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SAS/STAT 14.1 User's Guide

Examples from Documentation

Select a procedure PROC ACECLUS PROC ADAPTIVEREG PROC ANOVA PROC BCHOICE PROC BOXPLOT PROC CALIS PROC CANCORR PROC CANDISC PROC CATMOD PROC CLUSTER PROC CORR PROC CORRESP PROC DISCRIM PROC DISTANCE PROC FACTOR PROC FASTCLUS PROC FMM PROC FREQ PROC GAM PROC GAMPL PROC GEE PROC GENMOD PROC GLIMMIX PROC GLM PROC GLMMOD PROC GLMPOWER PROC GLMSELECT PROC HPCANDISC PROC HPFMM PROC HPGENSELECT PROC HPLMIXED PROC HPLOGISTIC PROC HPMIXED PROC HPNLMOD PROC HPPLS PROC HPPRINCOMP PROC HPQUANTSELECT PROC HPREG PROC HPSPLIT PROC ICLIFETEST PROC ICPHREG PROC INBREED PROC IRT PROC KDE PROC KRIGE2D PROC LATTICE PROC LIFEREG PROC LIFETEST PROC LOESS PROC LOGISTIC PROC MCMC PROC MDS PROC MI PROC MIANALYZE PROC MIXED PROC MODECLUS PROC MULTTEST PROC NESTED PROC NLIN PROC NLMIXED PROC NPAR1WAY PROC ORTHOREG PROC PHREG PROC PLAN PROC PLM PROC PLS PROC POWER PROC PRINCOMP PROC PRINQUAL PROC PROBIT PROC QUANTLIFE PROC QUANTREG PROC QUANTSELECT PROC REG PROC ROBUSTREG PROC RSREG PROC SCORE PROC SEQDESIGN PROC SEQTEST PROC SIM2D PROC SIMNORMAL PROC SPP PROC STDRATE PROC STEPDISC PROC SURVEYFREQ PROC SURVEYIMPUTE PROC SURVEYLOGISTIC PROC SURVEYMEANS PROC SURVEYPHREG PROC SURVEYREG PROC SURVEYSELECT PROC TCALIS PROC TPSPLINE PROC TRANSREG PROC TREE PROC TTEST PROC UNIVARIATE PROC VARCLUS PROC VARCOMP PROC VARIOGRAM

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ACECLUS Procedure

• Getting Started: ACECLUS Procedure

• Example 24.1: Transformation and Cluster Analysis of Fisher Iris Data

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ADAPTIVEREG Procedure

• Getting Started: ADAPTIVEREG Procedure

• Example 25.1: Surface Fitting with Many Noisy Variables
• Example 25.2: Fitting Data with Mixture Structures
• Example 25.3: Predicting E-Mail Spam
• Example 25.4: Nonparametric Poisson Model for Mackerel Egg Density

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ANOVA Procedure

• One-Way Layout with Means Comparisons
• Randomized Complete Block with One Factor

• Example 26.1: Randomized Complete Block With Factorial Treatment Structure
• Example 26.2: Alternative Multiple Comparison Procedures
• Example 26.3: Split Plot
• Example 26.4: Latin Square Split Plot
• Example 26.5: Strip-Split Plot

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BCHOICE Procedure

• A Simple Logit Model
• A Logit Model with Random Effects

• Example 27.1: Alternative-Specific and Individual-Specific Effects
• Example 27.2: Nested Logit Modeling
• Example 27.3: Probit Modeling
• Example 27.4: A Random-Effects-Only Logit Model
• Example 27.5: Heterogeneity Affected by Individual Characteristics
• Example 27.6: Inference on Quantities of Interest
• Example 27.7: Predict the Choice Probabilities

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BOXPLOT Procedure

• Creating Box Plots from Raw Data
• Creating Box Plots from Summary Data
• Saving Summary Data with Outliers

• Example 28.1: Displaying Summary Statistics in a Box Plot
• Example 28.2: Using Box Plots to Compare Groups
• Example 28.3: Creating Various Styles of Box-and-Whiskers Plots
• Example 28.4: Creating Notched Box-and-Whiskers Plots
• Example 28.5: Creating Box-and-Whiskers Plots with Varying Widths
• Example 28.6: Creating Horizontal Box-and-Whiskers Plots

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CALIS Procedure

• A Structural Equation Example
• A Factor Model Example
• Direct Covariance Structures Analysis
• Which Modeling Language?

• Example 29.1: Estimating Covariances and Correlations
• Example 29.2: Estimating Covariances and Means Simultaneously
• Example 29.3: Testing Uncorrelatedness of Variables
• Example 29.4: Testing Covariance Patterns
• Example 29.5: Testing Some Standard Covariance Pattern Hypotheses
• Example 29.6: Linear Regression Model
• Example 29.7: Multivariate Regression Models
• Example 29.8: Measurement Error Models
• Example 29.9: Testing Specific Measurement Error Models
• Example 29.10: Measurement Error Models with Multiple Predictors
• Example 29.11: Measurement Error Models Specified As Linear Equations
• Example 29.12: Confirmatory Factor Models
• Example 29.13: Confirmatory Factor Models: Some Variations
• Example 29.14: Residual Diagnostics and Robust Estimation
• Example 29.15: The Full Information Maximum Likelihood Method
• Example 29.16: Comparing the ML and FIML Estimation
• Example 29.17: Path Analysis: Stability of Alienation
• Example 29.18: Simultaneous Equations with Mean Structures and Reciprocal Paths
• Example 29.19: Fitting Direct Covariance Structures
• Example 29.20: Confirmatory Factor Analysis: Cognitive Abilities
• Example 29.21: Testing Equality of Two Covariance Matrices Using a Multiple-Group Analysis
• Example 29.22: Testing Equality of Covariance and Mean Matrices between Independent Groups
• Example 29.23: Illustrating Various General Modeling Languages
• Example 29.24: Testing Competing Path Models for the Career Aspiration Data
• Example 29.25: Fitting a Latent Growth Curve Model
• Example 29.26: Higher-Order and Hierarchical Factor Models
• Example 29.27: Linear Relations among Factor Loadings
• Example 29.28: Multiple-Group Model for Purchasing Behavior
• Example 29.29: Fitting the RAM and EQS Models by the COSAN Modeling Language
• Example 29.30: Second-Order Confirmatory Factor Analysis
• Example 29.31: Linear Relations among Factor Loadings: COSAN Model Specification
• Example 29.32: Ordinal Relations among Factor Loadings
• Example 29.33: Longitudinal Factor Analysis

