Linear Mixed Models: A Practical Guide using Statistical Software,9781584884804

Linear Mixed Models: A Practical Guide using Statistical Software

by ;
Edition: 1st
ISBN13: 9781584884804
ISBN10: 1584884800
Format: Hardcover
Pub. Date: 2006-11-22
Publisher(s): Chapman & Hall/
  • Free Shipping Icon

    This Item Qualifies for Free Shipping!*

    *Excludes marketplace orders.

List Price: $104.95

Rent Textbook

Select for Price
Add to Cart
There was a problem. Please try again later.

New Textbook

We're Sorry
Sold Out

Used Textbook

We're Sorry
Sold Out

eTextbook

We're Sorry
Not Available

Buy from our Marketplace starting at $32.27

How Marketplace Works:

  • This item is offered by an independent seller and not shipped from our warehouse
  • Item details like edition and cover design may differ from our description; see seller's comments before ordering.
  • Sellers much confirm and ship within two business days; otherwise, the order will be cancelled and refunded.
  • Marketplace purchases cannot be returned to eCampus.com. Contact the seller directly for inquiries; if no response within two days, contact customer service.
  • Additional shipping costs apply to Marketplace purchases. Review shipping costs at checkout.

Summary

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 implementation, model interpretation, and visualization of clustered and longitudinal data. This easy-to-navigate reference details the use of procedures for fitting LMMs in five popular statistical software packages: SAS, SPSS, Stata, R/S-plus, and HLM.The authors introduce basic theoretical concepts, present a heuristic approach to fitting LMMs based on both general and hierarchical model specifications, develop the model-building process step-by-step, and demonstrate the estimation, testing, and interpretation of fixed-effect parameters and covariance parameters associated with random effects. These concepts are illustrated through examples using real-world data sets that enable comparisons of model fitting options and results across the software procedures. The book also gives an overview of important options and features available in each procedure.Making popular software procedures for fitting LMMs easy-to-use, this valuable resource shows how to perform LMM analyses and provides a clear explanation of mixed modeling techniques and theories.

