Latent Class and Latent Transition Analysis E-Book

Linda M. Collins

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Serie: Wiley Series in Probability and Statistics
• Sprache: Englisch

Seitenzahl: 482

Veröffentlichungsjahr: 2013

Beschreibung

A modern, comprehensive treatment of latent class and latent transition analysis for categorical data On a daily basis, researchers in the social, behavioral, and health sciences collect information and fit statistical models to the gathered empirical data with the goal of making significant advances in these fields. In many cases, it can be useful to identify latent, or unobserved, subgroups in a population, where individuals' subgroup membership is inferred from their responses on a set of observed variables. Latent Class and Latent Transition Analysis provides a comprehensive and unified introduction to this topic through one-of-a-kind, step-by-step presentations and coverage of theoretical, technical, and practical issues in categorical latent variable modeling for both cross-sectional and longitudinal data. The book begins with an introduction to latent class and latent transition analysis for categorical data. Subsequent chapters delve into more in-depth material, featuring: * A complete treatment of longitudinal latent class models * Focused coverage of the conceptual underpinnings of interpretation and evaluationof a latent class solution * Use of parameter restrictions and detection of identification problems * Advanced topics such as multi-group analysis and the modeling and interpretation of interactions between covariates The authors present the topic in a style that is accessible yet rigorous. Each method is presented with both a theoretical background and the practical information that is useful for any data analyst. Empirical examples showcase the real-world applications of the discussed concepts and models, and each chapter concludes with a "Points to Remember" section that contains a brief summary of key ideas. All of the analyses in the book are performed using Proc LCA and Proc LTA, the authors' own software packages that can be run within the SAS® environment. A related Web site houses information on these freely available programs and the book's data sets, encouraging readers to reproduce the analyses and also try their own variations. Latent Class and Latent Transition Analysis is an excellent book for courses on categorical data analysis and latent variable models at the upper-undergraduate and graduate levels. It is also a valuable resource for researchers and practitioners in the social, behavioral, and health sciences who conduct latent class and latent transition analysis in their everyday work.

