SAS/STAT(R) 13.1 User's Guide - Navigation
Contents
Topics
About
Acknowledgments
Credits
Documentation
Software
Testing
Technical Support
Acknowledgments
What’s New in SAS/STAT 13.1
Overview
New Procedures
Highlights of Enhancements
Highlights of Enhancements in SAS/STAT 12.1 and SAS/STAT 12.3
Enhancements
ADAPTIVEREG Procedure
CALIS Procedure
FMM Procedure
FREQ Procedure
GAM Procedure
GENMOD Procedure
GLIMMIX Procedure
GLMPOWER Procedure
GLMSELECT Procedure
LIFETEST Procedure
MCMC Procedure
MI Procedure
MIANALYZE Procedure
NLIN Procedure
NPAR1WAY Procedure
PHREG Procedure
PLM Procedure
PROBIT Procedure
QUANTLIFE Procedure
QUANTSELECT Procedure
REG Procedure
SEQDESIGN Procedure
SURVEYFREQ Procedure
SURVEYMEANS Procedure
SURVEYPHREG Procedure
SURVEYREG Procedure
SURVEYSELECT Procedure
Enhancements to the High-Performance Procedures
HPCANDISC Procedure
HPFMM Procedure
HPLMIXED Procedure
HPPRINCOMP Procedure
HPREG Procedure
What’s Changed
FMM Procedure
FREQ Procedure
LOGISTIC Procedure
MCMC Procedure
NLMIXED Procedure
NPAR1WAY Procedure
References
Getting Started/Overview
Overview of SAS/STAT Software
Experimental Software
About This Book
Chapter Organization
Typographical Conventions
Options Used in Examples
Where to Turn for More Information
Accessing the SAS/STAT Sample Library
Sashelp Data Sets
Online Documentation
SAS Technical Support Services
Related SAS Software
SAS/IML Software
Base SAS Software
ODS Graphics
SAS/ETS Software
SAS/GRAPH Software
SAS/INSIGHT Software
SAS/OR Software
SAS/QC Software
SAS/IML Studio
Introductions
Introduction to Statistical Modeling with SAS/STAT Software
Overview: Statistical Modeling
Statistical Models
Classes of Statistical Models
Linear and Nonlinear Models
Regression Models and Models with Classification Effects
Univariate and Multivariate Models
Fixed, Random, and Mixed Models
Generalized Linear Models
Latent Variable Models
Bayesian Models
Classical Estimation Principles
Least Squares
Likelihood
Inference Principles for Survey Data
Statistical Background
Hypothesis Testing and Power
Important Linear Algebra Concepts
Expectations of Random Variables and Vectors
Mean Squared Error
Linear Model Theory
Finding the Least Squares Estimators
Analysis of Variance
Estimating the Error Variance
Maximum Likelihood Estimation
Estimable Functions
Test of Hypotheses
Residual Analysis
Sweep Operator
References
Introduction to Regression Procedures
Overview: Regression Procedures
Introduction
Introductory Example: Linear Regression
Model Selection Methods
Linear Regression: The REG Procedure
Model Selection: The GLMSELECT Procedure
Response Surface Regression: The RSREG Procedure
Partial Least Squares Regression: The PLS Procedure
Generalized Linear Regression
Contingency Table Data: The CATMOD Procedure
Generalized Linear Models: The GENMOD Procedure
Generalized Linear Mixed Models: The GLIMMIX Procedure
Logistic Regression: The LOGISTIC Procedure
Discrete Event Data: The PROBIT Procedure
Correlated Data: The GENMOD and GLIMMIX Procedures
Ill-Conditioned Data: The ORTHOREG Procedure
Quantile Regression: The QUANTREG and QUANTSELECT Procedures
Nonlinear Regression: The NLIN and NLMIXED Procedures
Nonparametric Regression
Adaptive Regression: The ADAPTIVEREG Procedure
Local Regression: The LOESS Procedure
Thin Plate Smoothing Splines: 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
Parametric Accelerated Failure Time Models: The LIFEREG Procedure
Nonparametric Methods for Right-Censored Data: The LIFETEST Procedure
Nonparametric Methods for Interval-Censored Data: The ICLIFETEST Procedure
Quantile Regression: The QUANTLIFE Procedure
Cox Regression and Extensions: The PHREG Procedure
Cox Regression for Survey Data: The SURVEYPHREG Procedure
Survival Analysis with SAS/STAT Procedures
Bayesian Survival Analysis with SAS/STAT Procedures
References
Introduction to Survey Sampling and Analysis Procedures
Overview: Survey Sampling and Analysis Procedures
The Survey Procedures
PROC SURVEYSELECT
PROC SURVEYMEANS
PROC SURVEYFREQ
PROC SURVEYREG
PROC SURVEYLOGISTIC
PROC SURVEYPHREG
Survey Design Specification
Population
Stratification
Clustering
Multistage Sampling
Sampling Weights
Population Totals and Sampling Rates
Variance Estimation
