Hierarchical Linear Modeling : Guide and Applications

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  • Format: Paperback
  • Copyright: 2012-04-10
  • Publisher: SAGE Publications, Inc
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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

Prefacep. xiii
About the Editorp. xv
About the Contributorsp. xvii
Guidep. 1
Fundamentals of Hierarchical Linear and Multilevel Modelingp. 3
Introductionp. 3
Why Use Linear Mixed/Hierarchical Linear? Multilevel Modeling?p. 5
Types of Linear Mixed Modelsp. 7
Generalized Linear Mixed Modelsp. 12
Repeated Measures, Longitudinal and Growth Modelsp. 18
Repeated Measuresp. 18
Longitudinal and Growth Modelsp. 19
Multivariate Modelsp. 20
Cross-Classified Modelsp. 21
Summaryp. 23
Preparing to Analyze Multilevel Datap. 27
Testing if Linear Mixed Modeling Is Needed for One's Datap. 27
Types of Estimationp. 28
Converging on a Solution in Linear Mixed Modelingp. 33
Meeting Other Assumptions of Linear Mixed Modelingp. 36
Covariance Structure Typesp. 40
Selecting the Best Covariance Structure Assumptionp. 44
Comparing Model Goodness of Fit With Information Theory Measuresp. 44
Comparing Models With Likelihood Ratio Testsp. 45
Effect Size in Linear Mixed Modelingp. 47
Summaryp. 48
Introductory Guide to HLM With HLM 7 Softwarep. 55
HLM Softwarep. 55
Entering Data Into HLM 7p. 56
Input Method 1: Separate Files for Each Levelp. 56
Input Method 2: Using a Single Statistics Program Data Filep. 57
Making the MDM Filep. 57
The Null Model in HLM 7p. 61
A Random Coefficients Regression Model in HLM 7p. 67
Homogenous and Heterogeneous Full Random Coefficients Modelsp. 72
Three-Level Hierarchical Linear Modelsp. 81
Model Ap. 84
Model Bp. 85
Model Cp. 87
Graphics in HLM 7p. 92
Summaryp. 95
Introductory Guide to HLM With SAS Softwarep. 97
Entering Data Into SASp. 97
Direct Data Entry Using VIEWTABLEp. 97
Data Entry Using the SAS Import Wizardp. 99
Data Entry Using SAS Commandsp. 100
The Null Model in SAS PROC MIXEDp. 101
A Random Coefficients Regression Model in SAS 9.2p. 104
A Full Random Coefficients Modelp. 106
Three-Level Hierarchical Linear Modelsp. 110
Model Ap. 111
Model Bp. 112
Model Cp. 115
Summaryp. 118
Introductory Guide to HLM With SPSS Softwarep. 121
The Null Model in SPSSp. 121
A Random Coefficients Regression Model in SPSS 19p. 128
A Full Random Coefficients Modelp. 133
Three-Level Hierarchical Linear Modelsp. 137
Model Ap. 137
Model Bp. 139
Model Cp. 141
Summaryp. 146
Introductory And Intermediate Applicationsp. 147
A Random Intercepts Model of Part-Time Employment and Standardized Testing Using SPSSp. 149
The Null Linear Mixed Modelp. 150
Interclass Correlation Coefficient (ICC)p. 151
One-Way ANCOVA With Random Effectsp. 152
Samplep. 152
Software and Procedurep. 153
Analyzing the Datap. 153
Output and Analysisp. 156
Traditional Ordinary Least Squares (OLS) Approachp. 156
Linear Mixed Model (LMM) Approachp. 158
Conclusionp. 162
Sample Write-Upp. 163
A Random Intercept Regression Model Using HLM: Cohort Analysis of a Mathematics Curriculum for Mathematically Promising Studentsp. 167
Samplep. 169
Software and Procedurep. 171
Analyzing the Datap. 171
Output and Analysisp. 175
Concluding Resultsp. 180
Summaryp. 181
Random Coefficients Modeling With HLM: Assessment Practices and the Achievement Gap in Schoolsp. 183
