SAS for Linear Models
Chapter 1: Introduction
- About This Book?
- Statistical Topics and SAS Procedures
Chapter 2: Regression
- Introduction
- The REG Procedure
- Using the REG Procedure to Fit a Model with One Independent Variable
- The P, CLM, and CLI Options: Predicted Values and Confidence Limits
- A Model with Several Independent Variables
- The SS1 and SS2 Options: Two Types of Sums of Squares
- Tests of Subsets and Linear Combinations of Coefficients
- Fitting Restricted Models: The RESTRICT Statement and NOINT Option
- Exact Linear Dependency
- The GLM Procedure
- Using the GLM Procedure to Fit a Linear Regression Model
- Using the CONTRAST Statement to Test Hypotheses about Regression Parameters
- Using the ESTIMATE Statement to Estimate Linear Combinations of Parameters
- Statistical Background
- Terminology and Notation
- Partitioning the Sums of Squares
- Hypothesis Tests and Confidence Intervals
- Using the Generalized Inverse
Chapter 3: Analysis of Variance for Balanced Data
- Introduction
- One- and Two-Sample Tests and Statistics
- One-Sample Statistics
- Two Related Samples
- Two Independent Samples
- The Comparison of Several Means: Analysis of Variance
- Terminology and Notation
- Crossed Classification and Interaction Sum of Squares
- Nested Effects and Nested Sum of Squares
- Using the ANOVA and GLM Procedures
- Multiple Comparisons and Preplanned Comparisons
- The Analysis of One-Way Classification of Data
- Computing the ANOVA Table
- Computing Means, Multiple Comparisons of Means, and Confidence Intervals
- Planned Comparisons of One-Way Classification: The CONTRAST Statement
- Linear Combinations of Model Parameters
- Testing Several Contrasts Simultaneously
- Orthogonal Contrasts
- Estimating Linear Combinations of Parameters: The ESTIMATE Statement
- Randomized-Blocks Designs
- Analysis of Variance for Randomized-Blocks Design
- Additional Multiple Comparisons Methods
- Dunnett's Test to Compare Each Treatment to a Control
- A Latin Square Design with Two Response Variables
- A Two-Way Factorial Experiment
- ANOVA for a Two-Way Factorial Experiment
- Multiple Comparisons for a Factorial Experiment
- Multiple Comparisons of METHOD Means by VARIETY
- Planned Comparisons in a Two-Way Factorial Experiment
- Simple Effect Comparisons
- Main Effect Comparisons
- Simultaneous contrasts in Two-Way Classification
- Comparing Levels of One Factor within Subgroups of Levels of Another Factor
- An Easier Way to Set Up CONTRAST and ESTIMATE Statements
Chapter 4: Analyzing Data with Random Effects
- Introduction
- Nested Classification
- Analysis of Variance for Nested Classifications
- Computing Variances of Means from Nested Classifications and Deriving Optimum Sampling Plans
- Analysis of Variance for Nested Classifications: Using Expected Means Squares to Obtain Valid Tests of Hypotheses
- Variance Component Estimation for Nested Classifications: Analysis Using PROC MIXED
- Additional Analysis of Nested Classifications Using PROC MIXED: Overall Mean and Best Linear Unbiased Prediction
- Blocked Designs with Random Blocks
- Random-Blocks Analysis Using PROC MIXED
- Differences between GLM and MIXED Randomized-Complete-Blocks Analysis: Fixed versus Random Blocks
- Treatment Means
- Treatment Differences
- The Two-Way Mixed Model
- Analysis of Variance for the Two-Way Mixed Model: Working with Expected Mean Squares to Obtain Valid Tests
- Standard of Errors for the Two-Way Mixed Model: GLM versus MIXED
- More on Expected Mean Squares: Determining Quadratic Forms and Null Hypotheses for Fixed Effects
- A Classification with Both Crossed and Nested Effects
- Analysis of Variance for Crossed-Nested Classification
- Using Expected Mean Squares to Set Up Several Tests of Hypotheses for Crossed-Nested Classification
- Satterthwaite's Formula for Approximate Degrees of Freedom
- PROC MIXED Analysis of Crossed-Nested Classification
- Split-Plot Experiments
- A Standard Split-Plot Experiment
- Analysis of Variance Using PROC GLM
- Analysis with PROC MIXED
Chapter 5: Unbalanced Data Analysis: Basic Methods
- Introduction
- Applied Concepts of Analyzing Unbalanced Data
- ANOVA for Unbalanced Data
- Using the CONTRAST and ESTIMATE Statements with Unbalanced Data
- The LSMEANS Statement
- More on Comparing Means: Other Hypotheses and Types of Sums of Squares
- Issues Associated with Empty Cells
- The Effect of Empty Cells on Types of Sums of Squares
- The Effect of Empty Cells on CONTRAST, ESTIMATE, and LSMEANS Results
- Some Problems with Unbalanced Mixed-Model Data
- Using the GLM Procedure to Analyze Unbalanced Mixed-Model Data
- Approximate F-Statistics from ANOVA Mean Squares with Unbalanced Mixed-Model Data
- Using the CONTRAST, ESTIMATE, and LSMEANS Statement in GLM with Unbalanced Mixed-Model Data
- Using the MIXED Procedure to Analyze Unbalanced Mixed-Model Data
- Using the GLM and MIXED Procedures to Analyze Mixed-Model Data with Empty Cells
- Summary and Conclusions about Using the GLM and MIXED Procedures to Analyze Unbalanced Mixed-Model Data