Example: Survey Sampling and Analysis Procedures
Sample Selection
Survey Data Analysis
References
The Four Types of Estimable Functions
Overview
Estimability
General Form of an Estimable Function
Introduction to Reduction Notation
Examples
Estimable Functions
Type I SS and Estimable Functions
Type II SS and Estimable Functions
Type III and IV SS and Estimable Functions
References
Introduction to Nonparametric Analysis
Overview: Nonparametric Analysis
Testing for Normality
Comparing Distributions
One-Sample Tests
Two-Sample Tests
Comparing Two Independent Samples
Comparing Two Related Samples
Tests for k Samples
Comparing k Independent Samples
Comparing k Dependent Samples
Measures of Correlation and Associated Tests
Obtaining Ranks
Kernel Density Estimation
References
Introduction to Structural Equation Modeling with Latent Variables
Overview of Structural Equation Modeling with Latent Variables
Testing Covariance Patterns
Testing Built-In Covariance Patterns in PROC CALIS
Direct and Implied Covariance Patterns
Regression with Measurement Errors
Simple Linear Regression
Errors-in-Variables Regression
Regression with Measurement Errors in X and Y
Model Identification
Illustration of Model Identification: Spleen Data
Path Diagrams and Path Analysis
A Simplified Path Diagram for the Spleen Data
Some Measurement Models
H4: Full Measurement Model for Lord Data
H3: Congeneric (One-Factor) Model for Lord Data
H2: Two-Factor Model with Parallel Tests for Lord Data
H1: One-Factor Model with Parallel Tests for Lord Data
The FACTOR and RAM Modeling Languages
Specifying the Full Measurement Model (H4) by the FACTOR Modeling Language: Lord Data
Specifying the Parallel Tests Model (H2) by the FACTOR Modeling Language: Lord Data
Specifying the Parallel Tests Model (H2) by the RAM Modeling Language: Lord Data
A Combined Measurement-Structural Model
Career Aspiration: Analysis 1
Career Aspiration: Analysis 2
Career Aspiration: Analysis 3
Fitting LISREL Models by the LISMOD Modeling Language
The Measurement Model for y
The Measurement Model for x
The Structural Model
Fit Summary of the LISMOD Model for Career Aspiration Analysis 3
Some Important PROC CALIS Features
Modeling Languages for Specifying Models
Estimation Methods
Statistical Inference
Multiple-Group Analysis
Goodness-of-Fit Statistics
Customizable Fit Summary Table
Standardized Solution
Testing Parametric Functions
Effect Analysis
Model Modifications
Optimization Methods
Other Commonly Used Options
Comparison of the CALIS and FACTOR Procedures for Exploratory Factor Analysis
Comparison of the CALIS and SYSLIN Procedures
References
Introduction to Power and Sample Size Analysis
Overview
Coverage of Statistical Analyses
Statistical Background
Hypothesis Testing, Power, and Confidence Interval Precision
Standard Hypothesis Tests
Equivalence and Noninferiority
Confidence Interval Precision
Computing Power and Sample Size
Power and Study Planning
Components of Study Planning
Effect Size
Uncertainty and Sensitivity Analysis
SAS/STAT Tools for Power and Sample Size Analysis
Basic Graphs (POWER, GLMPOWER, Power and Sample Size Application)
Highly Customized Graphs (POWER, GLMPOWER)
Formatted Tables (%POWTABLE Macro)
Narratives and Graphical User Interface (Power and Sample Size Application)
Customized Power Formulas (DATA Step)
Empirical Power Simulation (DATA Step, SAS/STAT Software)
References
Shared Concepts and Topics
Levelization of Classification Variables
Parameterization of Model Effects
GLM Parameterization of Classification Variables and Effects
Intercept
Regression Effects
Main Effects
Interaction Effects
Nested Effects
Continuous-Nesting-Class Effects
Continuous-by-Class Effects
General Effects
Other Parameterizations
CODE Statement
Syntax: CODE Statement
EFFECT Statement
Collection Effects
Lag Effects
Multimember Effects
Polynomial Effects
Spline Effects
Splines and Spline Bases
Truncated Power Function Basis
B-Spline Basis
Natural Cubic Spline Basis
EFFECTPLOT Statement
Syntax: EFFECTPLOT Statement
Dictionary of Options
ODS Graphics: EFFECTPLOT Statement
Examples: EFFECTPLOT Statement
A Saddle Surface
Unbalanced Two-Way ANOVA
Logistic Regression
ESTIMATE Statement
Syntax: ESTIMATE Statement
Positional and Nonpositional Syntax for Coefficients in Linear Functions