Table of Contents

Introduction
1(8)
What Are Linear Mixed Models (LMMs)?
1(4)
Models with Random Effects for Clustered Data
2(1)
Models for Longitudinal or Repeated-Measures Data
2(1)
The Purpose of this Book
3(1)
Outline of Book Contents
4(1)
A Brief History of LMMs
5(4)
Key Theoretical Developments
5(2)
Key Software Developments
7(2)
Linear Mixed Models: An Overview
9(42)
Introduction
9(6)
Types and Structures of Data Sets
9(1)
Clustered Data vs. Repeated-Measures and Longitudinal Data
9(1)
Levels of Data
10(1)
Types of Factors and their Related Effects in an LMM
11(1)
Fixed Factors
12(1)
Random Factors
12(1)
Fixed Factors vs. Random Factors
12(1)
Fixed Effects vs. Random Effects
13(1)
Nested vs. Crossed Factors and their Corresponding Effects
13(2)
Specification of LMMs
15(7)
General Specification for an Individual Observation
15(1)
General Matrix Specification
16(3)
Covariance Structures for the D Matrix
19(1)
Covariance Structures for the Ri Matrix
20(1)
Group-Specific Covariance Parameter Values for the D and Ri Matrices
21(1)
Alternative Matrix Specification for All Subjects
21(1)
Hierarchical Linear Model (HLM) Specification of the LMM
22(1)
The Marginal Linear Model
22(3)
Specification of the Marginal Model
22(1)
The Marginal Model Implied by an LMM
23(2)
Estimation in LMMs
25(5)
Maximum Likelihood (ML) Estimation
25(1)
Special Case: Assume θ is Known
26(1)
General Case: Assume θ is Unknown
27(1)
REML Estimation
28(1)
REML vs. ML Estimation
28(2)
Computational Issues
30(3)
Algorithms for Likelihood Function Optimization
30(1)
Computational Problems with Estimation of Covariance Parameters
31(2)
Tools for Model Selection
33(6)
Basic Concepts in Model Selection
34(1)
Nested Models
34(1)
Hypotheses: Specification and Testing
34(1)
Likelihood Ratio Tests (LRTs)
34(1)
Likelihood Ratio Tests for Fixed-Effect Parameters
35(1)
Likelihood Ratio Tests for Covariance Parameters
35(1)
Alternative Tests
36(1)
Alternative Tests for Fixed-Effect Parameters
37(1)
Alternative Tests for Covariance Parameters
38(1)
Information Criteria
38(1)
Model-Building Strategies
39(2)
The Top-Down Strategy
39(1)
The Step-Up Strategy
40(1)
Checking Model Assumptions (Diagnostics)
41(2)
Residual Diagnostics
41(1)
Conditional Residuals
41(1)
Standardized and Studentized Residuals
42(1)
Influence Diagnostics
42(1)
Diagnostics for Random Effects
43(1)
Other Aspects of LMMs
43(6)
Predicting Random Effects: Best Linear Unbiased Predictors
43(2)
Intraclass Correlation Coefficients (ICCs)
45(1)
Problems with Model Specification (Aliasing)
46(2)
Missing Data
48(1)
Centering Covariates
49(1)
Chapter Summary
49(2)
Two-Level Models for Clustered Data: The Rat Pup Example
51(64)
Introduction
51(1)
The Rat Pup Study
51(7)
Study Description
51(3)
Data Summary
54(4)
Overview of the Rat Pup Data Analysis
58(8)
Analysis Steps
58(2)
Model Specification
60(1)
General Model Specification
60(2)
Hierarchical Model Specification
62(1)
Hypothesis Tests
63(3)
Analysis Steps in the Software Procedures
66(24)
SAS
66(8)
SPSS
74(3)
R
77(5)
Stata
82(3)
HLM
85(1)
Data Set Preparation
85(1)
Preparing the Multivariate Data Matrix (MDM) File
86(4)
Results of Hypothesis Tests
90(2)
Likelihood Ratio Tests for Random Effects
90(1)
Likelihood Ratio Tests for Residual Variance
91(1)
F-tests and Likelihood Ratio Tests for Fixed Effects
91(1)
Comparing Results across the Software Procedures
92(4)
Comparing Model 3.1 Results
92(2)
Comparing Model 3.2B Results
94(1)
Comparing Model 3.3 Results
95(1)
Interpreting Parameter Estimates in the Final Model
96(2)
Fixed-Effect Parameter Estimates
96(1)
Covariance Parameter Estimates
97(1)
Estimating the Intraclass Correlation Coefficients (ICCs)
98(2)
Calculating Predicted Values
100(2)
Litter-Specific (Conditional) Predicted Values
100(1)
Population-Averaged (Unconditional) Predicted Values
101(1)
Diagnostics for the Final Model
102(6)
Residual Diagnostics
102(1)
Conditional Residuals
102(2)
