data Set
        • Computational Resources
        • ODS Table Names
        • ODS Graphics
      • Examples: ROBUSTREG Procedure
        • Comparison of Robust Estimates
        • Robust ANOVA
        • Growth Study of De Long and Summers
        • Constructed Effects
        • Robust Diagnostics
      • References
    • The RSREG Procedure
      • Overview: RSREG Procedure
        • Comparison to Other SAS Software
        • Terminology
      • Getting Started: RSREG Procedure
        • A Response Surface with a Simple Optimum
      • Syntax: RSREG Procedure
        • PROC RSREG Statement
        • BY Statement
        • ID Statement
        • MODEL Statement
        • RIDGE Statement
        • WEIGHT Statement
      • Details: RSREG Procedure
        • Introduction to Response Surface Experiments
        • Coding the Factor Variables
        • Missing Values
        • Plotting the Surface
        • Searching for Multiple Response Conditions
        • Handling Covariates
        • Computational Method
        • Output Data Sets
        • Displayed Output
        • ODS Table Names
        • ODS Graphics
      • Examples: RSREG Procedure
        • A Saddle Surface Response Using Ridge Analysis
        • Response Surface Analysis with Covariates
      • References
    • The SCORE Procedure
      • Overview: SCORE Procedure
        • Raw Data Set
        • Scoring Coefficients Data Set
        • Standardization of Raw Data
      • Getting Started: SCORE Procedure
      • Syntax: SCORE Procedure
        • PROC SCORE Statement
        • BY Statement
        • ID Statement
        • VAR Statement
      • Details: SCORE Procedure
        • Missing Values
        • Regression Parameter Estimates from PROC REG
        • Output Data Set
        • Computational Resources
      • Examples: SCORE Procedure
        • Factor Scoring Coefficients
        • Regression Parameter Estimates
        • Custom Scoring Coefficients
      • References
    • The SEQDESIGN Procedure
      • Overview: SEQDESIGN Procedure
        • Features of the SEQDESIGN Procedure
        • Output from the SEQDESIGN Procedure
        • Boundaries for Group Sequential Designs
        • Group Sequential Methods
      • Getting Started: SEQDESIGN Procedure
      • Syntax: SEQDESIGN Procedure
        • PROC SEQDESIGN Statement
        • DESIGN Statement
        • SAMPLESIZE Statement
      • Details: SEQDESIGN Procedure
        • Fixed-Sample Clinical Trials
        • One-Sided Fixed-Sample Tests in Clinical Trials
        • Two-Sided Fixed-Sample Tests in Clinical Trials
        • Group Sequential Methods
        • Statistical Assumptions for Group Sequential Designs
        • Boundary Scales
        • Boundary Variables
        • Type I and Type II Errors
        • Unified Family Methods
        • Haybittle-Peto Method
        • Whitehead Methods
        • Error Spending Methods
        • Acceptance () Boundary
        • Boundary Adjustments for Overlapping Lower and Upper Boundaries
        • Specified and Derived Parameters
        • Applicable Boundary Keys
        • Sample Size Computation
        • Applicable One-Sample Tests and Sample Size Computation
        • Applicable Two-Sample Tests and Sample Size Computation
        • Applicable Regression Parameter Tests and Sample Size Computation
        • Aspects of Group Sequential Designs
        • Summary of Methods in Group Sequential Designs
        • Table Output
        • ODS Table Names
        • Graphics Output
        • ODS Graphics
      • Examples: SEQDESIGN Procedure
        • Creating Fixed-Sample Designs
        • Creating a One-Sided O’Brien-Fleming Design
        • Creating Two-Sided Pocock and O’Brien-Fleming Designs
        • Generating Graphics Display for Sequential Designs
        • Creating Designs Using Haybittle-Peto Methods
        • Creating Designs with Various Stopping Criteria
        • Creating Whitehead’s Triangular Designs
        • Creating a One-Sided Error Spending Design
        • Creating Designs with Various Number of Stages
        • Creating Two-Sided Error Spending Designs with and without Overlapping Lower and Upper Boundaries
        • Creating a Two-Sided Asymmetric Error Spending Design with Early Stopping to Reject
        • Creating a Two-Sided Asymmetric Error Spending Design with Early Stopping to Reject or Accept
        • Creating a Design with a Nonbinding Beta Boundary
        • Computing Sample Size for Survival Data
      • References
    • The SEQTEST Procedure
      • Overview: SEQTEST Procedure
        • Features of the SEQTEST Procedure
        • Output from the SEQTEST Procedure
      • Getting Started: SEQTEST Procedure
      • Syntax: SEQTEST Procedure
        • PROC SEQTEST Statement
      • Details: SEQTEST Procedure
        • Input Data Sets
        • Boundary Variables
        • Information Level Adjustments at Future Stages
        • Boundary Adjustments for Information Levels
        • Boundary Adjustments for Minimum Error Spending