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CANCORR Procedure

• Getting Started: CANCORR Procedure

• Example 30.1: Canonical Correlation Analysis of Fitness Club Data

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CANDISC Procedure

• Getting Started: CANDISC Procedure

• Example 31.1: Analyzing Iris Data by Using PROC CANDISC

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The CATMOD Procedure

• Weighted Least Squares Analysis of Mean Response
• Generalized Logits Model

• Example 32.1: Linear Response Function, r=2 Responses
• Example 32.2: Mean Score Response Function, r=3 Responses
• Example 32.3: Logistic Regression, Standard Response Function
• Example 32.4: Log-Linear Model, Three Dependent Variables
• Example 32.5: Log-Linear Model, Structural and Sampling Zeros
• Example 32.6: Repeated Measures, 2 Response Levels, 3 Populations
• Example 32.7: Repeated Measures, 4 Response Levels, 1 Population
• Example 32.8: Repeated Measures, Logistic Analysis of Growth Curve
• Example 32.9: Repeated Measures, Two Repeated Measurement Factors
• Example 32.10: Direct Input of Response Functions and Covariance Matrix
• Example 32.11: Predicted Probabilities

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CLUSTER Procedure

• Getting Started: CLUSTER Procedure

• Example 33.1: Cluster Analysis of Flying Mileages between 10 American Cities
• Example 33.2: Crude Birth and Death Rates
• Example 33.3: Cluster Analysis of Fisher’s Iris Data
• Example 33.4: Evaluating the Effects of Ties

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CORR Procedure

• Getting Started: CORR Procedure

• Example 2.1: Computing Four Measures of Association
• Example 2.2: Computing Correlations between Two Sets of Variables
• Example 2.3: Analysis Using Fisher’s
• Example 2.4: Applications of Fisher’s
• Example 2.5: Computing Polyserial Correlations
• Example 2.6: Computing Cronbach’s Coefficient Alpha
• Example 2.7: Saving Correlations in an Output Data Set
• Example 2.8: Creating Scatter Plots
• Example 2.9: Computing Partial Correlations

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CORRESP Procedure

• Getting Started: CORRESP Procedure

• Example 34.1: Simple and Multiple Correspondence Analysis of Automobiles and Their Owners
• Example 34.2: Simple Correspondence Analysis of U.S. Population

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DISCRIM Procedure

• Getting Started: DISCRIM Procedure

• Example 35.1: Univariate Density Estimates and Posterior Probabilities
• Example 35.2: Bivariate Density Estimates and Posterior Probabilities
• Example 35.3: Normal-Theory Discriminant Analysis of Iris Data
• Example 35.4: Linear Discriminant Analysis of Remote-Sensing Data on Crops

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DISTANCE Procedure

• Creating a Distance Matrix as Input for a Subsequent Cluster Analysis

• Example 36.1: Divorce Grounds – the Jaccard Coefficient
• Example 36.2: Financial Data – Stock Dividends

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FACTOR Procedure

• Getting Started: FACTOR Procedure

• Example 37.1: Principal Component Analysis
• Example 37.2: Principal Factor Analysis
• Example 37.3: Maximum Likelihood Factor Analysis
• Example 37.4: Using Confidence Intervals to Locate Salient Factor Loadings
• Example 37.5: Creating Path Diagrams for Factor Solutions

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FASTCLUS Procedure

• Getting Started: FASTCLUS Procedure

• Example 38.1: Fisher’s Iris Data
• Example 38.2: Outliers

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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?

• Example 39.1: Modeling Mixing Probabilities: All Mice Are Created Equal, but Some Are More Equal
• Example 39.2: The Usefulness of Custom Starting Values: When Do Cows Eat?
• Example 39.3: Enforcing Homogeneity Constraints: Count and Dispersion—It Is All Over!
• Example 39.4: Modeling Multinomial Overdispersion: Town and Country

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FREQ Procedure

• Frequency Tables and Statistics
• Agreement Study

• Example 3.1: Output Data Set of Frequencies
• Example 3.2: Frequency Dot Plots
• Example 3.3: Chi-Square Goodness-of-Fit Tests
• Example 3.4: Binomial Proportions
• Example 3.5: Analysis of a 2x2 Contingency Table
• Example 3.6: Output Data Set of Chi-Square Statistics
• Example 3.7: Cochran-Mantel-Haenszel Statistics
• Example 3.8: Cochran-Armitage Trend Test
• Example 3.9: Friedman’s Chi-Square Test
• Example 3.10: Cochran’s Q Test

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GAM Procedure

• Getting Started: GAM Procedure

• Example 41.1: Generalized Additive Model with Binary Data
• Example 41.2: Poisson Regression Analysis of Component Reliability
• Example 41.3: Comparing PROC GAM with PROC LOESS

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GAMPL Procedure

• Getting Started: GAMPL Procedure

• Example 7.1: Scatter Plot Smoothing
• Example 7.2: Nonparametric Logistic Regression
• Example 7.3: Nonparametric Negative Binomial Model for Mackerel Egg Density