Leseprobe

CONTENTS

List of Figures

List of Tables

Acknowledgments

Acronyms

PART I FUNDAMENTALS

CHAPTER 1 GENERAL INTRODUCTION

1.1 OVERVIEW

1.2 CONCEPTUAL FOUNDATION AND BRIEF HISTORY OF THE LATENT CLASS MODEL

1.3 WHY SELECT A CATEGORICAL LATENT VARIABLE APPROACH?

1.4 SCOPE OF THIS BOOK

1.5 EMPIRICAL EXAMPLE OF LCA: ADOLESCENT DELINQUENCY

1.6 EMPIRICAL EXAMPLE OF LTA: ADOLESCENT DELINQUENCY

1.7 ABOUT THIS BOOK

1.8 THE EXAMPLES IN THIS BOOK

1.9 SOFTWARE

1.10 ADDITIONAL RESOURCES: THE BOOK’S WEB SITE

1.11 SUGGESTED SUPPLEMENTAL READINGS

1.12 POINTS TO REMEMBER

1.13 WHAT’S NEXT

CHAPTER 2 THE LATENT CLASS MODEL

2.1 OVERVIEW

2.2 EMPIRICAL EXAMPLE: PUBERTAL DEVELOPMENT

2.3 THE ROLE OF ITEM-RESPONSE PROBABILITIES IN INTERPRETING LATENT CLASSES

2.4 EMPIRICAL EXAMPLE: HEALTH RISK BEHAVIORS

2.5 LCA: MODEL AND NOTATION

2.6 SUGGESTED SUPPLEMENTAL READINGS

2.7 POINTS TO REMEMBER

2.8 WHAT’S NEXT

CHAPTER 3 THE RELATION BETWEEN THE LATENT VARIABLE AND ITS INDICATORS

3.1 OVERVIEW

3.2 THE LATENT CLASS MEASUREMENT MODEL

3.3 HOMOGENEITY AND LATENT CLASS SEPARATION

3.4 THE PRECISION WITH WHICH THE OBSERVED VARIABLES MEASURE THE LATENT VARIABLE

3.5 EXPRESSING THE DEGREE OF UNCERTAINTY: MEAN POSTERIOR PROBABILITIES AND ENTROPY

3.6 POINTS TO REMEMBER

3.7 WHAT’S NEXT

CHAPTER 4 PARAMETER ESTIMATION AND MODEL SELECTION

4.1 OVERVIEW

4.2 MAXIMUM LIKELIHOOD ESTIMATION

4.3 MODEL FIT AND MODEL SELECTION

4.4 FINDING THE ML SOLUTION: MODEL IDENTIFICATION, STARTING VALUES, AND LABEL SWITCHING

4.5 EMPIRICAL EXAMPLE OF USING MANY STARTING VALUES: POSITIVE HEALTH BEHAVIORS

4.6 EMPIRICAL EXAMPLES OF SELECTING THE NUMBER OF LATENT CLASSES

4.7 MORE ABOUT PARAMETER RESTRICTIONS

4.8 STANDARD ERRORS

4.9 SUGGESTED SUPPLEMENTAL READINGS

4.10 POINTS TO REMEMBER

4.11 WHAT’S NEXT

PART II ADVANCED LCA

CHAPTER 5 MULTIPLE-GROUP LATENT CLASS ANALYSIS

5.1 OVERVIEW

5.2 INTRODUCTION

5.3 MULTIPLE-GROUP LCA: MODEL AND NOTATION

5.4 COMPUTING THE NUMBER OF PARAMETERS ESTIMATED

5.5 EXPRESSING GROUP DIFFERENCES IN THE LCA MODEL

5.6 MEASUREMENT INVARIANCE

5.7 ESTABLISHING WHETHER THE NUMBER OF LATENT CLASSES IS IDENTICAL ACROSS GROUPS

5.8 ESTABLISHING INVARIANCE OF ITEM-RESPONSE PROBABILITIES ACROSS GROUPS

5.9 INTERPRETATION WHEN MEASUREMENT INVARIANCE DOES NOT HOLD

5.10 STRATEGIES WHEN MEASUREMENT INVARIANCE DOES NOT HOLD

5.1 1 SIGNIFICANT DIFFERENCES AND IMPORTANT DIFFERENCES

5.12 TESTING EQUIVALENCE OF LATENTCLASSPREVALENCES ACROSS GROUPS

5.13 SUGGESTED SUPPLEMENTAL READINGS

5.14 POINTS TO REMEMBER

5.15 WHAT’S NEXT

CHAPTER 6 LATENT CLASS ANALYSIS WITH COVARIATES

6.1 OVERVIEW

6.2 EMPIRICAL EXAMPLE: POSITIVE HEALTH BEHAVIORS

6.3 PREPARING TO CONDUCT LCA WITH COVARIATES

6.5 HYPOTHESIS TESTING IN LCA WITH COVARIATES

6.6 INTERPRETATION OF THE INTERCEPTS AND REGRESSION COEFFICIENTS

6.8 EMPIRICAL EXAMPLE OF MULTIPLE COVARIATES AND INTERACTION TERMS: POSITIVE HEALTH BEHAVIORS

6.9 MULTIPLE-GROUP LCA WITH COVARIATES: MODEL AND NOTATION

6.10 GROUPING VARIABLE OR COVARIATE?

6.11 USE OF A BAYESIAN PRIOR TO STABILIZE ESTIMATION

6.12 COMBINING LATENT CLASSES TO APPLY BINOMIAL LOGISTIC REGRESSION IN LCA

6.13 SUGGESTED SUPPLEMENTAL READINGS

6.14 POINTS TO REMEMBER

6.15 WHAT’S NEXT

PART III LATENT CLASS MODELS FOR LONGITUDINAL DATA

CHAPTER 7 REPEATED-MEASURES LATENT CLASS ANALYSIS AND LATENT TRANSITION ANALYSIS

7.1 OVERVIEW

7.2 RMLCA

7.3 LTA

7.4 LTA MODEL PARAMETERS

7.5 LTA: MODEL AND NOTATION

7.6 DEGREES OF FREEDOM ASSOCIATED WITH LATENT TRANSITION MODELS

7.7 EMPIRICAL EXAMPLE: ADOLESCENT DEPRESSION

7.8 EMPIRICAL EXAMPLE: DATING AND SEXUAL RISK behavior

7.9 INTERPRETING WHAT A LATENT TRANSITION MODEL REVEALS ABOUT CHANGE

7.10 PARAMETER RESTRICTIONS IN LTA

7.11 TESTING THE HYPOTHESIS OF MEASUREMENT INVARIANCE ACROSS TIMES

7.12 TESTING HYPOTHESES ABOUT CHANGE BETWEEN TIMES

7.13 RELATION BETWEEN RMLCA AND LTA

7.14 INVARIANCE OF THE TRANSITION PROBABILITY MATRIX WHEN THERE ARE THREE OR MORE TIMES

7.15 SUGGESTED SUPPLEMENTAL READINGS

7.16 POINTS TO REMEMBER

7.17 WHAT’S NEXT

CHAPTER 8 MULTIPLE-GROUPS LATENT TRANSITION ANALYSIS AND LATENT TRANSITION ANALYSIS WITH COVARIATES

8.1 OVERVIEW

8.2 LTA WITH A GROUPING VARIABLE

8.3 MULTIPLE-GROUP LTA: MODEL AND NOTATION

8.5 HYPOTHESIS TESTS CONCERNING GROUP DIFFERENCES IN LATENT STATUS PREVALENCES AND TRANSITION PROBABILITIES: GENERAL CONSIDERATIONS

