Hierarchical Linear Modeling : Guide and Applications

by G. David Garson

• ISBN13: 9781412998857
• ISBN10: 1412998859
• Format: Paperback
• Copyright: 2012-04-10
• Publisher: SAGE Publications, Inc

Summary

This book provides a brief, easy-to-read guide to implementing hierarchical linear modeling using three leading software platforms, followed by a set of original how-to applications articles following a standardard instructional format. The "guide" portion consists of five chapters by the editor, providing an overview of HLM, discussion of methodological assumptions, and parallel worked model examples in SPSS, SAS, and HLM software. The "applications" portion consists of ten contributions in which authors provide step by step presentations of how HLM is implemented and reported for introductory to intermediate applications.

Table of Contents

Preface	p. xiii
About the Editor	p. xv
About the Contributors	p. xvii
Guide	p. 1
Fundamentals of Hierarchical Linear and Multilevel Modeling	p. 3
Introduction	p. 3
Why Use Linear Mixed/Hierarchical Linear? Multilevel Modeling?	p. 5
Types of Linear Mixed Models	p. 7
Generalized Linear Mixed Models	p. 12
Repeated Measures, Longitudinal and Growth Models	p. 18
Repeated Measures	p. 18
Longitudinal and Growth Models	p. 19
Multivariate Models	p. 20
Cross-Classified Models	p. 21
Summary	p. 23
Preparing to Analyze Multilevel Data	p. 27
Testing if Linear Mixed Modeling Is Needed for One's Data	p. 27
Types of Estimation	p. 28
Converging on a Solution in Linear Mixed Modeling	p. 33
Meeting Other Assumptions of Linear Mixed Modeling	p. 36
Covariance Structure Types	p. 40
Selecting the Best Covariance Structure Assumption	p. 44
Comparing Model Goodness of Fit With Information Theory Measures	p. 44
Comparing Models With Likelihood Ratio Tests	p. 45
Effect Size in Linear Mixed Modeling	p. 47
Summary	p. 48
Introductory Guide to HLM With HLM 7 Software	p. 55
HLM Software	p. 55
Entering Data Into HLM 7	p. 56
Input Method 1: Separate Files for Each Level	p. 56
Input Method 2: Using a Single Statistics Program Data File	p. 57
Making the MDM File	p. 57
The Null Model in HLM 7	p. 61
A Random Coefficients Regression Model in HLM 7	p. 67
Homogenous and Heterogeneous Full Random Coefficients Models	p. 72
Three-Level Hierarchical Linear Models	p. 81
Model A	p. 84
Model B	p. 85
Model C	p. 87
Graphics in HLM 7	p. 92
Summary	p. 95
Introductory Guide to HLM With SAS Software	p. 97
Entering Data Into SAS	p. 97
Direct Data Entry Using VIEWTABLE	p. 97
Data Entry Using the SAS Import Wizard	p. 99
Data Entry Using SAS Commands	p. 100
The Null Model in SAS PROC MIXED	p. 101
A Random Coefficients Regression Model in SAS 9.2	p. 104
A Full Random Coefficients Model	p. 106
Three-Level Hierarchical Linear Models	p. 110
Model A	p. 111
Model B	p. 112
Model C	p. 115
Summary	p. 118
Introductory Guide to HLM With SPSS Software	p. 121
The Null Model in SPSS	p. 121
A Random Coefficients Regression Model in SPSS 19	p. 128
A Full Random Coefficients Model	p. 133
Three-Level Hierarchical Linear Models	p. 137
Model A	p. 137
Model B	p. 139
Model C	p. 141
Summary	p. 146
Introductory And Intermediate Applications	p. 147
A Random Intercepts Model of Part-Time Employment and Standardized Testing Using SPSS	p. 149
The Null Linear Mixed Model	p. 150
Interclass Correlation Coefficient (ICC)	p. 151
One-Way ANCOVA With Random Effects	p. 152
Sample	p. 152
Software and Procedure	p. 153
Analyzing the Data	p. 153
Output and Analysis	p. 156
Traditional Ordinary Least Squares (OLS) Approach	p. 156
Linear Mixed Model (LMM) Approach	p. 158
Conclusion	p. 162
Sample Write-Up	p. 163
A Random Intercept Regression Model Using HLM: Cohort Analysis of a Mathematics Curriculum for Mathematically Promising Students	p. 167