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GEE Procedure

• Example 43.1: Comparison of the Marginal and Random Effect Models for Binary Data
• Example 43.2: Log-Linear Model for Count Data
• Example 43.3: Weighted GEE for Longitudinal Data That Have Missing Values
• Example 43.4: GEE for Binary Data with Logit Link Function
• Example 43.5: Alternating Logistic Regression for Ordinal Multinomial Data
• Example 43.6: GEE for Nominal Multinomial Data

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GENMOD Procedure

• Poisson Regression
• Bayesian Analysis of a Linear Regression Model
• Generalized Estimating Equations

• Example 44.1: Logistic Regression
• Example 44.2: Normal Regression, Log Link
• Example 44.3: Gamma Distribution Applied to Life Data
• Example 44.4: Ordinal Model for Multinomial Data
• Example 44.5: GEE for Binary Data with Logit Link Function
• Example 44.6: Log Odds Ratios and the ALR Algorithm
• Example 44.7: Log-Linear Model for Count Data
• Example 44.8: Model Assessment of Multiple Regression Using Aggregates of Residuals
• Example 44.9: Assessment of a Marginal Model for Dependent Data
• Example 44.10: Bayesian Analysis of a Poisson Regression Model
• Example 44.11: Exact Poisson Regression
• Example 44.12: Tweedie Regression

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GLIMMIX Procedure

• Logistic Regressions with Random Intercepts

• Example 45.1: Binomial Counts in Randomized Blocks
• Example 45.2: Mating Experiment with Crossed Random Effects
• Example 45.3: Smoothing Disease Rates; Standardized Mortality Ratios
• Example 45.4: Quasi-likelihood Estimation for Proportions with Unknown Distribution
• Example 45.5: Joint Modeling of Binary and Count Data
• Example 45.6: Radial Smoothing of Repeated Measures Data
• Example 45.7: Isotonic Contrasts for Ordered Alternatives
• Example 45.8: Adjusted Covariance Matrices of Fixed Effects
• Example 45.9: Testing Equality of Covariance and Correlation Matrices
• Example 45.10: Multiple Trends Correspond to Multiple Extrema in Profile Likelihoods
• Example 45.11: Maximum Likelihood in Proportional Odds Model with Random Effects
• Example 45.12: Fitting a Marginal (GEE-Type) Model
• Example 45.13: Response Surface Comparisons with Multiplicity Adjustments
• Example 45.14: Generalized Poisson Mixed Model for Overdispersed Count Data
• Example 45.15: Comparing Multiple B-Splines
• Example 45.16: Diallel Experiment with Multimember Random Effects
• Example 45.17: Linear Inference Based on Summary Data
• Example 45.18: Weighted Multilevel Model for Survey Data
• Example 45.19: Quadrature Method for Multilevel Model

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GLM Procedure

• PROC GLM for Unbalanced ANOVA
• PROC GLM for Quadratic Least Squares Regression

• Example 46.1: Randomized Complete Blocks with Means Comparisons and Contrasts
• Example 46.2: Regression with Mileage Data
• Example 46.3: Unbalanced ANOVA for Two-Way Design with Interaction
• Example 46.4: Analysis of Covariance
• Example 46.5: Three-Way Analysis of Variance with Contrasts
• Example 46.6: Multivariate Analysis of Variance
• Example 46.7: Repeated Measures Analysis of Variance
• Example 46.8: Mixed Model Analysis of Variance with the RANDOM Statement
• Example 46.9: Analyzing a Doubly Multivariate Repeated Measures Design
• Example 46.10: Testing for Equal Group Variances
• Example 46.11: Analysis of a Screening Design

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GLMMOD Procedure

• A One-Way Design

• Example 47.1: A Two-Way Design
• Example 47.2: Factorial Screening

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GLMPOWER Procedure

• Simple Two-Way ANOVA
• Incorporating Contrasts, Unbalanced Designs, and Multiple Means Scenarios

• Example 48.1: One-Way ANOVA
• Example 48.2: Two-Way ANOVA with Covariate
• Example 48.3: Repeated Measures ANOVA

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GLMSELECT Procedure

• Getting Started: GLMSELECT Procedure

• Example 49.1: Modeling Baseball Salaries Using Performance Statistics
• Example 49.2: Using Validation and Cross Validation
• Example 49.3: Scatter Plot Smoothing by Selecting Spline Functions
• Example 49.4: Multimember Effects and the Design Matrix
• Example 49.5: Model Averaging
• Example 49.6: Elastic Net and External Cross Validation
• Example 49.7: LASSO with Screening
• Example 49.8: Group LASSO Selection

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HPCANDISC Procedure

• Getting Started: HPCANDISC Procedure

• Example 5.1: Analyzing Iris Data with PROC HPCANDISC
• Example 5.2: Performing Canonical Discriminant Analysis in Single-Machine and Distributed Modes

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HPFMM 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?

• Example 6.1: Modeling Mixing Probabilities: All Mice Are Created Equal, but Some Are More Equal
• Example 6.2: The Usefulness of Custom Starting Values: When Do Cows Eat?
• Example 6.3: Enforcing Homogeneity Constraints: Count and Dispersion—It Is All Over!

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HPGENSELECT Procedure

• Getting Started: HPGENSELECT Procedure

• Example 8.1: Model Selection
• Example 8.2: Modeling Binomial Data
• Example 8.3: Tweedie Model
• Example 8.4: Model Selection by the LASSO Method

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HPLMIXED Procedure

• Mixed Model Analysis of Covariance with Many Groups

• Example 9.1: Computing BLUPs for a Large Number of Subjects

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HPLOGISTIC Procedure

• Binary Logistic Regression

• Example 10.1: Model Selection
• Example 10.2: Modeling Binomial Data
• Example 10.3: Ordinal Logistic Regression
• Example 10.4: Partitioning Data

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HPMIXED Procedure

• Mixed Model with Large Number of Fixed and Random Effects

• Example 55.1: Ranking Many Random-Effect Coefficients
• Example 55.2: Comparing Results from PROC HPMIXED and PROC MIXED
• Example 55.3: Using PROC GLIMMIX for Further Analysis of PROC HPMIXED Fit
• Example 55.4: Mixed Model Analysis of Microarray Data
• Example 55.5: Repeated Measures