Statistical Formulationsp. 185
An Application of the RC Model: Assessment Practices and the Achievement Gap in Schoolsp. 187
Samplep. 188
Software and Procedurep. 190
Analyzing the Datap. 191
Output and Analysisp. 193
Conclusionp. 199
Baseline Modelp. 199
Student Modelp. 200
School Modelp. 201
Emotional Reactivity to Daily Stressors Using a Random Coefficients Model With SAS PROC Mixed: A Repeated Measures Analysisp. 205
Sample and Procedurep. 206
Measuresp. 206
Equationsp. 207
SAS Commandsp. 208
Structural Specificationp. 208
Model Specificationp. 209
Unconditional Model Outputp. 210
Interpretation of Unconditional Model Resultsp. 212
Random Coefficients Regression Modelp. 212
Random Coefficients Regression Outputp. 213
Interpretation of Random Coefficients Regression Resultsp. 217
Conclusionp. 217
Hierachical Linear Modeling of Growth Curve Trajectories Using HLMp. 219
The Challenges Posed by Longitudinal Datap. 219
The Hierarchical Modeling Approach to Longitudinal Datap. 221
Application: Growth Trajectories of U.S. Country Robbery Ratesp. 224
Exploratory Analysesp. 225
Estimation of the Linear Hierachical Modelp. 226
Modeling the Variability of the Level 1 Coefficientsp. 232
Residual Analysisp. 236
Estimating a Model for Countsp. 239
Assessment of the Methodsp. 243
A Piecewise Growth Model Using HLM 7 to Examine Change in Teaching Practices Following a Science Teacher Professional Development Interventionp. 249
Samplep. 250
Software and Procedurep. 252
Analyzing the Datap. 254
Preparing the Datap. 254
HLM Data Analysesp. 255
Output and Analysisp. 257
Examination of Timep. 257
School as a Level 2 Predictorp. 262
Alternative Error Covariance Structuresp. 264
Conclusionp. 269
Discussion of Resultsp. 269
Limitations of the Studyp. 270
Studying Reaction to Repeated Life Events With Discontinuous Change Models Using HLMp. 273
Samplep. 276
Software and Procedurep. 277
Analyzing the Datap. 277
Preparing the Datap. 278
Analytic Modelp. 279
Output and Analysisp. 283
Conclusionp. 287
A Cross-Classified Multilevel Model for First-Year College Natural Science Performance Using SASp. 291
Samplep. 292
Predictorsp. 293
Software and Procedurep. 294
Analyzing the Datap. 297
Evaluating Residual Variability Due to the Cross-Classified Levelsp. 297
Specifying a Covariance Structurep. 299
Building the Student-Level Modelp. 299
Building the College- and High School-Level Modelsp. 300
Evaluating Model Fitp. 300
Output and Analysisp. 301
Evaluating Residual Variability Due to the Cross-Classified Levelsp. 301
Specifying a Covariance Structurep. 302
Building the Student-Level Modelp. 303
Evaluating Model Fitp. 305
Evaluating Residual Variability in the Final Modelp. 305
Conclusionp. 306
Interpreting Fixed Parameter Estimatesp. 306
Cross-Classified Multilevel Models Using Stata: How Important Are Schools and Neighborhoods for Students' Educational Attainment?p. 311
Samplep. 312
Software and Procedurep. 315
Analyzing the Datap. 316
Output and Analysisp. 319
Conclusionp. 330
Predicting Future Events From Longitudinal Data With Multivariate Hierarchical Models and Bayes' Theorem Using SASp. 333
Samplep. 336
Software and Procedurep. 337
Analyzing the Datap. 344
Output and Analysisp. 344
Conclusionp. 350
Author Indexp. 353
Subject Indexp. 357
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