Sample	p. 169
Software and Procedure	p. 171
Analyzing the Data	p. 171
Output and Analysis	p. 175
Concluding Results	p. 180
Summary	p. 181
Random Coefficients Modeling With HLM: Assessment Practices and the Achievement Gap in Schools	p. 183
Statistical Formulations	p. 185
An Application of the RC Model: Assessment Practices and the Achievement Gap in Schools	p. 187
Sample	p. 188
Software and Procedure	p. 190
Analyzing the Data	p. 191
Output and Analysis	p. 193
Conclusion	p. 199
Baseline Model	p. 199
Student Model	p. 200
School Model	p. 201
Emotional Reactivity to Daily Stressors Using a Random Coefficients Model With SAS PROC Mixed: A Repeated Measures Analysis	p. 205
Sample and Procedure	p. 206
Measures	p. 206
Equations	p. 207
SAS Commands	p. 208
Structural Specification	p. 208
Model Specification	p. 209
Unconditional Model Output	p. 210
Interpretation of Unconditional Model Results	p. 212
Random Coefficients Regression Model	p. 212
Random Coefficients Regression Output	p. 213
Interpretation of Random Coefficients Regression Results	p. 217
Conclusion	p. 217
Hierachical Linear Modeling of Growth Curve Trajectories Using HLM	p. 219
The Challenges Posed by Longitudinal Data	p. 219
The Hierarchical Modeling Approach to Longitudinal Data	p. 221
Application: Growth Trajectories of U.S. Country Robbery Rates	p. 224
Exploratory Analyses	p. 225
Estimation of the Linear Hierachical Model	p. 226
Modeling the Variability of the Level 1 Coefficients	p. 232
Residual Analysis	p. 236
Estimating a Model for Counts	p. 239
Assessment of the Methods	p. 243
A Piecewise Growth Model Using HLM 7 to Examine Change in Teaching Practices Following a Science Teacher Professional Development Intervention	p. 249
Sample	p. 250
Software and Procedure	p. 252
Analyzing the Data	p. 254
Preparing the Data	p. 254
HLM Data Analyses	p. 255
Output and Analysis	p. 257
Examination of Time	p. 257
School as a Level 2 Predictor	p. 262
Alternative Error Covariance Structures	p. 264
Conclusion	p. 269
Discussion of Results	p. 269
Limitations of the Study	p. 270
Studying Reaction to Repeated Life Events With Discontinuous Change Models Using HLM	p. 273
Sample	p. 276
Software and Procedure	p. 277
Analyzing the Data	p. 277
Preparing the Data	p. 278
Analytic Model	p. 279
Output and Analysis	p. 283
Conclusion	p. 287
A Cross-Classified Multilevel Model for First-Year College Natural Science Performance Using SAS	p. 291
Sample	p. 292
Predictors	p. 293
Software and Procedure	p. 294
Analyzing the Data	p. 297
Evaluating Residual Variability Due to the Cross-Classified Levels	p. 297
Specifying a Covariance Structure	p. 299
Building the Student-Level Model	p. 299
Building the College- and High School-Level Models	p. 300
Evaluating Model Fit	p. 300
Output and Analysis	p. 301
Evaluating Residual Variability Due to the Cross-Classified Levels	p. 301
Specifying a Covariance Structure	p. 302
Building the Student-Level Model	p. 303
Evaluating Model Fit	p. 305
Evaluating Residual Variability in the Final Model	p. 305
Conclusion	p. 306
Interpreting Fixed Parameter Estimates	p. 306
Cross-Classified Multilevel Models Using Stata: How Important Are Schools and Neighborhoods for Students' Educational Attainment?	p. 311
Sample	p. 312
Software and Procedure	p. 315
Analyzing the Data	p. 316
Output and Analysis	p. 319
Conclusion	p. 330
Predicting Future Events From Longitudinal Data With Multivariate Hierarchical Models and Bayes' Theorem Using SAS	p. 333
Sample	p. 336
Software and Procedure	p. 337
Analyzing the Data	p. 344
Output and Analysis	p. 344
Conclusion	p. 350
Author Index	p. 353
Subject Index	p. 357
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