Latent Variable Models and Factor Analysis,9780340692431

Latent Variable Models and Factor Analysis

by ;
Edition: 2nd
ISBN13: 9780340692431
ISBN10: 034069243X
Format: Hardcover
Pub. Date: 1999-07-29
Publisher(s): Hodder Education Publishers
  • Free Shipping Icon

    This Item Qualifies for Free Shipping!*

    *Excludes marketplace orders.

List Price: $99.75

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 $90.30

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

Hitherto latent variable modelling has hovered on the fringes of the statistical mainstream but if the purpose of statistics is to deal with real problems, there is every reason for it to move closer to centre stage. In the social sciences especially, latent variables are common and if they are to be handled in a truly scientific manner, statistical theory must be developed to include them. This book aims to show how that should be done.This second edition is a complete re-working of the book of the same name which appeared in the Griffin's Statistical Monographs in 1987. Since then there has been a surge of interest in latent variable methods which has necessitated a radical revision of the material but the prime object of the book remains the same. It provides a unified and coherent treatment of the field from a statistical perspective. This is achieved by setting up a sufficiently general framework to enable the derivation of the commonly used models. The subsequent analysis is then done wholly within the realm of probability calculus and the theory of statistical inference. Numerical examples are provided as well as the software to carry them out ( where this is not otherwise available). Additional data sets are provided in some cases so that the reader can aquire a wider experience of analysis and interpretation.

Author Biography

David Bartholomew is Professor of Statistics at the London School of Economics.

Table of Contents

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

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.