Applied Latent Class Analysis

✍ Scribed by Jacques A. Hagenaars, Allan L. McCutcheon

• Publisher: Cambridge University Press
• Year: 2002
• Tongue: English
• Leaves: 478
• Edition: 1
• Category: Library

✦ Synopsis

This study introduces several recent innovations in latent class analysis to a wider audience of researchers. Many of the world's leading innovators in the field of latent class analysis have contributed essays to the volume, each presenting a key innovation to the basic LCM and illustrating how it can prove useful in situations typically encountered in actual research.

✦ Table of Contents

Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Dedication......Page 7
Contents......Page 9
Contributors......Page 11
Preface......Page 13
INTRODUCTION......Page 25
1. INTRODUCTION......Page 27
2. THE LATENT CLASS MODEL......Page 30
3. FIRST EXAMPLE: THE ANALYSIS OF THE RELATIONSHIP BETWEEN TWO OBSERVED VARIABLES......Page 31
4. SECOND EXAMPLE: THE ANALYSIS OF THE RELATIONSHIPS AMONG FOUR OBSERVED VARIABLES......Page 37
5. ANOTHER EXAMPLE: THE SIMPLE 2 × 2 CROSS-CLASSIFICATION TABLE REVISITED: A NINETEENTH-CENTURY LATENT STRUCTURE AND SOME…......Page 46
6. SOME NOTES ON THE HISTORY OF LATENT CLASS ANALYSIS......Page 51
APPENDIX......Page 55
REFERENCES......Page 68
NOTES......Page 73
TWO Basic Concepts and Procedures in Single-and Multiple-Group Latent Class Analysis......Page 80
1. PARAMETERIZATIONS OF THE BASIC LATENT CLASS MODEL......Page 81
A. Probabilistic Parameterization......Page 82
B. Loglinear Parameterization......Page 85
2. MODEL ESTIMATION......Page 88
3. MODEL EVALUATION......Page 90
4. RESTRICTED LATENT CLASS MODELS......Page 94
A. Restricted Loglinear Models......Page 97
5. MULTI-SAMPLE LATENT CLASS MODELS......Page 101
6. CONCLUSION......Page 105
REFERENCES......Page 106
NOTES......Page 108
CLASSIFICATION AND MEASUREMENT......Page 111
1. INTRODUCTION......Page 113
2. CONTINUOUS INDICATOR VARIABLES......Page 115
3. MIXED INDICATOR VARIABLES......Page 118
4. COVARIATES......Page 119
5. ESTIMATION......Page 120
6. MODEL SELECTION......Page 121
7. TWO EMPIRICAL EXAMPLES......Page 122
A. Diabetes Data......Page 123
B. Prostate Cancer Data......Page 125
8. CONCLUSIONS......Page 127
REFERENCES......Page 129
1. INTRODUCTION......Page 131
2. THE WORKS OF PLATO......Page 135
3. ETHNIC DIFFERENCES AMONG PEOPLE STARTING A TRADE: AN EXAMPLE OF SIMULTANEOUS LATENT BUDGET ANALYSIS......Page 142
4. SOCIAL MILIEU AND SECONDARY EDUCATION: AN EXAMPLE OF CONSTRAINED LATENT BUDGET ANALYSIS......Page 150
5. CONCLUSIONS......Page 157
REFERENCES......Page 159
A. The Problem of Ordering the Classes in Latent Class Analysis......Page 161
B. Some Previous Solutions......Page 162
C. What Is There to Come?......Page 164
B. Dichotomous Items......Page 165
C. Polytomous Items......Page 166
D. Estimating and Testing the Model......Page 167
E. OLCA and Regression Dependence......Page 169
F. OLCA and Latent Trait Models......Page 170
A. The Data......Page 171
B. Separate Analyses for the Subscales......Page 172
C. A Joint Analysis for the Two Subscales......Page 173
D. A One-Dimensional Analysis for the Total Scale......Page 175
A. Scalogram Analysis: Deterministic and Probabilistic Formulations......Page 176
B. A Latent Class Formulation of the Double-Monotony Condition......Page 178
B. The Analyses......Page 179
A. Monotonic Local and Adjacent Odds Ratios......Page 181
B. Ordered Classes with Nonmonotonic Items......Page 182
7. DISCUSSION......Page 183
REFERENCES......Page 185
1. INTRODUCTION......Page 187
2. LATENT CLASS MODELS FOR PICK ANY/J AND RANKING DATA......Page 188
3. PICK ANY/J DATA......Page 190
A. Coombs’ Unfolding Model......Page 191
B. Example Continued......Page 193
4. INCOMPLETE AND PARTIAL RANKING DATA......Page 194
A. Paired Comparisons......Page 195
B. Incomplete Rankings......Page 196
5. PARTY PREFERENCES IN GERMANY......Page 197
A. Results from Luce’s Ranking Model......Page 199
B. Results from Unfolding Analysis......Page 200
6. EXTENSIONS......Page 202
7. CONCLUSION......Page 203
REFERENCES......Page 204
NOTE......Page 206
2. UNCONSTRAINED LATENT CLASS ANALYSIS......Page 207
3. LINEAR LOGISTIC LATENT CLASS ANALYSIS......Page 209