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HPNLMOD Procedure

• Least Squares Model
• Binomial Model

• Example 11.1: Segmented Model

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HPPLS Procedure

• Spectrometric Calibration

• Example 12.1: Choosing a PLS Model by Test Set Validation
• Example 12.2: Fitting a PLS Model in Single-Machine and Distributed Modes

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HPPRINCOMP Procedure

• Getting Started: HPPRINCOMP Procedure

• Example 13.1: Analyzing Mean Temperatures of US Cities
• Example 13.2: Computing Principal Components in Single-Machine and Distributed Modes
• Example 13.3: Extracting Principal Components with NIPALS

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HPQUANTSELECT Procedure

• Getting Started: HPQUANTSELECT Procedure

• Example 14.1: Simulation Study
• Example 14.2: Growth Charts for Body Mass Index

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HPREG Procedure

• Getting Started: HPREG Procedure

• Example 15.1: Model Selection with Validation
• Example 15.2: Backward Selection in Single-Machine and Distributed Modes
• Example 15.3: Forward-Swap Selection
• Example 15.4: Forward Selection with Screening

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HPSPLIT Procedure

• Getting Started: HPSPLIT Procedure

• Example 16.1: Building a Classification Tree for a Binary Outcome
• Example 16.2: Cost-Complexity Pruning with Cross Validation
• Example 16.3: Creating a Regression Tree
• Example 16.4: Creating a Binary Classification Tree with Validation Data
• Example 16.5: Assessing Variable Importance
• Example 16.6: Applying Breiman’s 1-SE Rule with Misclassification Rate

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ICLIFETEST Procedure

• Getting Started: ICLIFETEST Procedure

• Example 62.1: Analyzing Data with Observations below a Limit of Detection
• Example 62.2: Controlling the Plotting of Survival Estimates
• Example 62.3: Plotting Kernel-Smoothed Hazard Functions
• Example 62.4: Outputting Scores for Permutation Tests

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ICPHREG Procedure

• Getting Started: ICPHREG Procedure

• Example 63.1: Fitting Cubic Spline Models
• Example 63.2: Plotting Predicted Survival and Cumulative Hazard Functions
• Example 63.3: Fitting Stratified Weibull Models

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INBREED Procedure

• The Format of the Input Data Set
• Performing the Analysis

• Example 64.1: Monoecious Population Analysis
• Example 64.2: Pedigree Analysis
• Example 64.3: Pedigree Analysis with BY Groups

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IRT Procedure

• Getting Started: IRT Procedure

• Example 65.1: Unidimensional IRT Models
• Example 65.2: Multidimensional Exploratory and Confirmatory IRT Models
• Example 65.3: Multiple-Group Analysis
• Example 65.4: Item Selection Using Item and Test Information
• Example 65.5: Subject Scoring

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KDE Procedure

• Getting Started: KDE Procedure

• Example 66.1: Computing a Basic Kernel Density Estimate
• Example 66.2: Changing the Bandwidth
• Example 66.3: Changing the Bandwidth (Bivariate)
• Example 66.4: Requesting Additional Output Tables
• Example 66.5: Univariate KDE Graphics
• Example 66.6: Bivariate KDE Graphics

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KRIGE2D Procedure

• Spatial Prediction Using Kriging, Contour Plots

• Example 67.1: Spatial Prediction of Pollutant Concentration
• Example 67.2: Investigating the Effect of Model Specification on Spatial Prediction
• Example 67.3: Data Quality and Prediction with Missing Values

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LATTICE Procedure

• Getting Started: LATTICE Procedure

• Example 68.1: Analysis of Variance through PROC LATTICE

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LIFEREG Procedure

• Modeling Right-Censored Failure Time Data
• Bayesian Analysis of Right-Censored Data

• Example 69.1: Motorette Failure
• Example 69.2: Computing Predicted Values for a Tobit Model
• Example 69.3: Overcoming Convergence Problems by Specifying Initial Values
• Example 69.4: Analysis of Arbitrarily Censored Data with Interaction Effects
• Example 69.5: Probability Plotting—Right Censoring
• Example 69.6: Probability Plotting—Arbitrary Censoring
• Example 69.7: Bayesian Analysis of Clinical Trial Data
• Example 69.8: Model Postfitting Analysis

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LIFETEST Procedure

• Getting Started: LIFETEST Procedure

• Example 70.1: Product-Limit Estimates and Tests of Association
• Example 70.2: Enhanced Survival Plot and Multiple-Comparison Adjustments
• Example 70.3: Life-Table Estimates for Males with Angina Pectoris
• Example 70.4: Nonparametric Analysis of Competing-Risks Data

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LOESS Procedure

• Scatter Plot Smoothing

• Example 71.1: Engine Exhaust Emissions
• Example 71.2: Sulfate Deposits in the U.S. for 1990
• Example 71.3: Catalyst Experiment
• Example 71.4: El Niño Southern Oscillation

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LOGISTIC Procedure

• Getting Started: LOGISTIC Procedure

• Example 72.1: Stepwise Logistic Regression and Predicted Values
• Example 72.2: Logistic Modeling with Categorical Predictors
• Example 72.3: Ordinal Logistic Regression
• Example 72.4: Nominal Response Data: Generalized Logits Model
• Example 72.5: Stratified Sampling
• Example 72.6: Logistic Regression Diagnostics
• Example 72.7: ROC Curve, Customized Odds Ratios, Goodness-of-Fit Statistics, R-Square, and Confidence Limits
• Example 72.8: Comparing Receiver Operating Characteristic Curves
• Example 72.9: Goodness-of-Fit Tests and Subpopulations
• Example 72.10: Overdispersion
• Example 72.11: Conditional Logistic Regression for Matched Pairs Data
• Example 72.12: Exact Conditional Logistic Regression
• Example 72.13: Firth’s Penalized Likelihood Compared with Other Approaches
• Example 72.14: Complementary Log-Log Model for Infection Rates
• Example 72.15: Complementary Log-Log Model for Interval-Censored Survival Times
• Example 72.16: Scoring Data Sets
• Example 72.17: Using the LSMEANS Statement
• Example 72.18: Partial Proportional Odds Model

