Univariate and Multivariate General Linear Models

Univariate and Multivariate General Linear Models : Theory and Applications with SAS

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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.show more

Product details

  • Hardback | 549 pages
  • 160 x 226.1 x 38.1mm | 884.52g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • Revised
  • 2nd Revised edition
  • 7 black & white illustrations, 53 black & white tables
  • 158488634X
  • 9781584886341
  • 2,389,661

Table of 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 INDEXshow more