Chapter 6: Understanding Linear Model Concepts
- Introduction
- The Dummy-Variable Model
- The Simplest Case: A One-Way Classification
- Parameter Estimates for a One-Way Classification
- Using PROC GLM for Analysis of Variance
- Estimable Functions in a One-Way Classification
- Two-Way Classification: Unbalanced Data
- General Considerations
- Sums of Squares Computed by PROC GLM
- Interpreting Sums of Squares in Reduction Notation
- Interpreting Sums of Squares in u-Model Notation
- An Example of Unbalanced Two-Way Classification
- The MEANS, LSMEANS, CONTRAST, and ESTIMATE Statement in a Two-Way Layout
- The General Form of Estimable Functions
- Interpreting Sums of Squares Using Estimable Functions
- Estimating Estimable Functions
- Interpreting LSMEANS, CONTRAST, and ESTIMATE Results Using Estimable Functions
- Empty Cells
- Mixed-Model Issues
- Proper Error Terms
- More on Expected Mean Squares
- An Issue of Model Formulation Related to Expected Mean Squares
- ANOVA Issues for Unbalanced Mixed Models
- Using Expected Mean Squares to Construct Approximate F-Tests for Fixed Effects
- GLS and Likelihood Methodology Mixed Model
- An Overview of Generalized Least Squares Methodology
- Some Practical Issues about Generalized Least Squares Methodology
Chapter 7: Analysis of Covariance
- Introduction
- A One-Way Structure
- Covariance Model
- Means and Least-Squares Means
- Contrasts
- Multiple Covariates
- Unequal Slopes
- Testing the Heterogeneity of Slopes
- Estimating Different Slopes
- Testing Treatment Differences with Unequal Slopes
- A Two-Way Structure without Interaction
- A Two-Way Structure with Interaction
- Orthogonal Polynomials and Covariance Methods
- A 2x3 Example
- Use of the IML ORPOL Function to Obtain Orthogonal Polynomial Contrast Coefficients
- Use of Analysis of Covariance to Compute ANOVA and Fit Regression
Chapter 8: Repeated-Measures Analysis
- Introduction
- The Univariate ANOVA Method for Analyzing Repeated Measures
Using GLM to Perform Univariate ANOVA of Repeated-Measures Data
The CONTRAST, ESTIMATE, and LSMEANS Statements in Univariate ANOVA of Repeated-Measures Data
- Multivariate and Univariate Methods Based on Contrasts of the Repeated Measures
- Univariate ANOVA of Repeated Measures at Each Time
- Using the REPEATED Statement in PROC GLM to Perform Multivariate Analysis of Repeated-Measures Data
- Univariate ANOVA of Contrasts of Repeated Measures
- Mixed-Model Analysis of Repeated Measures
- The Fixed-Effects Model and Related Considerations
- Selecting an Appropriate Covariance Model
- Reassessing the Covariance Structure with a Means Model Accounting for Baseline Measurement
- Information Criteria to Compare Covariance Models
- PROC MIXED Analysis of FEV1 Data
- Inference on the Treatment and Time Effects of FEV1 Data Using PROC MIXED
- Comparisons of DRUG*HOUR Means
- Comparisons Using Regression
Chapter 9: Multivariate Linear Models
- Introduction
- A One-Way Multivariate Analysis of Variance
- Hotelling's T2 Test
- A Two-Factor Factorial
- Multivariate Analysis of Covariance
- Contrasts in Multivariate Analyses
- Statistical Background
Chapter 10: Generalized Linear Models
- Introduction
- The Logistic and Probit Regression Models
- Logistic Regression: The Challenger Shuttle O-Ring Data Example
- Using the Inverse Link to Get the Predicted Probability
- Alternative Logistic Regression Analysis Using 0-1 Data
- An Alternative Link: Probit Regression
- Bionomial Models for Analysis of Variance and Analysis of Covariance
- Logistic ANOVA
- The Analysis-of-Variance Model with a Probit Link
- Logistic Analysis of Covariance
- Count Data and Overdispersion
- An Insect Count Example
- Model Checking
- Correction for Overdispersion
- Fitting a Negative Binomial Model
- Using PROC GENMOD to Fit the Negative Binomial with a Log Link
- Fitting the Negative Binomial with a Canonical Link
- Advanced Application: A User-Supplied Program to Fit the Negative Binomial with a Canonical Link
- Generalized Linear Models with Repeated Measures-Generalized Estimating Equations
- A Poisson Repeated-Measures Example
- Using PROC GENMOD to Compute a GEE Analysis of Repeated Measures
- Background Theory
- The Generalized Linear Model Defined
- How the GzLM's Parameters Are Estimated
- Standard Errors and Test Statistics
- Quasi-Likelihood
- Repeated Measures and Generalized Estimating Equations
Chapter 11: Examples of Special Applications
- Introduction
- Confounding in a Factorial Experiment
- Confounding with Blocks
- A Fractional Factorial Example
- A Balanced Incomplete-Blocks Design
- A Crossover Design with Residual Effects
- Models for Experiments with Qualitative and Quantitative Variables
- A Lack-of-Fit Analysis
- An Unbalanced Nested Structure
- An Analysis of Multi-Location Data
- An Analysis Assuming No Location_Treatment Interaction
- A Fixed-Location Analysis with an Interaction
- A Random-Location Analysis
- Further Analysis of a Location_Treatment Interaction Using a Location Index
- Absorbing Nesting Effects
References
Index