Joint Hypothesis Tests with Complex Alternatives, the Chi-Bar-Square Statistic
ODS Table Names: ESTIMATE Statement
ODS Graphics: ESTIMATE Statement
LSMEANS Statement
Syntax: LSMEANS Statement
ODS Table Names: LSMEANS Statement
ODS Graphics: LSMEANS Statement
LSMESTIMATE Statement
Syntax: LSMESTIMATE Statement
ODS Table Names: LSMESTIMATE Statement
ODS Graphics: LSMESTIMATE Statement
NLOPTIONS Statement
Syntax: NLOPTIONS Statement
Choosing an Optimization Algorithm
First- or Second-Order Algorithms
Algorithm Descriptions
SLICE Statement
Syntax: SLICE Statement
ODS Table Names: SLICE Statement
STORE Statement
Syntax: STORE Statement
TEST Statement
Syntax: TEST Statement
ODS Table Names: TEST Statement
Programming Statements
References
Using the Output Delivery System
Overview: Using the Output Delivery System
Output Defaults
HTML Output in the SAS Windowing Environment
LISTING Output in the SAS Windowing Environment
Assumptions about ODS Defaults in this Chapter
The HTMLBLUE Style
Default Open Destination
Setting the Default Destination in the Results Tab
Setting the Default Destination in the SAS Registry
Setting the Default Destination in SAS System Options
Setting the Destination in ODS Statements
Output Objects and ODS Destinations
The ODS Statement
Paths and Selection
RUN-Group Processing
The SAS Results Window
The ODS PATH Statement
The Master Template Store
Controlling Output Appearance with Templates
ODS and the NOPRINT Option
Examples: Using the Output Delivery System
Creating HTML Output with ODS
Selecting ODS Tables for Display
Excluding ODS Tables from Display
Creating an Output Data Set from an ODS Table
Creating an Output Data Set: Subsetting the Data
RUN-Group Processing
ODS Output Data Sets and Using PROC TEMPLATE to Customize Output
HTML Output with Hyperlinks between Tables
HTML Output with Graphics and Hyperlinks
Correlation and Covariance Matrices
References
Statistical Graphics Using ODS
Statistical Graphics Using ODS
Introduction
Chapter Reading Guide
Assumptions about ODS Defaults in This Chapter
Getting Started with ODS Statistical Graphics
Default Plots for Simple Linear Regression with PROC REG
Survival Estimate Plot with PROC LIFETEST
Contour and Surface Plots with PROC KDE
Contour Plots with PROC KRIGE2D
Partial Least Squares Plots with PROC PLS
Box-Cox Transformation Plot with PROC TRANSREG
LS-Means Diffogram with PROC GLIMMIX
Principal Component Analysis Plots with PROC PRINCOMP
Grouped Scatter Plot with PROC SGPLOT
A Primer on ODS Statistical Graphics
Enabling and Disabling ODS Graphics
Graph Styles
ODS Destinations
Accessing Individual Graphs
Specifying the Size and Resolution of Graphs
Modifying Your Graphs
Procedures That Support ODS Graphics
Procedures That Support ODS Graphics and Traditional Graphics
Syntax
ODS GRAPHICS Statement
ODS Destination Statements
PLOTS= Option
Selecting and Viewing Graphs
Specifying an ODS Destination for Graphics
Viewing Your Graphs in the SAS Windowing Environment
Determining Graph Names and Labels
Selecting and Excluding Graphs
Graphics Image Files
Image File Types
Scalable Vector Graphics
Naming Graphics Image Files
Saving Graphics Image Files
Creating Graphs in Multiple Destinations
Graph Size and Resolution
ODS Graphics Editor
Enabling the Creation of Editable Graphs
Editing a Graph with the ODS Graphics Editor
The Default Template Stores and the Template Search Path
Styles
An Overview of Styles
Style Elements and Attributes
Style Templates and Colors
Some Common Style Elements
Style Comparisons
Modifying the HTMLBLUE Style
Style Template Modification Macro
Creating an All-Color Style
Changing the Default Markers and Lines
Changing the Default Style
Statistical Graphics Procedures
The SGPLOT Procedure
The SGSCATTER Procedure
The SGPANEL Procedure
The SGRENDER Procedure
Examples of ODS Statistical Graphics
Creating Graphs with Tool Tips in HTML
Creating Graphs for a Presentation
Creating Graphs in PostScript Files
Displaying Graphs Using the DOCUMENT Procedure
Customizing the Style for Box Plots
References
ODS Graphics Template Modification
Graph Templates
The Graph Template Language
Locating Templates
Displaying Templates
Editing Templates
Saving Customized Templates
