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Linear Mixed Models: A Practical Guide Using Statistical Software Book

Linear Mixed Models: A Practical Guide Using Statistical Software
Linear Mixed Models: A Practical Guide Using Statistical Software, Simplifying the often confusing array of software programs for fitting linear mixed models (LMMs), Linear Mixed Models: A Practical Guide Using Statistical Software provides a basic introduction to primary concepts, notation, software implementatio, Linear Mixed Models: A Practical Guide Using Statistical Software has a rating of 4.5 stars
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Linear Mixed Models: A Practical Guide Using Statistical Software, Simplifying the often confusing array of software programs for fitting linear mixed models (LMMs), Linear Mixed Models: A Practical Guide Using Statistical Software provides a basic introduction to primary concepts, notation, software implementatio, Linear Mixed Models: A Practical Guide Using Statistical Software
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  • Linear Mixed Models: A Practical Guide Using Statistical Software
  • Written by author Brady West
  • Published by Taylor & Francis, Inc., January 2007
  • Simplifying the often confusing array of software programs for fitting linear mixed models (LMMs), Linear Mixed Models: A Practical Guide Using Statistical Software provides a basic introduction to primary concepts, notation, software implementatio
  • Simplifying the often confusing array of software programs for fitting linear mixed models (LMMs), Linear Mixed Models: A Practical Guide Using Statistical Software provides a basic introduction to primary concepts, notation, software implement
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Introduction     1
What Are Linear Mixed Models (LMMs)?     1
Models with Random Effects for Clustered Data     2
Models for Longitudinal or Repeated-Measures Data     2
The Purpose of this Book     3
Outline of Book Contents     4
A Brief History of LMMs     5
Key Theoretical Developments     5
Key Software Developments     7
Linear Mixed Models: An Overview     9
Introduction     9
Types and Structures of Data Sets     9
Clustered Data vs. Repeated-Measures and Longitudinal Data     9
Levels of Data     10
Types of Factors and their Related Effects in an LMM     11
Fixed Factors     12
Random Factors     12
Fixed Factors vs. Random Factors     12
Fixed Effects vs. Random Effects     13
Nested vs. Crossed Factors and their Corresponding Effects     13
Specification of LMMs     15
General Specification for an Individual Observation     15
General Matrix Specification     16
Covariance Structures for the D Matrix     19
Covariance Structures for the R[subscript i] Matrix     20
Group-SpecificCovariance Parameter Values for the D and R[subscript i] Matrices     21
Alternative Matrix Specification for All Subjects     21
Hierarchical Linear Model (HLM) Specification of the LMM     22
The Marginal Linear Model     22
Specification of the Marginal Model     22
The Marginal Model Implied by an LMM     23
Estimation in LMMs     25
Maximum Likelihood (ML) Estimation     25
Special Case: Assume [theta] is Known     26
General Case: Assume [theta] is Unknown     27
REML Estimation     28
REML vs. ML Estimation     28
Computational Issues     30
Algorithms for Likelihood Function Optimization     30
Computational Problems with Estimation of Covariance Parameters     31
Tools for Model Selection     33
Basic Concepts in Model Selection     34
Nested Models     34
Hypotheses: Specification and Testing     34
Likelihood Ratio Tests (LRTs)     34
Likelihood Ratio Tests for Fixed-Effect Parameters     35
Likelihood Ratio Tests for Covariance Parameters     35
Alternative Tests     36
Alternative Tests for Fixed-Effect Parameters      37
Alternative Tests for Covariance Parameters     38
Information Criteria     38
Model-Building Strategies     39
The Top-Down Strategy     39
The Step-Up Strategy     40
Checking Model Assumptions (Diagnostics)     41
Residual Diagnostics     41
Conditional Residuals     41
Standardized and Studentized Residuals     42
Influence Diagnostics     42
Diagnostics for Random Effects     43
Other Aspects of LMMs     43
Predicting Random Effects: Best Linear Unbiased Predictors     43
Intraclass Correlation Coefficients (ICCs)     45
Problems with Model Specification (Aliasing)     46
Missing Data     48
Centering Covariates     49
Chapter Summary     49
Two-Level Models for Clustered Data: The Rat Pup Example     51
Introduction     51
The Rat Pup Study     51
Study Description     51
Data Summary     54
Overview of the Rat Pup Data Analysis     58
Analysis Steps     58
Model Specification     60
General Model Specification     60
Hierarchical Model Specification     63