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MCMC Procedure

• Simple Linear Regression
• The Behrens-Fisher Problem
• Random-Effects Model

• Example 73.1: Simulating Samples From a Known Density
• Example 73.2: Box-Cox Transformation
• Example 73.3: Logistic Regression Model with a Diffuse Prior
• Example 73.4: Logistic Regression Model with Jeffreys’ Prior
• Example 73.5: Poisson Regression
• Example 73.6: Nonlinear Poisson Regression Models
• Example 73.7: Logistic Regression Random-Effects Model
• Example 73.8: Nonlinear Poisson Regression Multilevel Random-Effects Model
• Example 73.9: Multivariate Normal Random-Effects Model
• Example 73.10: Missing at Random Analysis
• Example 73.11: Nonignorably Missing Data (MNAR) Analysis
• Example 73.12: Change Point Models
• Example 73.13: Exponential and Weibull Survival Analysis
• Example 73.14: Time Independent Cox Model
• Example 73.15: Time Dependent Cox Model
• Example 73.16: Piecewise Exponential Frailty Model
• Example 73.17: Normal Regression with Interval Censoring
• Example 73.18: Constrained Analysis
• Example 73.19: Implement a New Sampling Algorithm
• Example 73.20: Using a Transformation to Improve Mixing
• Example 73.21: Gelman-Rubin Diagnostics
• Example 73.22: One-Compartment Model with Pharmacokinetic Data

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MDS Procedure

• Getting Started: MDS Procedure

• Example 74.1: Jacobowitz Body Parts Data from Children and Adults

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MI Procedure

• Getting Started: MI Procedure

• Example 75.1: EM Algorithm for MLE
• Example 75.2: Monotone Propensity Score Method
• Example 75.3: Monotone Regression Method
• Example 75.4: Monotone Logistic Regression Method for CLASS Variables
• Example 75.5: Monotone Discriminant Function Method for CLASS Variables
• Example 75.6: FCS Methods for Continuous Variables
• Example 75.7: FCS Method for CLASS Variables
• Example 75.8: FCS Method with Trace Plot
• Example 75.9: MCMC Method
• Example 75.10: Producing Monotone Missingness with MCMC
• Example 75.11: Checking Convergence in MCMC
• Example 75.12: Saving and Using Parameters for MCMC
• Example 75.13: Transforming to Normality
• Example 75.14: Multistage Imputation
• Example 75.15: Creating Control-Based Pattern Imputation in Sensitivity Analysis
• Example 75.16: Adjusting Imputed Continuous Values in Sensitivity Analysis
• Example 75.17: Adjusting Imputed Classification Levels in Sensitivity Analysis
• Example 75.18: Adjusting Imputed Values with Parameters in a Data Set

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MIANALYZE Procedure

• Getting Started: MIANALYZE Procedure

• Example 76.1: Reading Means and Standard Errors from a DATA= Data Set
• Example 76.2: Reading Means and Covariance Matrices from a DATA= COV Data Set
• Example 76.3: Reading Regression Results from a DATA= EST Data Set
• Example 76.4: Reading Mixed Model Results from PARMS= and COVB= Data Sets
• Example 76.5: Reading Generalized Linear Model Results
• Example 76.6: Reading GLM Results from PARMS= and XPXI= Data Sets
• Example 76.7: Reading Logistic Model Results from a PARMS= Data Set
• Example 76.8: Reading Mixed Model Results with Classification Covariates
• Example 76.9: Reading Nominal Logistic Model Results
• Example 76.10: Using a TEST statement
• Example 76.11: Combining Correlation Coefficients
• Example 76.12: Sensitivity Analysis with Control-Based Pattern Imputation
• Example 76.13: Sensitivity Analysis with the Tipping-Point Approach

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MIXED Procedure

• Clustered Data Example

• Example 77.1: Split-Plot Design
• Example 77.2: Repeated Measures
• Example 77.3: Plotting the Likelihood
• Example 77.4: Known G and R
• Example 77.5: Random Coefficients
• Example 77.6: Line-Source Sprinkler Irrigation
• Example 77.7: Influence in Heterogeneous Variance Model
• Example 77.8: Influence Analysis for Repeated Measures Data
• Example 77.9: Examining Individual Test Components
• Example 77.10: Isotonic Contrasts for Ordered Mean Values

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MODECLUS Procedure

• Getting Started: MODECLUS Procedure

• Example 78.1: Cluster Analysis of Samples from Univariate Distributions
• Example 78.2: Cluster Analysis of Flying Mileages between Ten American Cities
• Example 78.3: Cluster Analysis with Significance Tests
• Example 78.4: Cluster Analysis: Hertzsprung-Russell Plot
• Example 78.5: Using the TRACE Option When METHOD=6

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MULTTEST Procedure

• Drug Example

• Example 79.1: Cochran-Armitage Test with Permutation Resampling
• Example 79.2: Freeman-Tukey and
• Example 79.3: Peto Mortality-Prevalence Test
• Example 79.4: Fisher Test with Permutation Resampling
• Example 79.5: Inputting Raw
• Example 79.6: Adaptive Adjustments and ODS Graphics

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NESTED Procedure

• Reliability of Automobile Models

• Example 80.1: Variability of Calcium Concentration in Turnip Greens

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NLIN Procedure

• Nonlinear or Linear Model
• Notation for Nonlinear Regression Models
• Estimating the Parameters in the Nonlinear Model