        • Boundary Adjustments for Overlapping Lower and Upper Boundaries
        • Stochastic Curtailment
        • Repeated Confidence Intervals
        • Analysis after a Sequential Test
        • Available Sample Space Orderings in a Sequential Test
        • Applicable Tests and Sample Size Computation
        • Table Output
        • ODS Table Names
        • Graphics Output
        • ODS Graphics
      • Examples: SEQTEST Procedure
        • Testing the Difference between Two Proportions
        • Testing an Effect in a Regression Model
        • Testing an Effect with Early Stopping to Accept
        • Testing a Binomial Proportion
        • Comparing Two Proportions with a Log Odds Ratio Test
        • Comparing Two Survival Distributions with a Log-Rank Test
        • Testing an Effect in a Proportional Hazards Regression Model
        • Testing an Effect in a Logistic Regression Model
        • Conducting a Trial with a Nonbinding Acceptance Boundary
      • References
    • The SIM2D Procedure
      • Overview: SIM2D Procedure
        • Introduction to Spatial Simulation
      • Getting Started: SIM2D Procedure
        • Preliminary Spatial Data Analysis
        • Investigating Variability by Simulation
      • Syntax: SIM2D Procedure
        • PROC SIM2D Statement
        • BY Statement
        • COORDINATES Statement
        • GRID Statement
        • ID Statement
        • RESTORE Statement
        • SIMULATE Statement
        • MEAN Statement
      • Details: SIM2D Procedure
        • Computational and Theoretical Details of Spatial Simulation
          • Introduction
          • Theoretical Development
          • Computational Details
        • Output Data Set
        • Displayed Output
        • ODS Table Names
        • ODS Graphics
      • Examples: SIM2D Procedure
        • Simulation and Economic Feasibility
          • Simulating a Subregion for Economic Feasibility
          • Implementation Using PROC SIM2D
        • Variability at Selected Locations
        • Risk Analysis with Simulation
      • References
    • The SIMNORMAL Procedure
      • Overview: SIMNORMAL Procedure
      • Getting Started: SIMNORMAL Procedure
      • Syntax: SIMNORMAL Procedure
        • PROC SIMNORMAL Statement
        • BY Statement
        • CONDITION Statement
        • VAR Statement
        • OUT= Output Data Set
      • Computational Details: SIMNORMAL Procedure
        • Introduction
        • Unconditional Simulation
        • Conditional Simulation
      • References
    • The STDIZE Procedure
      • Overview: STDIZE Procedure
      • Getting Started: STDIZE Procedure
      • Syntax: STDIZE Procedure
        • PROC STDIZE Statement
        • BY Statement
        • FREQ Statement
        • LOCATION Statement
        • SCALE Statement
        • VAR Statement
        • WEIGHT Statement
      • Details: STDIZE Procedure
        • Standardization Methods
        • Computation of the Statistics
        • Computing Quantiles
        • Constant Data
        • Missing Values
        • Output Data Sets
        • Displayed Output
        • ODS Table Names
      • Example: STDIZE Procedure
        • Standardization of Variables in Cluster Analysis
      • References
    • The STDRATE Procedure
      • Overview: STDRATE Procedure
      • Getting Started: STDRATE Procedure
      • Syntax: STDRATE Procedure
        • PROC STDRATE Statement
        • BY Statement
        • POPULATION Statement
        • REFERENCE Statement
        • STRATA Statement
      • Details: STDRATE Procedure
        • Rate
        • Risk
        • Direct Standardization
        • Mantel-Haenszel Effect Estimation
        • Indirect Standardization and Standardized Morbidity/Mortality Ratio
        • Attributable Fraction and Population Attributable Fraction
        • Applicable Data Sets and Required Variables for Method Specifications
        • Applicable Confidence Limits for Rate and Risk Statistics
        • Table Output
        • ODS Table Names
        • Graphics Output
        • ODS Graphics
      • Examples: STDRATE Procedure
        • Comparing Directly Standardized Rates
        • Computing Mantel-Haenszel Risk Estimation
        • Computing Attributable Fraction Estimates
        • Displaying SMR Results from BY Groups
      • References
    • The STEPDISC Procedure
      • Overview: STEPDISC Procedure
      • Getting Started: STEPDISC Procedure
      • Syntax: STEPDISC Procedure
        • PROC STEPDISC Statement
        • BY Statement
        • CLASS Statement
        • FREQ Statement
        • VAR Statement
        • WEIGHT Statement
      • Details: STEPDISC Procedure
        • Missing Values
        • Input Data Sets
        • Computational Resources
        • Displayed Output
        • ODS Table Names
      • Example: STEPDISC Procedure
        • Performing a Stepwise Discriminant Analysis
      • References
    • The SURVEYFREQ Procedure
      • Overview: SURVEYFREQ Procedure