Conditional Studentized Residuals
104(2)
Influence Diagnostics
106(1)
Overall and Fixed-Effects Influence Diagnostics
106(1)
Influence on Covariance Parameters
107(1)
Software Notes
108(7)
Data Structure
108(1)
Syntax vs. Menus
109(1)
Heterogeneous Residual Variances for Level 2 Groups
109(1)
Display of the Marginal Covariance and Correlation Matrices
109(1)
Differences in Model Fit Criteria
109(1)
Differences in Tests for Fixed Effects
110(1)
Post-Hoc Comparisons of LS Means (Estimated Marginal Means)
111(1)
Calculation of Studentized Residuals and Influence Statistics
112(1)
Calculation of EBLUPs
112(1)
Tests for Covariance Parameters
112(1)
Refeernce Categories for Fixed Factors
112(3)
Three-Level Models for Clustered Data: The Classroom Example
115(60)
Introduction
115(2)
The Classroom Study
117(5)
Study Description
117(1)
Data Summary
118(1)
Data Set Preparation
119(1)
Preparing the Multivariate Data Matrix (MDM) File
119(3)
Overview of the Classroom Data Analysis
122(8)
Analysis Steps
122(3)
Model Specification
125(1)
General Model Specification
125(1)
Hierarchical Model Specification
126(2)
Hypothesis Tests
128(2)
Analysis Steps in the Software Procedures
130(23)
SAS
130(6)
SPSS
136(5)
R
141(3)
Stata
144(3)
HLM
147(6)
Results of Hypothesis Tests
153(2)
Likelihood Ratio Test for Random Effects
153(1)
Likelihood Ratio Tests and t-Tests for Fixed Effects
154(1)
Comparing Results across the Software Procedures
155(4)
Comparing Model 4.1 Results
155(1)
Comparing Model 4.2 Results
156(1)
Comparing Model 4.3 Results
157(2)
Comparing Model 4.4 Results
159(1)
Interpreting Parameter Estimates in the Final Model
159(3)
Fixed-Effect Parameter Estimates
159(2)
Covariance Parameter Estimates
161(1)
Estimating the Intraclass Correlation Coefficients (ICCs)
162(3)
Calculating Predicted Values
165(2)
Conditional and Marginal Predicted Values
165(1)
Plotting Predicted Values Using HLM
166(1)
Diagnostics for the Final Model
167(4)
Plots of the EBLUPs
167(2)
Residual Diagnostics
169(2)
Software Notes
171(4)
REML vs. ML Estimation
171(1)
Setting up Three-Level Models in HLM
171(1)
Calculation of Degrees of Freedom for t-Tests in HLM
171(1)
Analyzing Cases with Complete Data
172(1)
Miscellaneous Differences
173(2)
Models for Repeated-Measures Data: The Rat Brain Example
175(44)
Introduction
175(1)
The Rat Brain Study
176(4)
Study Description
176(2)
Data Summary
178(2)
Overview of the Rat Brain Data Analysis
180(7)
Analysis Steps
180(2)
Model Specification
182(1)
General Model Specification
182(2)
Hierarchical Model Specification
184(1)
Hypothesis Tests
185(2)
Analysis Steps in the Software Procedures
187(16)
SAS
187(3)
SPSS
190(3)
R
193(2)
Stata
195(3)
HLM
198(1)
Data Set Preparation
198(1)
Preparing the MDM File
199(4)
Results of Hypothesis Tests
203(1)
Likelihood Ratio Tests for Random Effects
203(1)
Likelihood Ratio Tests for Residual Variance
203(1)
F-Tests for Fixed Effects
204(1)
Comparing Results across the Software Procedures
204(3)
Comparing Model 5.1 Results
204(2)
Comparing Model 5.2 Results
206(1)
Interpreting Parameter Estimates in the Final Model
207(2)
Fixed-Effect Parameter Estimates
207(2)
Covariance Parameter Estimates
209(1)
The Implied Marginal Variance-Covariance Matrix for the Final Model
209(2)
Diagnostics for the Final Model
211(3)
Software Notes
214(1)
Heterogeneous Residual Variances for Level 1 Groups
214(1)
EBLUPs for Multiple Random Effects
214(1)
Other Analytic Approaches
214(5)
Kronecker Product for More Flexible Residual Covariance Structures
214(2)
Fitting the Marginal Model
216(1)
Repeated-Measures ANOVA
217(2)
Random Coefficient Models for Longitudinal Data: The Autism Example
219(54)
Introduction
219(1)
The Autism Study
220(5)
Study Description
220(1)
Data Summary
221(4)
Overview of the Autism Data Analysis
225(7)
Analysis Steps
226(1)
Model Specification
227(1)
General Model Specification
227(2)
Hierarchical Model Specification
229(1)
Hypothesis Tests
230(2)