• Example 81.1: Segmented Model
• Example 81.2: Iteratively Reweighted Least Squares
• Example 81.3: Probit Model with Likelihood Function
• Example 81.4: Affecting Curvature through Parameterization
• Example 81.5: Comparing Nonlinear Trends among Groups
• Example 81.6: ODS Graphics and Diagnostics
• Example 81.7: Parameter Profiling and Bootstrapping

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NLMIXED Procedure

• Nonlinear Growth Curves with Gaussian Data
• Logistic-Normal Model with Binomial Data

• Example 82.1: One-Compartment Model with Pharmacokinetic Data
• Example 82.2: Probit-Normal Model with Binomial Data
• Example 82.3: Probit-Normal Model with Ordinal Data
• Example 82.4: Poisson-Normal Model with Count Data
• Example 82.5: Failure Time and Frailty Model
• Example 82.6: Simulated Nested Linear Random-Effects Model
• Example 82.7: Overdispersion Hierarchical Nonlinear Mixed Model

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NPAR1WAY Procedure

• Getting Started: NPAR1WAY Procedure

• Example 83.1: Two-Sample Location Tests and Plots
• Example 83.2: EDF Statistics and EDF Plot
• Example 83.3: Exact Wilcoxon Two-Sample Test
• Example 83.4: Hodges-Lehmann Estimation
• Example 83.5: Exact Savage Multisample Test

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ORTHOREG Procedure

• Longley Data

• Example 84.1: Precise Analysis of Variance
• Example 84.2: Wampler Data
• Example 84.3: Fitting Polynomials

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PHREG Procedure

• Classical Method of Maximum Likelihood
• Bayesian Analysis

• Example 85.1: Stepwise Regression
• Example 85.2: Best Subset Selection
• Example 85.3: Modeling with Categorical Predictors
• Example 85.4: Firth’s Correction for Monotone Likelihood
• Example 85.5: Conditional Logistic Regression for m:n Matching
• Example 85.6: Model Using Time-Dependent Explanatory Variables
• Example 85.7: Time-Dependent Repeated Measurements of a Covariate
• Example 85.8: Survival Curves
• Example 85.9: Analysis of Residuals
• Example 85.10: Analysis of Recurrent Events Data
• Example 85.11: Analysis of Clustered Data
• Example 85.12: Model Assessment Using Cumulative Sums of Martingale Residuals
• Example 85.13: Bayesian Analysis of the Cox Model
• Example 85.14: Bayesian Analysis of Piecewise Exponential Model
• Example 85.15: Analysis of Competing-Risks Data

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PLAN Procedure

• Three Replications with Four Factors
• Randomly Assigning Subjects to Treatments

• Example 86.1: A Split-Plot Design
• Example 86.2: A Hierarchical Design
• Example 86.3: An Incomplete Block Design
• Example 86.4: A Latin Square Design
• Example 86.5: A Generalized Cyclic Incomplete Block Design
• Example 86.6: Permutations and Combinations
• Example 86.7: Crossover Designs

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PLM Procedure

• Getting Started: PLM Procedure

• Example 87.1: Scoring with PROC PLM
• Example 87.2: Working with Item Stores
• Example 87.3: Group Comparisons in an Ordinal Model
• Example 87.4: Posterior Inference for Binomial Data
• Example 87.5: BY-Group Processing
• Example 87.6: Comparing Multiple B-Splines
• Example 87.7: Linear Inference with Arbitrary Estimates

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PLS Procedure

• Spectrometric Calibration

• Example 88.1: Examining Model Details
• Example 88.2: Examining Outliers
• Example 88.3: Choosing a PLS Model by Test Set Validation
• Example 88.4: Partial Least Squares Spline Smoothing

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POWER Procedure

• Computing Power for a One-Sample
• Determining Required Sample Size for a Two-Sample

• Example 89.1: One-Way ANOVA
• Example 89.2: The Sawtooth Power Function in Proportion Analyses
• Example 89.3: Simple AB/BA Crossover Designs
• Example 89.4: Noninferiority Test with Lognormal Data
• Example 89.5: Multiple Regression and Correlation
• Example 89.6: Comparing Two Survival Curves
• Example 89.7: Confidence Interval Precision
• Example 89.8: Customizing Plots
• Example 89.9: Binary Logistic Regression with Independent Predictors
• Example 89.10: Wilcoxon-Mann-Whitney Test

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PRINCOMP Procedure

• Getting Started: PRINCOMP Procedure

• Example 91.1: Analyzing Mean Temperatures of US Cities
• Example 91.2: Analyzing Rankings of US College Basketball Teams
• Example 91.3: Analyzing Job Ratings of Police Officers

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PRINQUAL Procedure

• Getting Started: PRINQUAL Procedure

• Example 92.1: Multidimensional Preference Analysis of Automobile Data
• Example 92.2: Principal Components of Basketball Rankings

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PROBIT Procedure

• Estimating the Natural Response Threshold Parameter

• Example 93.1: Dosage Levels
• Example 93.2: Multilevel Response
• Example 93.3: Logistic Regression and Scoring New Data
• Example 93.4: An Epidemiology Study
• Example 93.5: Model Postfitting Analysis

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QUANTLIFE Procedure

• Getting Started: QUANTLIFE Procedure

• Example 94.1: Primary Biliary Cirrhosis Study
• Example 94.2: Drug Abuse Study

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QUANTREG Procedure

• Analysis of Fish-Habitat Relationships
• Growth Charts for Body Mass Index

• Example 95.1: Comparison of Algorithms
• Example 95.2: Quantile Regression for Econometric Growth Data
• Example 95.3: Quantile Regression Analysis of Birth-Weight Data
• Example 95.4: Nonparametric Quantile Regression for Ozone Levels
• Example 95.5: Quantile Polynomial Regression for Salary Data