      • Getting Started: SURVEYFREQ Procedure
      • Syntax: SURVEYFREQ Procedure
        • PROC SURVEYFREQ Statement
        • BY Statement
        • CLUSTER Statement
        • REPWEIGHTS Statement
        • STRATA Statement
        • TABLES Statement
        • WEIGHT Statement
      • Details: SURVEYFREQ Procedure
        • Specifying the Sample Design
        • Domain Analysis
        • Missing Values
        • Statistical Computations
          • Variance Estimation
          • Definitions and Notation
          • Totals
          • Covariance of Totals
          • Proportions
          • Row and Column Proportions
          • Balanced Repeated Replication (BRR)
          • The Jackknife Method
          • Confidence Limits for Totals
          • Confidence Limits for Proportions
          • Degrees of Freedom
          • Coefficient of Variation
          • Design Effect
          • Expected Weighted Frequency
          • Risks and Risk Difference
          • Odds Ratio and Relative Risks
          • Rao-Scott Chi-Square Test
          • Rao-Scott Likelihood Ratio Chi-Square Test
          • Wald Chi-Square Test
          • Wald Log-Linear Chi-Square Test
        • Output Data Sets
        • Displayed Output
        • ODS Table Names
        • ODS Graphics
      • Examples: SURVEYFREQ Procedure
        • Two-Way Tables
        • Multiway Tables (Domain Analysis)
        • Output Data Sets
      • References
    • The SURVEYLOGISTIC Procedure
      • Overview: SURVEYLOGISTIC Procedure
      • Getting Started: SURVEYLOGISTIC  Procedure
      • Syntax: SURVEYLOGISTIC  Procedure
        • PROC SURVEYLOGISTIC  Statement
        • BY Statement
        • CLASS Statement
        • CLUSTER Statement
        • CONTRAST Statement
        • DOMAIN Statement
        • EFFECT Statement
        • ESTIMATE Statement
        • FREQ Statement
        • LSMEANS Statement
        • LSMESTIMATE Statement
        • MODEL Statement
          • Response Variable Options
          • Model Options
        • OUTPUT Statement
          • Details of the PREDPROBS= Option
        • REPWEIGHTS Statement
        • SLICE Statement
        • STORE Statement
        • STRATA Statement
        • TEST Statement
        • UNITS Statement
        • WEIGHT Statement
      • Details: SURVEYLOGISTIC  Procedure
        • Missing Values
        • Model Specification
          • Response Level Ordering
          • CLASS Variable Parameterization
          • Link Functions and the Corresponding Distributions
        • Model Fitting
          • Determining Observations for Likelihood Contributions
          • Iterative Algorithms for Model Fitting
          • Iteratively Reweighted Least Squares Algorithm (Fisher Scoring)
          • Newton-Raphson Algorithm
          • Convergence Criteria
          • Existence of Maximum Likelihood Estimates
          • Model Fitting Statistics
          • Generalized Coefficient of Determination
          • INEST= Data Set
        • Survey Design Information
          • Specification of Population Totals and Sampling Rates
          • Primary Sampling Units (PSUs)
        • Logistic Regression Models and Parameters
          • Notation
          • Logistic Regression Models
          • Cumulative Logit Model
          • Complementary Log-Log Model
          • Probit Model
          • Generalized Logit Model
          • Likelihood Function
        • Variance Estimation
          • Taylor Series (Linearization)
          • Adjustments to the Variance Estimation
          • Balanced Repeated Replication (BRR) Method
          • Fay’s BRR Method
          • Jackknife Method
          • Hadamard Matrix
        • Domain Analysis
        • Hypothesis Testing and Estimation
          • Score Statistics and Tests
          • Testing the Parallel Lines Assumption
          • Wald Confidence Intervals for Parameters
          • Testing Linear Hypotheses about the Regression Coefficients
          • Odds Ratio Estimation
          • Rank Correlation of Observed Responses and Predicted Probabilities
        • Linear Predictor, Predicted Probability, and Confidence Limits
          • Cumulative Response Models
          • Generalized Logit Model
        • Output Data Sets
          • OUT= Data Set in the OUTPUT Statement
          • Replicate Weights Output Data Set
          • Jackknife Coefficients Output Data Set
        • Displayed Output
          • Model Information
          • Variance Estimation
          • Data Summary
          • Response Profile
          • Class Level Information
          • Stratum Information
          • Maximum Likelihood Iteration History
          • Score Test
          • Model Fit Statistics
          • Type III Analysis of Effects
          • Analysis of Maximum Likelihood Estimates
          • Odds Ratio Estimates
          • Association of Predicted Probabilities and Observed Responses
          • Wald Confidence Interval for Parameters
          • Wald Confidence Interval for Odds Ratios