Hypothesis Tests     63
Analysis Steps in the Software Procedures     66
SAS     66
SPSS     74
R     77
Stata     82
HLM     85
Data Set Preparation     85
Preparing the Multivariate Data Matrix (MDM) File     86
Results of Hypothesis Tests     90
Likelihood Ratio Tests for Random Effects     90
Likelihood Ratio Tests for Residual Variance     91
F-tests and Likelihood Ratio Tests for Fixed Effects     91
Comparing Results across the Software Procedures     92
Comparing Model 3.1 Results     92
Comparing Model 3.2B Results     94
Comparing Model 3.3 Results     95
Interpreting Parameter Estimates in the Final Model     96
Fixed-Effect Parameter Estimates     96
Covariance Parameter Estimates     97
Estimating the Intraclass Correlation Coefficients (ICCs)     98
Calculating Predicted Values     100
Litter-Specific (Conditional) Predicted Values     100
Population-Averaged (Unconditional) Predicted Values     101
Diagnostics for the Final Model     102
Residual Diagnostics     102
Conditional Residuals     102
Conditional Studentized Residuals     104
Influence Diagnostics     106
Overall and Fixed-Effects Influence Diagnostics     106
Influence on Covariance Parameters     107
Software Notes     108
Data Structure     108
Syntax vs. Menus     109
Heterogeneous Residual Variances for Level 2 Groups     109
Display of the Marginal Covariance and Correlation Matrices     109
Differences in Model Fit Criteria     109
Differences in Tests for Fixed Effects     110
Post-Hoc Comparisons of LS Means (Estimated Marginal Means)     111
Calculation of Studentized Residuals and Influence Statistics     112
Calculation of EBLUPs     112
Tests for Covariance Parameters     112
Refeernce Categories for Fixed Factors     112
Three-Level Models for Clustered Data: The Classroom Example     115
Introduction     115
The Classroom Study     117
Study Description     117
Data Summary     118
Data Set Preparation     119
Preparing the Multivariate Data Matrix (MDM) File     119
Overview of the Classroom Data Analysis     122
Analysis Steps     122
Model Specification     125
General Model Specification     125
Hierarchical Model Specification     126
Hypothesis Tests     128
Analysis Steps in the Software Procedures     130
SAS     130
SPSS     136
R     141
Stata     144
HLM     147
Results of Hypothesis Tests     153
Likelihood Ratio Test for Random Effects     153
Likelihood Ratio Tests and t-Tests for Fixed Effects     154
Comparing Results across the Software Procedures     155
Comparing Model 4.1 Results     155
Comparing Model 4.2 Results     156
Comparing Model 4.3 Results     157
Comparing Model 4.4 Results     159
Interpreting Parameter Estimates in the Final Model     159
Fixed-Effect Parameter Estimates     159
Covariance Parameter Estimates     161
Estimating the Intraclass Correlation Coefficients (ICCs)     162
Calculating Predicted Values     165
Conditional and Marginal Predicted Values     165
Plotting Predicted Values Using HLM      166
Diagnostics for the Final Model     167
Plots of the EBLUPs     167
Residual Diagnostics     169
Software Notes     171
REML vs. ML Estimation     171
Setting up Three-Level Models in HLM     171
Calculation of Degrees of Freedom for t-Tests in HLM     171
Analyzing Cases with Complete Data     172
Miscellaneous Differences     173
Models for Repeated-Measures Data: The Rat Brain Example     175
Introduction     175
The Rat Brain Study     176
Study Description     176
Data Summary     178
Overview of the Rat Brain Data Analysis     180
Analysis Steps     180
Model Specification     182
General Model Specification     182
Hierarchical Model Specification     184
Hypothesis Tests     185
Analysis Steps in the Software Procedures     187
SAS     187
SPSS     190
R     193
Stata     195
HLM     198
Data Set Preparation     198
Preparing the MDM File     199
Results of Hypothesis Tests      203
Likelihood Ratio Tests for Random Effects     203
Likelihood Ratio Tests for Residual Variance     203
F-Tests for Fixed Effects     204
Comparing Results across the Software Procedures     204
Comparing Model 5.1 Results     204
Comparing Model 5.2 Results     206
Interpreting Parameter Estimates in the Final Model     207
Fixed-Effect Parameter Estimates     207
Covariance Parameter Estimates     209
The Implied Marginal Variance-Covariance Matrix for the Final Model     209
Diagnostics for the Final Model     211
Software Notes     214
Heterogeneous Residual Variances for Level 1 Groups     214
EBLUPs for Multiple Random Effects     214
Other Analytic Approaches     214
Kronecker Product for More Flexible Residual Covariance Structures     214
Fitting the Marginal Model     216
Repeated-Measures ANOVA     217
Random Coefficient Models for Longitudinal Data: The Autism Example     219
Introduction     219