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QUANTSELECT Procedure

• Getting Started: QUANTSELECT Procedure

• Example 96.1: Simulation Study
• Example 96.2: Econometric Growth Data
• Example 96.3: Pollution and Mortality
• Example 96.4: Surface Fitting with Many Noisy Variables
• Example 96.5: Quantile Process Regression

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REG Procedure

• Simple Linear Regression
• Polynomial Regression
• Using PROC REG Interactively

• Example 97.1: Modeling Salaries of Major League Baseball Players
• Example 97.2: Aerobic Fitness Prediction
• Example 97.3: Predicting Weight by Height and Age
• Example 97.4: Regression with Quantitative and Qualitative Variables
• Example 97.5: Ridge Regression for Acetylene Data
• Example 97.6: Chemical Reaction Response

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ROBUSTREG Procedure

• M Estimation
• LTS Estimation

• Example 98.1: Comparison of Robust Estimates
• Example 98.2: Robust ANOVA
• Example 98.3: Growth Study of De Long and Summers
• Example 98.4: Constructed Effects
• Example 98.5: Robust Diagnostics

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RSREG Procedure

• A Response Surface with a Simple Optimum

• Example 99.1: A Saddle Surface Response Using Ridge Analysis
• Example 99.2: Response Surface Analysis with Covariates

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SEQDESIGN Procedure

• Getting Started: SEQDESIGN Procedure

• Example 101.1: Creating Fixed-Sample Designs
• Example 101.2: Creating a One-Sided O’Brien-Fleming Design
• Example 101.3: Creating Two-Sided Pocock and O’Brien-Fleming Designs
• Example 101.4: Generating Graphics Display for Sequential Designs
• Example 101.5: Creating Designs Using Haybittle-Peto Methods
• Example 101.6: Creating Designs with Various Stopping Criteria
• Example 101.7: Creating Whitehead’s Triangular Designs
• Example 101.8: Creating a One-Sided Error Spending Design
• Example 101.9: Creating Designs with Various Number of Stages
• Example 101.10: Creating Two-Sided Error Spending Designs with and without Overlapping Lower and Upper
• Example 101.11: Creating a Two-Sided Asymmetric Error Spending Design with Early Stopping to Reject
• Example 101.12: Creating a Two-Sided Asymmetric Error Spending Design with Early Stopping to Reject or Accept
• Example 101.13: Creating a Design with a Nonbinding Beta Boundary
• Example 101.14: Computing Sample Size for Survival Data That Have Uniform Accrual
• Example 101.15: Computing Sample Size for Survival Data with Truncated Exponential Accrual

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SEQTEST Procedure

• Getting Started: SEQTEST Procedure

• Example 102.1: Testing the Difference between Two Proportions
• Example 102.2: Testing an Effect in a Regression Model
• Example 102.3: Testing an Effect with Early Stopping to Accept
• Example 102.4: Testing a Binomial Proportion
• Example 102.5: Comparing Two Proportions with a Log Odds Ratio Test
• Example 102.6: Comparing Two Survival Distributions with a Log-Rank Test
• Example 102.7: Testing an Effect in a Proportional Hazards Regression Model
• Example 102.8: Testing an Effect in a Logistic Regression Model
• Example 102.9: Conducting a Trial with a Nonbinding Acceptance Boundary

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SCORE Procedure

• Getting Started: SCORE Procedure

• Example 100.1: Factor Scoring Coefficients
• Example 100.2: Regression Parameter Estimates
• Example 100.3: Custom Scoring Coefficients

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SIM2D Procedure

• Preliminary Spatial Data Analysis
• Investigating Variability by Simulation

• Example 103.1: Simulation and Economic Feasibility
• Example 103.2: Variability at Selected Locations
• Example 103.3: Risk Analysis with Simulation

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SIMNORMAL Procedure

• Getting Started: SIMNORMAL Procedure

• Example : Example: SIMNORM Procedure

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SPP Procedure

• Getting Started: SPP Procedure

• Example 105.1: Exploration of a Multitype Point Pattern
• Example 105.2: Testing Covariate Dependence of a Point Pattern
• Example 105.3: Intensity Model Validation Diagnostics

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STDIZE Procedure

• Getting Started: STDIZE Procedure

• Example 106.1: Standardization of Variables in Cluster Analysis

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STDRATE Procedure

• Getting Started: STDRATE Procedure

• Example 107.1: Comparing Directly Standardized Rates
• Example 107.2: Computing Mantel-Haenszel Risk Estimation
• Example 107.3: Computing Attributable Fraction Estimates
• Example 107.4: Displaying SMR Results from BY Groups

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STEPDISC Procedure

• Getting Started: STEPDISC Procedure

• Example 108.1: Performing a Stepwise Discriminant Analysis

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SURVEYFREQ Procedure

• Getting Started: SURVEYFREQ Procedure

• Example 109.1: Two-Way Tables
• Example 109.2: Multiway Tables (Domain Analysis)
• Example 109.3: Output Data Sets

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SURVEYIMPUTE Procedure

• Getting Started: SURVEYIMPUTE Procedure

• Example 110.1: Approximate Bayesian Bootstrap Imputation
• Example 110.2: Fully Efficient Fractional Imputation
• Example 110.3: Fully Efficient Fractional Imputation, Fay’s Balanced Repeated Replication, and Domain Analysis

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SURVEYLOGISTIC Procedure

• Getting Started: SURVEYLOGISTIC Procedure

• Example 111.1: Stratified Cluster Sampling
• Example 111.2: The Medical Expenditure Panel Survey (MEPS)

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SURVEYMEANS Procedure

• Simple Random Sampling
• Stratified Sampling
• Output Data Sets

• Example 112.1: Stratified Cluster Sample Design
• Example 112.2: Domain Analysis
• Example 112.3: Ratio Analysis
• Example 112.4: Analyzing Survey Data with Missing Values
• Example 112.5: Variance Estimation Using Replication Methods