          • Estimated Covariance Matrix
          • Linear Hypotheses Testing Results
          • Hadamard Matrix
        • ODS Table Names
        • ODS Graphics
      • Examples: SURVEYLOGISTIC  Procedure
        • Stratified Cluster Sampling
        • The Medical Expenditure Panel Survey (MEPS)
      • References
    • The SURVEYMEANS Procedure
      • Overview: SURVEYMEANS Procedure
      • Getting Started: SURVEYMEANS  Procedure
        • Simple Random Sampling
        • Stratified Sampling
        • Output Data Sets
      • Syntax: SURVEYMEANS  Procedure
        • PROC SURVEYMEANS  Statement
        • BY Statement
        • CLASS Statement
        • CLUSTER Statement
        • DOMAIN Statement
        • POSTSTRATA Statement
        • RATIO Statement
        • REPWEIGHTS Statement
        • STRATA Statement
        • VAR Statement
        • WEIGHT Statement
      • Details: SURVEYMEANS  Procedure
        • Missing Values
        • Survey Data Analysis
          • Specification of Population Totals and Sampling Rates
          • Primary Sampling Units (PSUs)
          • Domain Analysis
        • Statistical Computations
          • Definitions and Notation
          • Mean
          • Variance and Standard Error of the Mean
          • t Test for the Mean
          • Degrees of Freedom
          • Confidence Limits for the Mean
          • Coefficient of Variation
          • Proportions
          • Total
          • Variance and Standard Deviation of the Total
          • Confidence Limits for the Total
          • Ratio
          • Domain Statistics
          • Quantiles
          • Geometric Mean
          • Poststratification
        • Replication Methods for Variance Estimation
          • Balanced Repeated Replication (BRR) Method
          • Fay’s BRR Method
          • Jackknife Method
          • Hadamard Matrix
        • Computational Resources
        • Output Data Sets
          • Replicate Weights Output Data Set
          • Jackknife Coefficients Output Data Set
          • Poststratification Weights Output Data Set
          • Rectangular and Stacking Structures in an Output Data Set
        • Displayed Output
          • Data and Sample Design Summary
          • Class Level Information
          • Stratum Information
          • Variance Estimation
          • Statistics
          • Quantiles
          • Domain Analysis
          • Ratio Analysis
          • Domain Ratio Analysis
          • Hadamard Matrix
          • Geometric Means
          • Domain Geometric Means
        • ODS Table Names
      • Examples: SURVEYMEANS  Procedure
        • Stratified Cluster Sample Design
        • Domain Analysis
        • Ratio Analysis
        • Analyzing Survey Data with Missing Values
        • Variance Estimation Using Replication Methods
      • References
    • The SURVEYPHREG Procedure
      • Overview: SURVEYPHREG Procedure
      • Getting Started: SURVEYPHREG Procedure
      • Syntax: SURVEYPHREG Procedure
        • PROC SURVEYPHREG Statement
        • BY Statement
        • CLASS Statement
        • CLUSTER Statement
        • DOMAIN Statement
        • ESTIMATE Statement
        • FREQ Statement
        • LSMEANS Statement
        • LSMESTIMATE Statement
        • MODEL Statement
        • NLOPTIONS Statement
        • OUTPUT Statement
        • Programming Statements
        • REPWEIGHTS Statement
        • SLICE Statement
        • STORE Statement
        • STRATA Statement
        • TEST Statement
        • WEIGHT Statement
      • Details: SURVEYPHREG Procedure
        • Notation and Estimation
        • Failure Time Distribution
        • Time and CLASS Variables Usage
        • Partial Likelihood Function for the Cox Model
        • Specifying the Sample Design
        • Missing Values
        • Variance Estimation
          • Taylor Series Linearization
          • Balanced Repeated Replication (BRR) Method
          • Jackknife Method
          • Degrees of Freedom
          • Variance Adjustment Factors
          • Variance Ratios and Standard Error Ratios
        • Domain Analysis
        • Hypothesis Tests, Confidence Intervals, and Residuals
          • Testing the Global Null Hypothesis
          • Model Fit Statistics
          • Contrasts
          • Confidence Intervals
          • Hazard Ratios
          • Residuals
        • Output Data Sets
        • Displayed Output
        • ODS Table Names
        • ODS Graphics
      • Examples: SURVEYPHREG Procedure
        • Analysis of Clustered Data
        • Stratification, Clustering, and Unequal Weights
        • Domain Analysis
        • Variance Estimation by Using Replicate Weights
        • A Test of the Proportional Hazards Assumption by Using the Programming Statements
      • References
    • The SURVEYREG Procedure
      • Overview: SURVEYREG  Procedure
      • Getting Started: SURVEYREG  Procedure
        • Simple Random Sampling
        • Stratified Sampling
        • Output Data Sets
      • Syntax: SURVEYREG  Procedure