8.6 OVERALL HYPOTHESIS TESTS ABOUT GROUP DIFFERENCES IN LTA

8.7 TESTING THE HYPOTHESIS OF EQUALITY OF LATENT STATUS PREVALENCES ACROSS GROUPS AT TIME 1

8.8 TESTING THE HYPOTHESIS OF EQUALITY OF TRANSITION PROBABILITIES ACROSS GROUPS

8.9 INCORPORATING COVARIATES IN LTA

8.12 INCLUDING BOTH A GROUPING VARIABLE AND A COVARIATE IN LTA

8.13 COMBINING LATENT STATUSES TO APPLY BINOMIAL LOGISTIC REGRESSION IN LTA

8.14 THE RELATION BETWEEN MULTIPLE-GROUP LTA AND LTA WITH A COVARIATE

8.15 SUGGESTED SUPPLEMENTAL READINGS

8.16 POINTS TO REMEMBER

Topic Index

Author Index

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Published simultaneously in Canada.

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Library of Congress Cataloging-in-Publication Data:

Collins, Linda M.

Latent class and latent transition analysis / Linda M. Collins, Stephanie T. Lanza,

p. cm.

Includes bibliographical references and index.

ISBN 978-0-470-22839-5 (cloth)

1. Latent structure analysis. 2. Latent variables. 3. Statistical methods. I. Lanza,

Stephanie T., 1969– II. Title.

QA278.6.C65 2010

519.5′35—dc22  2009025970

10 9 8 7 6 5 4 3 2 1

For David and Kathy with admiration (LMC)

For Dad my first math teacher (STL)

List of Figures

1.1    Latent variable with three observed variables as indicators.

2.8 Probability of endorsing sexual behavior items conditional on latent class membership (Youth Risk Behavior Survey, 2005; N= 13,840).

2.10    Figure 1.1, repeated here for convenience. Latent variable with three observed variables as indicators. This figure illustrates local independence. There are arrows connecting observed variables X1, X2, and X3 to the latent variable but no other arrows connecting any components of the observed variables to each other. This signifies that the three observed variables are related only through the latent variable.

2.11    Latent variable with three observed variables as indicators. This figure illustrates a violation of local independence. Observed variables X2 and X3 are related to each other not only through the latent variable, but also through their error components (e’s).

3.1 Probability of endorsing tobacco use behavior items conditional on latent class membership. Hypothetical data from Table 3.5 exhibit high homogeneity and high latent class separation.

3.2    Probability of endorsing tobacco use behavior items conditional on latent class membership. Hypothetical data from Table 3.6 exhibit high homogeneity overall and low separation between the Regular I and II latent classes.

3.3    Probability of endorsing tobacco use behavior items conditional on latent class membership. Hypothetical data from Table 3.7 exhibit low homogeneity and low latent class separation.

4.1    Unimodal likelihood function for a single parameter θ, indicative of good identification.

4.2    Multimodal likelihood function for a single parameter θ, indicative of underidentification.

4.3    Likelihood function for a single parameter θ. This function has a flat region, which suggests that the model being fit is unidentified.

7.1    Patterns of heavy drinking across four developmental periods, corresponding to the latent classes in Table 7.2 (from Lanza and Collins, 2006). Note that more precise values for item-response probabilities appear in Table 7.1.

List of Tables

1.1    Four Different Latent Variable Models

2.3    Item-Response Probabilities for a Hypothetical Two-Latent-Class Model

2.4    Item-Response Probabilities for a Hypothetical Three-Latent-Class Model

2.8    Hypothetical Example with Two Latent Classes and Two Observed Variables

2.9    Response Pattern Probabilities for Hypothetical Example in Table 2.8

3.2    Hypothetical Item-Response Probabilities Reflecting Independence of Observed Variables and Latent Variable

3.4    Item-Response Probabilities for a Hypothetical Three-Latent-Class Model

3.5    Item-Response Probabilities for a Hypothetical Three-Latent-Class Model with High Homogeneity and High Latent Class Separation

3.6    Item-Response Probabilities for a Hypothetical Three-Latent-Class Model with High Homogeneity and Low Latent Class Separation

3.7    Item-Response Probabilities for a Hypothetical Three-Latent-Class Model with Low Homogeneity and Low Latent Class Separation