Using Customized Templates
Reverting to the Default Templates
Graph Template Modification Macro
Examples of ODS Graphics Template Modification
Customizing Graphs Through Template Changes
Modifying Graph Titles and Axis Labels
Modifying Colors, Line Styles, and Markers
Modifying Tick Marks and Grid Lines
Modifying the Style to Show Grid Lines
Adding Equations and Special Characters to Fit Plots
Simple Linear Regression
Cubic Fit Function
Unicode and Special Characters
Customizing 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
Customizing the Kaplan-Meier Survival Plot
Overview
Controlling the Survival Plot by Specifying Procedure Options
Enabling ODS Graphics and the Default Kaplan-Meier Plot
Individual Survival Plots
Hall-Wellner Confidence Bands and Homogeneity Test
Equal-Precision Bands
Displaying the Patients-at-Risk Table inside the Plot
Displaying the Patients-at-Risk Table outside the Plot
Modifying At-Risk Table Times
Reordering the Groups
Suppressing the Censored Observations
Failure Plots
Controlling the Survival Plot by Modifying Graph Templates
The Modularized Templates
Changing the Plot Title
Modifying the Axis
Changing the Line Thickness
Changing the Group Color
Changing the Line Pattern
Changing the Font
Changing the Legend and Inset Position
Changing How the Censored Points Are Displayed
Adding a Y-Axis Reference Line
Changing the Homogeneity Test Inset
Suppressing the Second Title and Adding a Footnote
Adding a Small Inset Table with Event Information
Adding an External Table with Event Information
Suppressing the Legend
Kaplan-Meier Plot with Event Table and Other Customizations
Compiled Template Cleanup
Graph Templates, Macros, and Macro Variables
The Macro Variables
The Smaller Macros
The Larger Macros
Event Table Macros
Dynamic Variables
Dynamic Variables That Are Automatically Declared
Additional Dynamic Variables
Style Templates
Changing the Style
Color Priority Styles
Displaying a Style and Extracting Color Lists
Modifying Color Lists
Swapping Colors among Style Elements
Displaying a Style and Extracting Font Information
Displaying Other Style Elements
SAS Item Stores
References
Procedures
The ACECLUS Procedure
Overview: ACECLUS Procedure
Background
Getting Started: ACECLUS Procedure
Syntax: ACECLUS Procedure
PROC ACECLUS Statement
BY Statement
FREQ Statement
VAR Statement
WEIGHT Statement
Details: ACECLUS Procedure
Missing Values
Output Data Sets
Computational Resources
Displayed Output
ODS Table Names
Example: ACECLUS Procedure
Transformation and Cluster Analysis of Fisher Iris Data
References
The ADAPTIVEREG Procedure
Overview: ADAPTIVEREG Procedure
Getting Started: ADAPTIVEREG Procedure
Syntax: ADAPTIVEREG Procedure
PROC ADAPTIVEREG Statement
BY Statement
CLASS Statement
FREQ Statement
MODEL Statement
OUTPUT Statement
PARTITION Statement
SCORE Statement
WEIGHT Statement
Details: ADAPTIVEREG Procedure
Fitting Algorithms
Missing Values
ANOVA Decomposition
Computational Resources
ODS Table Names
ODS Graphics
Examples: ADAPTIVEREG Procedure
Surface Fitting with Many Noisy Variables
Fitting Data with Mixture Structures
Predicting E-Mail Spam
Nonparametric Poisson Model for Mackerel Egg Density
References
The ANOVA Procedure
Overview: ANOVA Procedure
Getting Started: ANOVA Procedure
One-Way Layout with Means Comparisons
Randomized Complete Block with One Factor
Syntax: ANOVA Procedure
PROC ANOVA Statement
ABSORB Statement
BY Statement
CLASS Statement
FREQ Statement
MANOVA Statement
MEANS Statement
MODEL Statement
REPEATED Statement
TEST Statement
Details: ANOVA Procedure
Specification of Effects
Using PROC ANOVA Interactively
Missing Values
Output Data Set
Computational Method
Displayed Output
ODS Table Names
ODS Graphics
Examples: ANOVA Procedure
Randomized Complete Block With Factorial Treatment Structure
Alternative Multiple Comparison Procedures
Split Plot
Latin Square Split Plot
Strip-Split Plot
References
The BCHOICE Procedure
Overview: BCHOICE Procedure
PROC BCHOICE Compared with Other SAS Procedures
Getting Started: BCHOICE Procedure
A Simple Logit Model
A Logit Model with Random Effects
Syntax: BCHOICE Procedure
PROC BCHOICE Statement
BY Statement
CLASS Statement
MODEL Statement
PREDDIST Statement
RANDOM Statement
Details: BCHOICE Procedure