        • PROC SURVEYREG  Statement
        • BY Statement
        • CLASS Statement
        • CLUSTER Statement
        • CONTRAST Statement
        • DOMAIN Statement
        • EFFECT Statement
        • ESTIMATE Statement
        • LSMEANS Statement
        • LSMESTIMATE Statement
        • MODEL Statement
        • OUTPUT Statement
        • REPWEIGHTS Statement
        • SLICE Statement
        • STORE Statement
        • STRATA Statement
        • TEST Statement
        • WEIGHT Statement
      • Details: SURVEYREG  Procedure
        • Missing Values
        • Survey Design Information
          • Specification of Population Totals and Sampling Rates
          • Primary Sampling Units (PSUs)
        • Computational Details
          • Notation
          • Regression Coefficients
          • Design Effect
          • Stratum Collapse
          • Sampling Rate of the Pooled Stratum from Collapse
        • Analysis of Variance (ANOVA)
        • Multiple R-Square
        • Adjusted R-Square
        • Root Mean Square Errors
        • Variance Estimation
          • Taylor Series (Linearization)
          • Balanced Repeated Replication (BRR) Method
          • Fay’s BRR Method
          • Jackknife Method
          • Hadamard Matrix
          • Degrees of Freedom
        • Testing
          • Testing Effects
          • Contrasts
        • Domain Analysis
        • Computational Resources
        • Output Data Sets
          • OUT= Data Set Created by the OUTPUT Statement
          • Replicate Weights Output Data Set
          • Jackknife Coefficients Output Data Set
        • Displayed Output
          • Data Summary
          • Design Summary
          • Domain Summary
          • Fit Statistics
          • Variance Estimation
          • Stratum Information
          • Class Level Information
          • X’X Matrix
          • Inverse Matrix of X’X
          • ANOVA for Dependent Variable
          • Tests of Model Effects
          • Estimated Regression Coefficients
          • Covariance of Estimated Regression Coefficients
          • Coefficients of Contrast
          • Analysis of Contrasts
          • Hadamard Matrix
        • ODS Table Names
        • ODS Graphics
      • Examples: SURVEYREG  Procedure
        • Simple Random Sampling
        • Cluster Sampling
        • Regression Estimator for Simple Random Sample
        • Stratified Sampling
        • Regression Estimator for Stratified Sample
        • Stratum Collapse
        • Domain Analysis
        • Compare Domain Statistics
        • Variance Estimate Using the Jackknife Method
      • References
    • The SURVEYSELECT Procedure
      • Overview: SURVEYSELECT Procedure
      • Getting Started: SURVEYSELECT Procedure
        • Simple Random Sampling
        • Stratified Sampling
        • Stratified Sampling with Control Sorting
      • Syntax: SURVEYSELECT Procedure
        • PROC SURVEYSELECT Statement
        • CONTROL Statement
        • FREQ Statement
        • ID Statement
        • SAMPLINGUNIT | CLUSTER Statement
        • SIZE Statement
        • STRATA Statement
      • Details: SURVEYSELECT Procedure
        • Missing Values
        • Sorting by CONTROL Variables
        • Random Number Generation
        • Sample Selection Methods
          • Simple Random Sampling
          • Unrestricted Random Sampling
          • Systematic Random Sampling
          • Sequential Random Sampling
          • Bernoulli Sampling
          • Poisson Sampling
          • PPS Sampling without Replacement
          • PPS Sampling with Replacement
          • PPS Systematic Sampling
          • PPS Sequential Sampling
          • Brewer’s PPS Method
          • Murthy’s PPS Method
          • Sampford’s PPS Method
        • Sample Size Allocation
          • Proportional Allocation
          • Optimal Allocation
          • Neyman Allocation
          • Specifying the Margin of Error
        • Secondary Input Data Set
        • Sample Output Data Set
        • Allocation Output Data Set
        • Displayed Output
        • ODS Table Names
      • Examples: SURVEYSELECT Procedure
        • Replicated Sampling
        • PPS Selection of Two Units per Stratum
        • PPS (Dollar-Unit) Sampling
        • Proportional Allocation
      • References
    • The TPSPLINE Procedure
      • Overview: TPSPLINE Procedure
        • Penalized Least Squares Estimation
        • PROC TPSPLINE with Large Data Sets
      • Getting Started: TPSPLINE Procedure
      • Syntax: TPSPLINE Procedure
        • PROC TPSPLINE Statement
        • BY Statement
        • FREQ Statement
        • ID Statement
        • MODEL Statement
        • OUTPUT Statement
        • SCORE Statement
      • Details: TPSPLINE Procedure
        • Computational Formulas
        • ODS Table Names
        • ODS Graphics
      • Examples: TPSPLINE Procedure
        • Partial Spline Model Fit
        • Spline Model with Higher-Order Penalty
        • Multiple Minima of the GCV Function
