# Univariate and Multivariate General Linear Models

## Theory and Applications with SAS, Second Edition

#### By **Kevin Kim**, **Neil Timm**

#### Series Editor: **N. Balakrishnan**

Chapman and Hall/CRC – 2006 – 549 pages

Chapman and Hall/CRC – 2006 – 549 pages

Reviewing the theory of the general linear model (GLM) using a general framework, Univariate and Multivariate General Linear Models: Theory and Applications with SAS, Second Edition presents analyses of simple and complex models, both univariate and multivariate, that employ data sets from a variety of disciplines, such as the social and behavioral sciences.

With revised examples that include options available using SAS 9.0, this expanded edition divides theory from applications within each chapter. Following an overview of the GLM, the book introduces unrestricted GLMs to analyze multiple regression and ANOVA designs as well as restricted GLMs to study ANCOVA designs and repeated measurement designs. Extensions of these concepts include GLMs with heteroscedastic errors that encompass weighted least squares regression and categorical data analysis, and multivariate GLMs that cover multivariate regression analysis, MANOVA, MANCOVA, and repeated measurement data analyses. The book also analyzes double multivariate linear, growth curve, seeming unrelated regression (SUR), restricted GMANOVA, and hierarchical linear models.

New to the Second Edition

A practical introduction to GLMs, Univariate and Multivariate General Linear Models demonstrates how to fully grasp the generality of GLMs by discussing them within a general framework.

"The attached CD contains well-illustrated examples from various disciplines using SAS formatted data and SAS code adapted from over 200 pre-written SAS procedures."

– Kassim S. Mwitondi, Sheffield Hallam University, in *Journal of Applied Statistics*, June 2008

PREFACE

OVERVIEW OF THE GENERAL LINEAR MODEL

Introduction

General Linear Model

Restricted General Linear Model

Multivariate Normal Distribution

Elementary Properties of Normal Random Variables

Hypothesis Testing

Generating Multivariate Normal Data

Assessing Univariate Normality

Assessing Multivariate Normality with Chi-Square Plots

Using SAS INSIGHT

Three-Dimensional Plots

UNRESTRICTED GENERAL LINEAR MODELS

Introduction

Linear Models without Restrictions

Hypothesis Testing

Simultaneous Inference

Multiple Linear Regression

Linear Mixed Models

One-Way Analysis of Variance

Multiple Linear Regression: Calibration

Two-Way Nested Designs

Intraclass Covariance Models

RESTRICTED GENERAL LINEAR MODELS

Introduction

Estimation and Hypothesis Testing

Two-Way Factorial Design without Interaction

Latin Square Designs

Repeated Measures Designs

Analysis of Covariance

WEIGHTED GENERAL LINEAR MODELS

Introduction

Estimation and Hypothesis Testing

OLSE versus FGLS

General Linear Mixed Model Continued

Maximum Likelihood Estimation and Fisher's Information Matrix

WLSE for data Data Heteroscedasticity

WLSE for Correlated Errors

FGLS for Categorical Data

MULTIVARIATE GENERAL LINEAR MODELS

Introduction

Developing the Model

Estimation Theory and Hypothesis Testing

Multivariate Regression

Classical and Normal Multivariate Linear Regression Models

Jointly Multivariate Normal Regression Model

Multivariate Mixed Models and the Analysis of Repeated Measurements

Extended Linear Hypotheses

Multivariate Regression: Calibration and Prediction

Multivariate Regression: Influential Observations

Nonorthogonal MANOVA Designs

MANCOVA Designs

Stepdown Analysis

Repeated Measures Analysis

Extended Linear Hypotheses

DOUBLY MULTIVARIATE LINEAR MODEL

Introduction

Classical Model Development

Responsewise Model Development

The Multivariate Mixed Model

Double Multivariate and Mixed Models

RESTRICTED MGLM AND GROWTH CURVE MODEL

Introduction

Restricted Multivariate General Linear Model

The GMANOVA Model

Canonical Form of the GMANOVA Model

Restricted Nonorthogonal Three-Factor Factorial MANOVA

Restricted Intraclass Covariance Design

Growth Curve Analysis

Multiple Response Growth Curves

Single Growth Curve

SUR MODEL AND RESTRICTED GMANOVA MODEL

Introduction

MANOVA-GMANOVA Model

Tests of Fit

Sum of Profiles and CGMANOVA Models

SUR Model

Restricted GMANOVA Model

GMANOVA-SUR: One Population

GMANOVA-SUR: Several Populations

SUR Model

Two-Period Crossover Design with Changing Covariates

Repeated Measurements with Changing Covariates

MANOVA-GMANOVA Model

CGMANOVA Model

SIMULTANEOUS INFERENCE USING FINITE INTERSECTION TESTS

Introduction

Finite Intersection Tests

Finite Intersection Tests of Univariate Means

Finite Intersection Tests for Linear Models

Comparison of Some Tests of Univariate Means with the FIT Procedure

Analysis of Means Analysis

Simultaneous Test Procedures for Mean Vectors

Finite Intersection Test of Mean Vectors

Finite Intersection Test of Mean Vectors with Covariates

Summary

Univariate: One-Way ANOVA

Multivariate: One-Way MANOVA

Multivariate: One-Way MANCOVA

COMPUTING POWER FOR UNIVARIATE AND MULTIVARIATE GLM

Introduction

Power for Univariate GLMs

Estimating Power, Sample Size, and Effect Size for the GLM

Power and Sample Size Based on Interval Estimation

Calculating Power and Sample Size for Some Mixed Models

Power for Multivariate GLMs

Power and Effect Size Analysis for Univariate GLMs

Power and Sample Size Based on Interval Estimation

Power Analysis for Multivariate GLMs

TWO-LEVEL HIERARCHICAL LINEAR MODELS

Introduction

Two-Level Hierarchical Linear Models

Random Coefficient Model: One Population

Random Coefficient Model: Several Populations

Mixed Model Repeated Measures

Mixed Model Repeated Measures with Changing Covariates

Application: Two-Level Hierarchical Linear Models

INCOMPLETE REPEATED MEASUREMENT DATA

Introduction

Missing Mechanisms

FGLS Procedure

ML Procedure

Imputations

Repeated Measures Analysis

Repeated Measures with Changing Covariates

Random Coefficient Model

Growth Curve Analysis

STRUCTURAL EQUATION MODELING

Introduction

Model Notation

Estimation

Model Fit in Practice

Model Modification

Summary

Path Analysis

Confirmatory Factor Analysis

General SEM

REFERENCES

AUTHOR INDEX

SUBJECT INDEX

Name: Univariate and Multivariate General Linear Models: Theory and Applications with SAS, Second Edition (Hardback) – Chapman and Hall/CRC

Description: By Kevin Kim, Neil TimmSeries Editor: N. Balakrishnan. Reviewing the theory of the general linear model (GLM) using a general framework, Univariate and Multivariate General Linear Models: Theory and Applications with SAS, Second Edition presents analyses of simple and complex models, both univariate and...

Categories: Psychological Methods & Statistics, Statistical Theory & Methods, Quantitative Methods, Statistical Computing