Analysis Steps in the Software Procedures
232(19)
SAS
232(4)
SPSS
236(4)
R
240(3)
Stata
243(3)
HLM
246(1)
Data Set Preparation
246(1)
Preparing the MDM File
246(5)
Results of Hypothesis Tests
251(2)
Likelihood Ratio Test for Random Effects
251(1)
Likelihood Ratio Tests for Fixed Effects
252(1)
Comparing Results across the Software Procedures
253(1)
Comparing Model 6.1 Results
253(1)
Comparing Model 6.2 Results
253(1)
Comparing Model 6.3 Results
253(1)
Interpreting Parameter Estimates in the Final Model
254(5)
Fixed-Effect Parameter Estimates
256(1)
Covariance Parameter Estimates
257(2)
Calculating Predicted Values
259(4)
Marginal Predicted Values
259(2)
Conditional Predicted Values
261(2)
Diagnostics for the Final Model
263(5)
Residual Diagnostics
263(2)
Diagnostics for the Random Effects
265(1)
Observed and Predicted Values
266(2)
Software Note: Computational Problems with the D Matrix
268(1)
An Alternative Approach: Fitting the Marginal Model with an Unstructured Covariance Matrix
268(5)
Models for Clustered Longitudinal Data: The Dental Veneer Example
273(56)
Introduction
273(1)
The Dental Veneer Study
274(3)
Study Description
274(1)
Data Summary
275(2)
Overview of the Dental Veneer Data Analysis
277(10)
Analysis Steps
278(2)
Model Specification
280(1)
General Model Specification
280(4)
Hierarchical Model Specification
284(1)
Hypothesis Tests
285(2)
Analysis Steps in the Software Procedures
287(22)
SAS
287(6)
SPSS
293(3)
R
296(4)
Stata
300(4)
HLM
304(1)
Data Set Preparation
304(1)
Preparing the Multivariate Data Matrix (MDM) File
304(5)
Results of Hypothesis Tests
309(1)
Likelihood Ratio Tests for Random Effects
309(1)
Likelihood Ratio Tests for Residual Variance
310(1)
Likelihood Ratio Tests for Fixed Effects
310(1)
Comparing Results across the Software Procedures
310(5)
Comparing Model 7.1 Results
310(2)
Comparing Software Results for Model 7.2A, Model 7.2B, and Model 7.2C
312(2)
Comparing Model 7.3 Results
314(1)
Interpreting Parameter Estimates in the Final Model
315(2)
Fixed-Effect Parameter Estimates
315(1)
Covariance Parameter Estimates
316(1)
The Implied Marginal Variance-Covariance Matrix for the Final Model
317(2)
Diagnostics for the Final Model
319(4)
Residual Diagnostics
319(2)
Diagnostics for the Random Effects
321(2)
Software Notes
323(3)
ML vs. REML Estimation
323(1)
The Ability to Remove Random Effects from a Model
324(1)
The Ability to Fit Models with Different Residual Covariance Structures
324(1)
Aliasing of Covariance Parameters
324(1)
Displaying the Marginal Covariance and Correlation Matrices
325(1)
Miscellaneous Software Notes
325(1)
Other Analytic Approaches
326(3)
Modeling the Covariance Structure
326(1)
The Step-Up vs. Step-Down Approach to Model Building
327(1)
Alternative Uses of Baseline Values for the Dependent Variable
327(2)
Appendix A Statistical Software Resources
329(4)
Descriptions/Availability of Software Packages
329(1)
SAS
329(1)
SPSS
329(1)
R
329(1)
Stata
330(1)
HLM
330(1)
Useful Internet Links
330(3)
Appendix B Calculation of the Marginal Variance-Covariance Matrix
333(2)
Appendix C Acronyms/Abbreviations
335(2)
References 337(4)
Index 341

An electronic version of this book is available through VitalSource.

This book is viewable on PC, Mac, iPhone, iPad, iPod Touch, and most smartphones.

By purchasing, you will be able to view this book online, as well as download it, for the chosen number of days.

Digital License

You are licensing a digital product for a set duration. Durations are set forth in the product description, with "Lifetime" typically meaning five (5) years of online access and permanent download to a supported device. All licenses are non-transferable.

More details can be found here.

A downloadable version of this book is available through the eCampus Reader or compatible Adobe readers.

Applications are available on iOS, Android, PC, Mac, and Windows Mobile platforms.

Please view the compatibility matrix prior to purchase.