        • Large Data Set Application
        • Computing a Bootstrap Confidence Interval
      • References
    • The TRANSREG Procedure
      • Overview: TRANSREG Procedure
      • Getting Started: TRANSREG Procedure
        • Fitting a Curve through a Scatter Plot
        • Main-Effects ANOVA
      • Syntax: TRANSREG Procedure
        • PROC TRANSREG Statement
        • BY Statement
        • FREQ Statement
        • ID Statement
        • MODEL Statement
        • OUTPUT Statement
        • WEIGHT Statement
      • Details: TRANSREG Procedure
        • Model Statement Usage
        • Box-Cox Transformations
        • Using Splines and Knots
        • Scoring Spline Variables
        • Linear and Nonlinear Regression Functions
        • Simultaneously Fitting Two Regression Functions
        • Penalized B-Splines
        • Smoothing Splines
        • Smoothing Splines Changes and Enhancements
        • Iteration History Changes and Enhancements
        • ANOVA Codings
        • Missing Values
        • Missing Values, UNTIE, and Hypothesis Tests
        • Controlling the Number of Iterations
        • Using the REITERATE Algorithm Option
        • Avoiding Constant Transformations
        • Constant Variables
        • Character OPSCORE Variables
        • Convergence and Degeneracies
        • Implicit and Explicit Intercepts
        • Passive Observations
        • Point Models
        • Redundancy Analysis
        • Optimal Scaling
        • OPSCORE, MONOTONE, UNTIE, and LINEAR Transformations
        • SPLINE and MSPLINE Transformations
        • Specifying the Number of Knots
        • SPLINE, BSPLINE, and PSPLINE Comparisons
        • Hypothesis Tests
        • Output Data Set
        • OUTTEST= Output Data Set
        • Computational Resources
        • Unbalanced ANOVA without CLASS Variables
        • Hypothesis Tests for Simple Univariate Models
        • Hypothesis Tests with Monotonicity Constraints
        • Hypothesis Tests with Dependent Variable Transformations
        • Hypothesis Tests with One-Way ANOVA
        • Using the DESIGN Output Option
        • Discrete Choice Experiments: DESIGN, NORESTORE, NOZERO
        • Centering
        • Displayed Output
        • ODS Table Names
        • ODS Graphics
      • Examples: TRANSREG Procedure
        • Transformation Regression of Exhaust Emissions Data
        • Box-Cox Transformations
        • Penalized B-Spline
        • Nonmetric Conjoint Analysis of Tire Data
        • Metric Conjoint Analysis of Tire Data
        • Preference Mapping of Automobile Data
      • References
    • The TREE Procedure
      • Overview: TREE Procedure
      • Getting Started: TREE Procedure
      • Syntax: TREE Procedure
        • PROC TREE Statement
        • BY Statement
        • COPY Statement
        • FREQ Statement
        • HEIGHT Statement
        • ID Statement
        • NAME Statement
        • PARENT Statement
      • Details: TREE Procedure
        • Missing Values
        • Output Data Set
        • Displayed Output
        • ODS Table Names
      • Examples: TREE Procedure
        • Mammals’ Teeth
        • Iris Data
      • References
    • The TTEST Procedure
      • Overview: TTEST Procedure
      • Getting Started: TTEST Procedure
        • One-Sample t Test
        • Comparing Group Means
      • Syntax: TTEST Procedure
        • PROC TTEST Statement
        • BY Statement
        • CLASS Statement
        • FREQ Statement
        • PAIRED Statement
        • VAR Statement
        • WEIGHT Statement
      • Details: TTEST Procedure
        • Input Data Set of Statistics
        • Missing Values
        • Computational Methods
          • Common Notation
          • Arithmetic and Geometric Means
          • Coefficient of Variation
          • One-Sample Design
          • Paired Design
          • Two-Independent-Sample Design
          • AB/BA Crossover Design
          • TOST Equivalence Test
        • Displayed Output
        • ODS Table Names
        • ODS Graphics
          • ODS Graph Names
          • Interpreting Graphs
      • Examples: TTEST Procedure
        • Using Summary Statistics to Compare Group Means
        • One-Sample Comparison with the FREQ Statement
        • Paired Comparisons
        • AB/BA Crossover Design
        • Equivalence Testing with Lognormal Data
      • References
    • The VARCLUS Procedure
      • Overview: VARCLUS Procedure
      • Getting Started: VARCLUS Procedure
      • Syntax: VARCLUS Procedure
        • PROC VARCLUS Statement
        • BY Statement
        • FREQ Statement
        • PARTIAL Statement
        • SEED Statement
        • VAR Statement
        • WEIGHT Statement
      • Details: VARCLUS Procedure
        • Missing Values
        • Using the VARCLUS procedure
        • Output Data Sets
        • Computational Resources
        • Interpreting VARCLUS Procedure Output
        • Displayed Output
        • ODS Table Names
        • ODS Graphics
