• Contents
  • Topics
  • About
  • Acknowledgments
    • Credits
      • Documentation
      • Software
      • Testing
      • Technical Support
    • Acknowledgments
  • What’s New in SAS/STAT 12.1 and 12.3
    • 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
  • Introduction
    • 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
  • 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
    • 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
  • 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 (beta) Boundary
      • Boundary Adjustments for Overlapping Lower and Upper beta 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 beta Boundaries
      • Creating a Two-Sided Asymmetric Error Spending Design with Early Stopping to Reject H0
      • Creating a Two-Sided Asymmetric Error Spending Design with Early Stopping to Reject or Accept H0
      • 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 beta 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 H0
      • 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 Nino Southern Oscillation Data
    • Finland’s Lake Laengelmavesi Fish Catch Data
    • Exhaust Emissions Data
    • Fisher Iris Data
    • Coal Seam Thickness Data
    • Flying Mileages between Five U.S. Cities Data
    • References


  • General
    • What's New in SAS/STAT 12.1 and 12.3
    • 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/STAT12.3
Type
Usage and Reference
Copyright Date
July 2013
Last Updated
11Jul2013