Discrete Choice Models
Types of Choice Models
Random Effects
Identification and Specification
Gamerman Algorithm
Autocall Macros for Postprocessing
Regenerating Diagnostics Plots
Displayed Output
ODS Table Names
ODS Graphics
Examples: BCHOICE Procedure
Alternative-Specific and Individual-Specific Effects
Nested Logit Modeling
Probit Modeling
A Random-Effects-Only Logit Model
Heterogeneity Affected by Individual Characteristics
Inference on Quantities of Interest
Predict the Choice Probabilities
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
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
PATHDIAGRAM 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
Path Diagrams: Layout Algorithms, Default Settings, and Customization
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
Analyzing Iris Data by Using 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 Bayesian 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
Common Risk Difference
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
Tweedie Distribution For Generalized Linear 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
Tweedie 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
Pseudo-likelihood Estimation for Weighted Multilevel Models
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
Weighted Multilevel Model for Survey 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
MANOVA Statement
MODEL Statement
PLOT Statement
POWER Statement
REPEATED Statement
WEIGHT Statement
Details: GLMPOWER Procedure
Specifying Value Lists in the POWER Statement
Number-Lists
Name-Lists
Keyword-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 in Univariate Models
Contrasts in Fixed-Effect Multivariate Models
ODS Graphics
Examples: GLMPOWER Procedure
One-Way ANOVA
Two-Way ANOVA with Covariate
Repeated Measures ANOVA
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
Elastic Net Selection (ELASTICNET)
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
External 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
Elastic Net and External Cross Validation
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 ICLIFETEST Procedure
Overview: ICLIFETEST Procedure
Features
Getting Started: ICLIFETEST Procedure
Syntax: ICLIFETEST Procedure
PROC ICLIFETEST Statement
BY Statement
FREQ Statement
STRATA Statement
TEST Statement
TIME Statement
Details: ICLIFETEST Procedure
Statistical Methods
Missing Values
Output Data Sets
Displayed Output
ODS Table Names
ODS Graphics
Examples: ICLIFETEST Procedure
Analyzing Data With Observations below a Limit of Detection
Controlling the Plotting of Survival Estimates
Plotting Kernel-Smoothed Hazard Functions
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 IRT Procedure
Overview: IRT Procedure
Basic Features
Getting Started: IRT Procedure
A Simple 2PL Model
Syntax: IRT Procedure
PROC IRT Statement
BY Statement
COV Statement
EQUALITY Statement
FACTOR Statement
FREQ Statement
GROUP Statement
MODEL Statement
VAR Statement
VARIANCE Statement
WEIGHT Statement
Details: IRT Procedure
Notation for the Item Response Theory Model
Assumptions
PROC IRT Contrasted with Other SAS Procedures
Response Models
Marginal Likelihood
Approximating the Marginal Likelihood
Maximizing the Marginal Likelihood
Factor Score Estimation
Model and Item Fit
ODS Table Names
ODS Graphics
Examples: IRT Procedure
Unidimensional IRT Models
Multidimensional Exploratory and Confirmatory IRT Models
Multiple-Group Analysis
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
Plot Options Superseded by ODS Graphics
ODS Table Names
ODS Graphics
Modifying the 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
MNAR 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 and FCS Discriminant Function Methods
Monotone and FCS Logistic Regression Methods
Monotone Propensity Score Method
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
Sensitivity Analysis for the MAR Assumption
Multiple Imputation with Pattern-Mixture Models
Specifying Sets of Observations for Imputation in Pattern-Mixture Models
Adjusting Imputed Values in Pattern-Mixture Models
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
Creating Control-Based Pattern Imputation in Sensitivity Analysis