      • Example: VARCLUS Procedure
        • Correlations among Physical Variables
      • References
    • The VARCOMP Procedure
      • Overview: VARCOMP Procedure
      • Getting Started: VARCOMP Procedure
        • Analyzing the Cure Rate of Rubber
      • Syntax: VARCOMP Procedure
        • PROC VARCOMP Statement
        • BY Statement
        • CLASS Statement
        • MODEL Statement
      • Details: VARCOMP Procedure
        • Missing Values
        • Fixed and Random Effects
        • Negative Variance Component Estimates
        • Computational Methods
        • Gauge Repeatability and Reproducibility Analysis
        • Confidence Limits
        • Displayed Output
        • ODS Table Names
        • Relationship to PROC MIXED
      • Examples: VARCOMP Procedure
        • Using the Four General Estimation Methods
        • Using the GRR Method
      • References
    • The VARIOGRAM Procedure
      • Overview: VARIOGRAM Procedure
        • Introduction to Spatial Prediction
      • Getting Started: VARIOGRAM Procedure
        • Preliminary Spatial Data Analysis
        • Empirical Semivariogram Computation
        • Autocorrelation Analysis
        • Theoretical Semivariogram Model Fitting
      • Syntax: VARIOGRAM Procedure
        • PROC VARIOGRAM Statement
        • BY Statement
        • COMPUTE Statement
        • COORDINATES Statement
        • DIRECTIONS Statement
        • ID Statement
        • MODEL Statement
        • PARMS Statement
        • NLOPTIONS Statement
        • STORE Statement
        • VAR Statement
      • Details: VARIOGRAM Procedure
        • Theoretical Semivariogram Models
          • Characteristics of Semivariogram Models
          • Nested Models
        • Theoretical and Computational Details of the Semivariogram
          • Stationarity
          • Ergodicity
          • Anisotropy
          • Pair Formation
          • Angle Classification
          • Distance Classification
          • Bandwidth Restriction
          • Computation of the Distribution Distance Classes
          • Semivariance Computation
          • Empirical Semivariograms and Surface Trends
        • Theoretical Semivariogram Model Fitting
          • Parameter Initialization
          • Parameter Estimates
          • Quality of Fit
          • Fitting with Matérn Forms
        • Autocorrelation Statistics
          • Autocorrelation Weights
          • Autocorrelation Statistics Types
          • Interpretation
          • The Moran Scatter Plot
        • Computational Resources
        • Output Data Sets
        • Displayed Output
        • ODS Table Names
        • ODS Graphics
      • Examples: VARIOGRAM Procedure
        • Aspects of Semivariogram Model Fitting
        • An Anisotropic Case Study with Surface Trend in the Data
          • Analysis with Surface Trend Removal
        • Analysis without Surface Trend Removal
        • Covariogram and Semivariogram
        • A Box Plot of the Square Root Difference Cloud
      • References
  • Special SAS Data Sets
    • Introduction to Special SAS Data Sets
    • Special SAS Data Sets
      • TYPE=ACE Data Sets
      • TYPE=BOXPLOT Data Sets
      • TYPE=CALISFIT Data Sets
      • TYPE=CALISMDL Data Sets
      • TYPE=CHARTSUM Data Sets
      • TYPE=CORR Data Sets
      • TYPE=COV Data Sets
      • TYPE=CSSCP Data Sets
      • TYPE=DISTANCE Data Sets
      • TYPE=EST Data Sets
      • TYPE=FACTOR Data Sets
      • TYPE=LINEAR Data Sets
      • TYPE=LOGISMOD Data Sets
      • TYPE=MIXED Data Sets
      • TYPE=QUAD Data Sets
      • TYPE=SSCP Data Sets
      • TYPE=TREE Data Sets
      • TYPE=UCORR Data Sets
      • TYPE=UCOV Data Sets
      • TYPE=WEIGHT Data Sets
    • Definitional Formulas
  • Sashelp Data Sets
    • Overview of Sashelp Data Sets
    • Bone Marrow Transplant Data
    • Class Data
    • El Niño Southern Oscillation Data
    • Finland’s Lake Laengelmavesi Fish Catch Data
    • Exhaust Emissions Data
    • Fisher (1936) Iris Data
    • Coal Seam Thickness Data
    • Flying Mileages between Five U.S. Cities Data
    • References


  • General
    • What's New in SAS/STAT 12.1
    • Shared Concepts and Topics
    • Using the Output Delivery System
    • Statistical Graphics Using ODS
    • Special SAS Data Sets
    • Sashelp Data Sets
  • Analysis of Variance
    • Introduction to Analysis of Variance Procedures
    • The Four Types of Estimable Functions
    • The ANOVA Procedure
    • The CATMOD Procedure
    • The GENMOD Procedure
    • The GLIMMIX Procedure
    • The GLM Procedure
    • The GLMMOD Procedure
    • The GLMSELECT Procedure
    • The INBREED Procedure
    • The LATTICE Procedure
    • The MIXED Procedure
    • The NESTED Procedure
    • The NPAR1WAY Procedure
    • The PLAN Procedure
    • The PLM Procedure
    • The TRANSREG Procedure
    • The TTEST Procedure
    • The VARCOMP Procedure
  • Bayesian
    • Introduction to Bayesian Analysis Procedures
    • The FMM Procedure
    • The GENMOD Procedure