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SURVEYPHREG Procedure

• Getting Started: SURVEYPHREG Procedure

• Example 113.1: Analysis of Clustered Data
• Example 113.2: Stratification, Clustering, and Unequal Weights
• Example 113.3: Domain Analysis
• Example 113.4: Variance Estimation by Using Replicate Weights
• Example 113.5: A Test of the Proportional Hazards Assumption by Using the Programming Statements

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SURVEYREG Procedure

• Simple Random Sampling
• Stratified Sampling
• Output Data Sets

• Example 114.1: Simple Random Sampling
• Example 114.2: Cluster Sampling
• Example 114.3: Regression Estimator for Simple Random Sample
• Example 114.4: Stratified Sampling
• Example 114.5: Regression Estimator for Stratified Sample
• Example 114.6: Stratum Collapse
• Example 114.7: Domain Analysis
• Example 114.8: Compare Domain Statistics
• Example 114.9: Variance Estimate Using the Jackknife Method

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SURVEYSELECT Procedure

• Simple Random Sampling
• Stratified Sampling
• Stratified Sampling with Control Sorting

• Example 115.1: Replicated Sampling
• Example 115.2: PPS Selection of Two Units per Stratum
• Example 115.3: PPS (Dollar-Unit) Sampling
• Example 115.4: Proportional Allocation

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TPSPLINE Procedure

• Getting Started: TPSPLINE Procedure

• Example 116.1: Partial Spline Model Fit
• Example 116.2: Spline Model with Higher-Order Penalty
• Example 116.3: Multiple Minima of the GCV Function
• Example 116.4: Large Data Set Application
• Example 116.5: Computing a Bootstrap Confidence Interval

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TRANSREG Procedure

• Fitting a Curve through a Scatter Plot
• Main-Effects ANOVA

• Example 117.1: Transformation Regression of Exhaust Emissions Data
• Example 117.2: Box-Cox Transformations
• Example 117.3: Penalized B-Spline
• Example 117.4: Nonmetric Conjoint Analysis of Tire Data
• Example 117.5: Metric Conjoint Analysis of Tire Data
• Example 117.6: Preference Mapping of Automobile Data

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TREE Procedure

• Getting Started: TREE Procedure

• Example 118.1: Mammals’ Teeth
• Example 118.2: Iris Data

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TTEST Procedure

• One-Sample
• Comparing Group Means

• Example 119.1: Using Summary Statistics to Compare Group Means
• Example 119.2: One-Sample Comparison with the FREQ Statement
• Example 119.3: Paired Comparisons
• Example 119.4: AB/BA Crossover Design
• Example 119.5: Equivalence Testing with Lognormal Data

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UNIVARIATE Procedure

• Capabilities of PROC UNIVARIATE
• Summarizing a Data Distribution
• Exploring a Data Distribution
• Modeling a Data Distribution

• Example 4.1: Computing Descriptive Statistics for Multiple Variables
• Example 4.2: Calculating Modes
• Example 4.3: Identifying Extreme Observations and Extreme Values
• Example 4.4: Creating a Frequency Table
• Example 4.5: Creating Basic Summary Plots
• Example 4.6: Analyzing a Data Set With a FREQ Variable
• Example 4.7: Saving Summary Statistics in an OUT= Output Data Set
• Example 4.8: Saving Percentiles in an Output Data Set
• Example 4.9: Computing Confidence Limits for the Mean, Standard Deviation, and Variance
• Example 4.10: Computing Confidence Limits for Quantiles and Percentiles
• Example 4.11: Computing Robust Estimates
• Example 4.12: Testing for Location
• Example 4.13: Performing a Sign Test Using Paired Data
• Example 4.14: Creating a Histogram
• Example 4.15: Creating a One-Way Comparative Histogram
• Example 4.16: Creating a Two-Way Comparative Histogram
• Example 4.17: Adding Insets with Descriptive Statistics
• Example 4.18: Binning a Histogram
• Example 4.19: Adding a Normal Curve to a Histogram
• Example 4.20: Adding Fitted Normal Curves to a Comparative Histogram
• Example 4.21: Fitting a Beta Curve
• Example 4.22: Fitting Lognormal, Weibull, and Gamma Curves
• Example 4.23: Computing Kernel Density Estimates
• Example 4.24: Fitting a Three-Parameter Lognormal Curve
• Example 4.25: Annotating a Folded Normal Curve
• Example 4.26: Creating Lognormal Probability Plots
• Example 4.27: Creating a Histogram to Display Lognormal Fit
• Example 4.28: Creating a Normal Quantile Plot
• Example 4.29: Adding a Distribution Reference Line
• Example 4.30: Interpreting a Normal Quantile Plot
• Example 4.31: Estimating Three Parameters from Lognormal Quantile Plots
• Example 4.32: Estimating Percentiles from Lognormal Quantile Plots
• Example 4.33: Estimating Parameters from Lognormal Quantile Plots
• Example 4.34: Comparing Weibull Quantile Plots
• Example 4.35: Creating a Cumulative Distribution Plot
• Example 4.36: Creating a P-P Plot

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VARCLUS Procedure

• Getting Started: VARCLUS Procedure

• Example 120.1: Correlations among Physical Variables

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VARCOMP Procedure

• Analyzing the Cure Rate of Rubber

• Example 121.1: Using the Four General Estimation Methods
• Example 121.2: Using the GRR Method

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VARIOGRAM Procedure

• Preliminary Spatial Data Analysis
• Empirical Semivariogram Computation
• Autocorrelation Analysis
• Theoretical Semivariogram Model Fitting

• Example 122.1: Aspects of Semivariogram Model Fitting
• Example 122.2: An Anisotropic Case Study with Surface Trend in the Data
• Example 122.3: Analysis without Surface Trend Removal
• Example 122.4: Covariogram and Semivariogram
• Example 122.5: A Box Plot of the Square Root Difference Cloud

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