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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

Series: Statistics: A Series of Textbooks and Monographs

Purchasing Options:

  • Add to CartHardback: $99.95
    978-1-58488-634-1
    October 10th 2006

Description

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

  • Two chapters on finite intersection tests and power analysis that illustrates the experimental GLMPOWER procedure

  • Expanded theory of unrestricted general linear, multivariate general linear, SUR, and restricted GMANOVA models to comprise recent developments

  • Expanded material on missing data to include multiple imputation and the EM algorithm

  • Applications of MI, MIANALYZE, TRANSREG, and CALIS procedures

    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.

  • Reviews

    "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

    Contents

    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: Regression Analysis and Multivariate Statistics, Statistical Theory & Methods, Quantitative Methods, Statistics & Computing