    • The LIFEREG Procedure
    • The MCMC Procedure
    • The PHREG Procedure
  • Categorical Analysis
    • Introduction to Categorical Data Analysis Procedures
    • The CATMOD Procedure
    • The CORRESP Procedure
    • The FMM Procedure
    • The FREQ Procedure
    • The GAM Procedure
    • The GENMOD Procedure
    • The GLIMMIX Procedure
    • The LOGISTIC Procedure
    • The PRINQUAL Procedure
    • The PROBIT Procedure
    • The SURVEYFREQ Procedure
    • The SURVEYLOGISTIC Procedure
    • The TRANSREG Procedure
  • Cluster Analysis
    • Introduction to Clustering Procedures
    • The ACECLUS Procedure
    • The CLUSTER Procedure
    • The FASTCLUS Procedure
    • The MODECLUS Procedure
    • The TREE Procedure
    • The VARCLUS Procedure
  • Descriptive Statistics
    • The BOXPLOT Procedure
    • The STDRATE Procedure
    • The SURVEYMEANS Procedure
  • Discriminant Analysis
    • Introduction to Discriminant Procedures
    • The CANDISC Procedure
    • The DISCRIM Procedure
    • The STEPDISC Procedure
  • Distribution Analysis
    • The KDE Procedure
  • Exact Methods
    • The FREQ Procedure
    • The LOGISTIC Procedure
    • The MULTTEST Procedure
    • The NPAR1WAY Procedure
  • Group Sequential Design and Analysis
    • The SEQDESIGN Procedure
    • The SEQTEST Procedure
  • Longitudinal Analysis
    • The ANOVA Procedure
    • The CATMOD Procedure
    • The FREQ Procedure
    • The GENMOD Procedure
    • The GLIMMIX Procedure
    • The GLM Procedure
    • The MIXED Procedure
  • Market Research
    • The CORRESP Procedure
    • The MDS Procedure
    • The PHREG Procedure
    • The PRINQUAL Procedure
    • The TRANSREG Procedure
  • Missing Value Imputation
    • The MI Procedure
    • The MIANALYZE Procedure
  • Mixed Models
    • Introduction to Mixed Modeling Procedures
    • The GLIMMIX Procedure
    • The HPMIXED Procedure
    • The MIXED Procedure
    • The NLMIXED Procedure
  • Multivariate Analysis
    • Introduction to Multivariate Procedures
    • The CALIS Procedure
    • The CANCORR Procedure
    • The CORRESP Procedure
    • The FACTOR Procedure
    • The MDS Procedure
    • The MULTTEST Procedure
    • The PLS Procedure
    • The PRINCOMP Procedure
    • The PRINQUAL Procedure
    • The TRANSREG Procedure
    • The TREE Procedure
  • Nonparametric Analysis
    • Introduction to Nonparametric Analysis
    • The FREQ Procedure
    • The GAM Procedure
    • The KDE Procedure
    • The LOESS Procedure
    • The NPAR1WAY Procedure
    • The TPSPLINE Procedure
  • Power and Sample Size
    • Introduction to Power and Sample Size Analysis
    • The GLMPOWER Procedure
    • The POWER Procedure
    • The Power and Sample Size Application
  • Psychometrics
    • The CORRESP Procedure
    • The FACTOR Procedure
    • The MDS Procedure
    • The PRINCOMP Procedure
    • The TRANSREG Procedure
  • Regression
    • Introduction to Statistical Modeling with SAS/STAT Software
    • Introduction to Regression Procedures
    • The ADAPTIVEREG Procedure
    • The CATMOD Procedure
    • The FMM Procedure
    • The GAM Procedure
    • The GENMOD Procedure
    • The GLIMMIX Procedure
    • The GLM Procedure
    • The GLMSELECT Procedure
    • The LIFEREG Procedure
    • The LOESS Procedure
    • The LOGISTIC Procedure
    • The MIXED Procedure
    • The NLIN Procedure
    • The NLMIXED Procedure
    • The ORTHOREG Procedure
    • The PHREG Procedure
    • The PLM Procedure
    • The PLS Procedure
    • The PROBIT Procedure
    • The QUANTLIFE Procedure
    • The QUANTREG Procedure
    • The QUANTSELECT Procedure
    • The REG Procedure
    • The ROBUSTREG Procedure
    • The RSREG Procedure
    • The SURVEYLOGISTIC Procedure
    • The SURVEYREG Procedure
    • The TPSPLINE Procedure
    • The TRANSREG Procedure
  • Spatial Analysis
    • The GLIMMIX Procedure
    • The KRIGE2D Procedure
    • The MIXED Procedure
    • The SIM2D Procedure
    • The VARIOGRAM Procedure
  • Statistical Graphics
    • Statistical Graphics Using ODS
    • ODS Graphics Template Modification
  • Structural Equations
    • Introduction to Structural Equation Modeling with Latent Variables
    • The CALIS Procedure
  • Survey Sampling and Analysis
    • Introduction to Survey Procedures
    • The SURVEYFREQ Procedure
    • The SURVEYLOGISTIC Procedure
    • The SURVEYMEANS Procedure
    • The SURVEYPHREG Procedure
    • The SURVEYREG Procedure
    • The SURVEYSELECT Procedure
  • Survival Analysis
    • Introduction to Survival Analysis Procedures
    • The LIFEREG Procedure
    • The LIFETEST Procedure
    • The PHREG Procedure
    • The QUANTLIFE Procedure
    • The SURVEYPHREG Procedure
  • Transformations
    • Introduction to Scoring, Standardization, and Ranking Procedures
    • The DISTANCE Procedure
    • The SCORE Procedure
    • The SIMNORMAL Procedure
    • The STDIZE Procedure
    • The TRANSREG Procedure


ProductRelease
SAS/STAT12.1
Type
Usage and Reference
Copyright Date
August 2012
Last Updated
17Sep2012