Adjusting Imputed Continuous Values in Sensitivity Analysis
Adjusting Imputed Classification Levels in Sensitivity Analysis
Adjusting Imputed Values with Parameters in a Data Set
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 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 a PARMS= Data Set
Reading Mixed Model Results with Classification Covariates
Reading Nominal Logistic Model Results
Using a TEST statement
Combining Correlation Coefficients
Sensitivity Analysis with Control-Based Pattern Imputation
Sensitivity Analysis with Tipping-Point Approach
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
BOOTSTRAP 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, Diagnostics and Inference
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 and Bootstrapping
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
Proportional Rates/Means Models for Recurrent Events
The Frailty Model
Proportional Subdistribution Hazards Model for Competing-Risks Data
Hazard Ratios
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
Schemper-Henderson Predictive Measure
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
Analysis of Competing-Risks Data
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
Scoring Data Sets for Zero-Inflated Models
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
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
Analyzing Mean Temperatures of US Cities
Analyzing Rankings of US College Basketball Teams
Analyzing Job Ratings of Police Officers
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
Relationship of Quantile Function and Survival Function
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
Quantile Regression
Quasi-Likelihood Information Criteria
Quasi-Likelihood Ratio Tests
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
Simulation Study
Econometric Growth Data
Pollution and Mortality
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
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
Plot Options Superseded by ODS Graphics
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 That Have Uniform Accrual
Computing Sample Size for Survival Data with Truncated Exponential Accrual
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
Details: SIMNORMAL Procedure
Introduction
Unconditional Simulation
Conditional Simulation
Example: SIMNORM Procedure
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
Kappa Coefficients
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
Domain Quantiles
Ratio Analysis
Domain Ratio Analysis
Hadamard Matrix
Geometric Means
Domain Geometric Means
ODS Table Names
ODS Graphics
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
Random Assignment 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
Baseball Data
Bone Marrow Transplant Data
Birth Weight Data
Class Data
Comet Data
El Nino–Southern Oscillation Data
Finland’s Lake Laengelmaevesi Fish Catch Data
Exhaust Emissions Data
Fisher (1936) Iris Data
Junk E-Mail Data
Leukemia Data Sets
Margarine Data
Coal Seam Thickness Data
Flying Mileages between Five US Cities Data
References
General
What's New in SAS/STAT 13.1
Shared Concepts and Topics
Using the Output Delivery System
Statistical Graphics Using ODS
Special SAS Data Sets
Sashelp Data Sets
Analysis of Variance
Introduction to Analysis of Variance Procedures
The Four Types of Estimable Functions
The ANOVA Procedure
The CATMOD Procedure
The GENMOD Procedure
The GLIMMIX Procedure
The GLM Procedure
The GLMMOD Procedure
The GLMSELECT Procedure
The INBREED Procedure
The LATTICE Procedure
The MIXED Procedure
The NESTED Procedure
The NPAR1WAY Procedure
The PLAN Procedure
The PLM Procedure
The TRANSREG Procedure
The TTEST Procedure
The VARCOMP Procedure
Bayesian
Introduction to Bayesian Analysis Procedures
The BCHOICE Procedure
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 BCHOICE Procedure
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 IRT 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 IRT 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 ICLIFETEST Procedure
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
Product
Release
SAS/STAT
13.1
Type
Usage and Reference
Copyright Date
December 2013
Last Updated
17Dec2013
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