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Tables of Contents for Latent Variable Models and Factor Analysis
Chapter/Section Title
Page #
Page Count
Preface
xi
 
Software and Data
xv
 
Basic Ideas and Examples
1
16
The Statistical Problem
1
2
A Theoretical Framework
3
4
Another Approach
7
2
Principal Components
9
1
The Historical Context
10
4
Closely Related Fields in Statistics
14
3
The General Linear Latent Variable Model
17
24
Introduction
17
1
The Model
17
1
Some Properties of the Model
18
1
A Special Case
19
1
The Sufficiency Principle
20
1
Principal Special Cases
21
3
Fitting the Models
24
2
Fitting by Maximum Likelihood
26
1
Rotation
26
2
Interpretation
28
2
Sampling Error of Parameter Estimates
30
1
The Prior Distribution
31
2
Posterior Analysis
33
3
A Further Note on the Prior
36
2
Bayesian and Psychometric Approaches to Inference
38
3
The Normal Linear Factor Model
41
36
The Model
41
1
Some Distributional Properties
42
1
Constraints on the Model
43
1
Maximum Likelihood Estimation
44
3
Maximum Likelihood Estimation by the E-M Algorithm
47
2
Sampling Variation of Estimators
49
3
Goodness of Fit and Choice of q
52
1
Fitting without Normality Assumptions: Least Squares Methods
53
3
Approximate Methods for Estimating ψ
56
1
Goodness of Fit and Choice of q for Least Squares Methods
57
1
Further Estimation Issues
58
5
Rotation and Related Matters
63
2
Posterior Analysis: The Normal Case
65
1
Posterior Analysis: Least Squares
66
2
Posterior Analysis: a Reliability Approach
68
1
Examples
68
9
Binary Data: Latent Trait Models
77
26
Preliminaries
77
1
The Logit/Normit Model
78
2
Fitting the Model: The E-M Algorithm
80
3
Divergence of the Estimation Algorithm
83
1
Sampling Properties of the Maximum Likelihood Estimators
84
1
Approximate Maximum Likelihood Estimators
85
1
The Normit/Normit Model
86
1
The Equivalence of the Response Function and Underlying Variable Approaches
87
2
Fitting the Normit/Normit Model
89
1
Generalized Least Squares Methods
89
2
Goodness of Fit
91
1
Posterior Analysis
92
2
Examples
94
9
Polytomous Data: Latent Trait Models
103
30
Introduction
103
1
A Response Function Model Based on the Sufficiency Principle
103
5
Rotation
108
1
Ordering of Categories
109
1
Maximum Likelihood Estimation of the Polytomous Logit Model
109
1
An Approximation to the Likelihood
110
7
Binary Data as a Special Case
117
2
An Underlying Variable Model
119
2
An Alternative Underlying Variable Model
121
4
Posterior Analysis
125
1
Further Observations
125
8
Latent Class Models
133
24
Introduction
133
1
The Latent Class Model with Binary Manifest Variables
134
1
The Latent Class Model for Binary Data as a Latent Trait Model
135
2
Maximum Likelihood Estimation
137
3
Standard Errors
140
1
Posterior Analysis of the Latent Class Model with Binary Manifest Variables
141
1
Goodness of Fit
141
1
Examples for Binary Data
142
3
Latent Class Models with Unordered Polytomous Manifest Variables
145
1
Maximum Likelihood Estimation
146
2
Examples for Unordered Polytomous Data
148
2
Latent Class Models with Ordered Polytomous Manifest Variables
150
1
Identifiability
150
1
Latent Class Models with Metrical Manifest Variables
151
1
Maximum Likelihood Estimation
152
1
Other Methods
153
2
Allocation to Categories
155
1
Models with Ordered Latent Classes
156
1
Models and Methods for Manifest Variables of Mixed Type
157
18
Introduction
157
1
Principal Results
158
1
The Binomial Distribution
159
1
The Poisson Distribution
159
1
The Gamma Distribution
160
1
Maximum Likelihood Estimation
160
6
Sampling Properties and Goodness of Fit
166
1
Mixed Latent Class Models
167
1
Posterior Analysis
168
1
Examples
169
4
Ordered Categorical Variables and Other Generalizations
173
2
Relationships between Latent Variables
175
16
Scope
175
1
Correlated Latent Variables
175
1
Procrustes Methods
176
1
Sources of Prior Knowledge
177
1
Linear Structural Relations Models
177
3
The Lisrel Model
180
1
Structural Relationships in a General Setting
181
1
Generalizations of the Lisrel Model
182
1
Examples of Models which are Indistinguishable
183
2
Alternative Approaches to the Relationships between Latent Variables
185
1
Estimation of Correlations and Regressions between Latent Variables
186
2
Implications for Analysis
188
3
Bibliography
191
15
Author Index
206
3
Subject Index
209