4. RASCH AND BIRNBAUM MODELS ASSUMING CONTINUOUS LATENT TRAITS......Page 210
5. LATENT CLASS RASCH AND BIRNBAUM MODELS......Page 213
6. PARAMETER ESTIMATION,GOODNESS OF FIT......Page 216
7. NOTES ON IDENTIFIABILITY......Page 220
8. EXAMPLE: GRADED PAIN STATUS......Page 225
9. FINAL REMARKS......Page 231
REFERENCES......Page 232
CAUSAL ANALYSIS AND DYNAMIC MODELS......Page 235
1. INTRODUCTION......Page 237
2. MODELS WITH BLOCKING VARIABLES......Page 238
3. EXEMPLARY ANALYSIS WITH BLOCKING VARIABLES......Page 240
4. COVARIATE MODELS......Page 247
5. EXEMPLARY ANALYSIS WITH COVARIATES......Page 252
REFERENCES......Page 256
1. INTRODUCTION......Page 258
A. Standard Two-Latent-Variable Model......Page 259
B. Models for Ordered Data: Linear × Linear Association Models......Page 263
C. Models for Ordered Data: Linear × Nominal Association Models......Page 266
D. Interpretation of the Outcomes......Page 269
A. Causal Model with Latent Variables......Page 271
B. The Modified Path Approach and Directed Loglinear Modeling......Page 273
C. The Modified LISREL Approach and DLM with Latent Variables......Page 278
D. Application: Selecting Models......Page 279
E. Application: Interpreting Parameter Estimates......Page 285
4. SYSTEMATIC, NONINDEPENDENT MISCLASSIFICATIONS......Page 294
5. CONCLUSIONS......Page 299
REFERENCES......Page 302
NOTES......Page 308
TEN Latent Class Models for Longitudinal Data......Page 311
1. STAGE-SEQUENTIAL MODELS AND LATENT CLASS THEORY......Page 312
A. Empirical Example......Page 315
C. Model 1......Page 316
Goodness of Fit......Page 317
Model Fit......Page 318
E. Model 3......Page 319
A. Substantive Results......Page 323
B. Latent Transition Analysis......Page 324
REFERENCES......Page 325
NOTE......Page 327
1. INTRODUCTION......Page 328
2. THE LATENT MIXED MARKOV MODEL FOR SEVERAL GROUPS......Page 331
3. THE SIMPLE MARKOV CHAIN......Page 333
4. THE MIXED MARKOV MODEL......Page 339
5. THE LATENT MARKOV MODEL......Page 347
6. THE LATENT MIXED MARKOV MODEL......Page 353
7. LATENT MIXED MARKOV MODELS FOR SEVERAL GROUPS......Page 356
8. EXTENSIONS, PROBLEMS, AND SOME SOLUTIONS......Page 359
REFERENCES......Page 361
UNOBSERVED HETEROGENEITY AND NONRESPONSE......Page 367
1. INTRODUCTION......Page 369
2. DIFFICULTIES WITH CHI-SQUARED TESTS OF FIT......Page 370
3. THE MIXTURE INDEX OF FIT......Page 372
4. APPLICATIONS......Page 378
5. GENERALIZATIONS TO OTHER STATISTICAL PROBLEMS......Page 386
APPENDIX: ALGORITHMS TO COMPUTE THE MIXTURE INDEX OF FIT Pi*......Page 387
REFERENCES......Page 388
1. INTRODUCTION......Page 390
2. FINITE MIXTURE MODELS......Page 391
3. MIXTURE REGRESSION MODELS......Page 394
B. Application: Trade Show Performance......Page 396
4. CONCOMITANT VARIABLE MIXTURE REGRESSION MODELS......Page 399
A. Identification......Page 400
B. Application: Conjoint Study on Banking......Page 401
5. CONCLUSION......Page 403
REFERENCES......Page 404
1. INTRODUCTION......Page 407
A. Basic Concepts......Page 408
B. Loglinear Models for the Hazard Rate......Page 409
C. Censoring......Page 412
E. Multiple Risks......Page 413
F. Multivariate Hazard Models......Page 414
A. Random-Effects Approach......Page 416
B. Fixed-Effects Approach......Page 419
C. General Nonparametric Random-Effects Approach......Page 420
A. Example I: First Interfirm Job Change......Page 422
B. Example II: First Experience with Relationships......Page 426
5. FINAL REMARKS......Page 428
REFERENCES......Page 429
1. INTRODUCTION......Page 432
2. EXAMPLE 1: PRENATAL CARE AND INFANT MORTALITY......Page 433
3. CONVENTIONAL APPROACHES TO MISSING DATA......Page 435
4. LATENT CLASS MODELS......Page 437
5. LOGLINEAR–LATENT CLASS MODELS FOR MISSING DATA......Page 438
B. MAR Models......Page 439
7. FITTING MISSING DATA MODELS TO INFANT MORTALITY DATA......Page 440
8. EXAMPLE 2: INTERGENERATIONAL EDUCATIONAL MOBILITY......Page 443
B. Identification......Page 451
REFERENCES......Page 454
NOTES......Page 455
Appendix A: Notational Conventions......Page 457
B. HISTORICAL DEVELOPMENTS (CHRONOLOGICAL ORDER)......Page 463
D. CAUSAL MODELS......Page 464
E. UNOBSERVED HETEROGENEITY......Page 465
PANMARK......Page 466
WINLTA......Page 467
WEBPAGE......Page 468
Author Index......Page 469
Subject Index......Page 474