The Autism Study     220
Study Description     220
Data Summary     221
Overview of the Autism Data Analysis     225
Analysis Steps     226
Model Specification     227
General Model Specification     227
Hierarchical Model Specification     229
Hypothesis Tests     230
Analysis Steps in the Software Procedures     232
SAS     232
SPSS     236
R     240
Stata     243
HLM     246
Data Set Preparation     246
Preparing the MDM File     246
Results of Hypothesis Tests     251
Likelihood Ratio Test for Random Effects     251
Likelihood Ratio Tests for Fixed Effects     252
Comparing Results across the Software Procedures     253
Comparing Model 6.1 Results     253
Comparing Model 6.2 Results     253
Comparing Model 6.3 Results     253
Interpreting Parameter Estimates in the Final Model     254
Fixed-Effect Parameter Estimates     256
Covariance Parameter Estimates     257
Calculating Predicted Values     259
Marginal Predicted Values     259
Conditional Predicted Values     261
Diagnostics for the Final Model     263
Residual Diagnostics     263
Diagnostics for the Random Effects     265
Observed and Predicted Values     266
Software Note: Computational Problems with the D Matrix     268
An Alternative Approach: Fitting the Marginal Model with an Unstructured Covariance Matrix     268
Models for Clustered Longitudinal Data: The Dental Veneer Example     273
Introduction     273
The Dental Veneer Study     274
Study Description     274
Data Summary     275
Overview of the Dental Veneer Data Analysis     277
Analysis Steps     278
Model Specification     280
General Model Specification     280
Hierarchical Model Specification     284
Hypothesis Tests     285
Analysis Steps in the Software Procedures     287
SAS     287
SPSS     293
R     296
Stata     300
HLM     304
Data Set Preparation     304
Preparing the Multivariate Data Matrix (MDM) File     304
Results of Hypothesis Tests     309
Likelihood Ratio Tests for Random Effects     309
Likelihood Ratio Tests for Residual Variance     310
Likelihood Ratio Tests for Fixed Effects      310
Comparing Results across the Software Procedures     310
Comparing Model 7.1 Results     310
Comparing Software Results for Model 7.2A, Model 7.2B, and Model 7.2C     312
Comparing Model 7.3 Results     314
Interpreting Parameter Estimates in the Final Model     315
Fixed-Effect Parameter Estimates     315
Covariance Parameter Estimates     316
The Implied Marginal Variance-Covariance Matrix for the Final Model     317
Diagnostics for the Final Model     319
Residual Diagnostics     319
Diagnostics for the Random Effects     321
Software Notes     323
ML vs. REML Estimation     323
The Ability to Remove Random Effects from a Model     324
The Ability to Fit Models with Different Residual Covariance Structures     324
Aliasing of Covariance Parameters     324
Displaying the Marginal Covariance and Correlation Matrices     325
Miscellaneous Software Notes     325
Other Analytic Approaches     326
Modeling the Covariance Structure     326
The Step-Up vs. Step-Down Approach to Model Building     327
Alternative Uses of Baseline Values for the Dependent Variable      327
Statistical Software Resources     329
Descriptions/Availability of Software Packages     329
SAS     329
SPSS     329
R     329
Stata     330
HLM     330
Useful Internet Links     330
Calculation of the Marginal Variance-Covariance Matrix     333
Acronyms/Abbreviations     335
References     337
Index     341


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Linear Mixed Models: A Practical Guide Using Statistical Software, Simplifying the often confusing array of software programs for fitting linear mixed models (LMMs), Linear Mixed Models: A Practical Guide Using Statistical Software provides a basic introduction to primary concepts, notation, software implementatio, Linear Mixed Models: A Practical Guide Using Statistical Software

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Linear Mixed Models: A Practical Guide Using Statistical Software, Simplifying the often confusing array of software programs for fitting linear mixed models (LMMs), Linear Mixed Models: A Practical Guide Using Statistical Software provides a basic introduction to primary concepts, notation, software implementatio, Linear Mixed Models: A Practical Guide Using Statistical Software

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Linear Mixed Models: A Practical Guide Using Statistical Software, Simplifying the often confusing array of software programs for fitting linear mixed models (LMMs), Linear Mixed Models: A Practical Guide Using Statistical Software provides a basic introduction to primary concepts, notation, software implementatio, Linear Mixed Models: A Practical Guide Using Statistical Software

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