Latent Class Analysis of Survey Error (Wiley Series in Survey Methodology)

Cover......Page 1
Latent Class Analysis of Survey Error......Page 5
Contents......Page 9
Preface......Page 15
Abbreviations......Page 19
1.1.1 An Overview of Surveys......Page 23
1.1.2 Survey Quality and Accuracy and Total Survey Error......Page 25
1.1.3 Nonsampling Error......Page 30
1.2.1 Purposes of MSE Evaluation......Page 36
1.2.2 Effects of Nonsampling Errors on Analysis......Page 38
1.2.3 Survey Error Evaluation Methods......Page 41
1.2.4 Latent Class Analysis......Page 43
1.3 ABOUT THIS BOOK......Page 44
CHAPTER 2: A General Model for Measurement Error......Page 47
2.1.1 A Simple Model of the Response Process......Page 50
2.1.2 The Reliability Ratio......Page 54
2.1.3 Effects of Response Variance on Statistical Inference......Page 56
2.2 VARIANCE ESTIMATION IN THE PRESENCE OF MEASUREMENT ERROR......Page 61
2.2.1 Binary Response Variables......Page 63
2.2.2 Special Case: Two Measurements......Page 65
2.2.3 Extension to Polytomous Response Variables......Page 71
2.3.1 Designs for Parallel Measurements......Page 73
2.3.2 Nonparallel Measurements......Page 75
2.3.3 Example: Reliability of Marijuana Use Questions......Page 78
2.3.4 Designs Based on a Subsample......Page 80
2.4.1 Scale Score Measures......Page 81
2.4.2 Cronbach’s Alpha......Page 83
2.5 TRUE VALUES, BIAS, AND VALIDITY......Page 85
2.5.1 A True Value Model......Page 86
2.5.2 Obtaining True Values......Page 88
2.5.3 Example: Poor- or Failing-Grade Data......Page 90
3.1 RESPONSE PROBABILITY MODEL......Page 93
3.1.1 Bross’ Model......Page 94
3.1.2 Implications for Survey Quality Investigations......Page 99
3.2 ESTIMATING π, θ, AND φ......Page 102
3.2.1 Maximum-Likelihood Estimates of π, θ, and φ......Page 104
3.2.2 The EM Algorithm for Two Measurements......Page 110
3.3.1 Notation and Assumptions......Page 115
3.3.2 Example: Labor Force Misclassifications......Page 120
3.3.3 Example: Mode of Data Collection Bias......Page 123
3.4.1 Two Polytomous Measurements......Page 128
3.4.2 Example: Misclassification with Three Categories......Page 129
3.4.3 Sensitivity of the Hui–Walter Method to Violations in the Underlying Assumptions......Page 132
3.4.4 Hui–Walter Estimates of Reliability......Page 133
3.5 THREE OR MORE POLYTOMOUS MEASUREMENTS......Page 134
4.1 THE STANDARD LATENT CLASS MODEL......Page 137
4.1.1 Latent Variable Models......Page 138
4.1.2 An Example from Typology Analysis......Page 141
4.1.3 Latent Class Analysis Software......Page 144
4.2.1 Model Assumptions......Page 147
4.2.2 Probability Model Parameterization of the Standard LC Model......Page 150
4.2.3 Estimation of the LC Model Parameters......Page 151
4.2.4 Loglinear Model Parameterization......Page 155
4.2.5 Example: Computing Probabilities Using Loglinear Parameters......Page 158
4.2.6 Modified Path Model Parameterization......Page 159
4.2.7 Recruitment Probabilities......Page 162
4.2.8 Example: Computing Probabilities Using Modifi ed Path Model Parameters......Page 164
4.3 INCORPORATING GROUPING VARIABLES......Page 166
4.3.1 Example: Loglinear Parameterization of the Hui–Walter Model......Page 169
4.3.2 Example: Analysis of Past-Year Marijuana Use with Grouping Variables......Page 172
4.4 MODEL ESTIMATION AND EVALUATION......Page 177
4.4.1 EM Algorithm for the LL Parameterization......Page 178
4.4.2 Assessing Model Fit......Page 180
4.4.3 Model Selection......Page 183
4.4.4 Model-Building Strategies......Page 185
4.4.5 Model Restrictions......Page 188
4.4.6 Example: Continuation of Marijuana Use Analysis......Page 190
5.1.1 Simulation and “Expeculation”......Page 203
5.1.2 Model Identifiability......Page 205
5.1.3 Checking Identifiability with Expeculation......Page 207
5.1.4 Data Sparseness......Page 210
5.1.5 Boundary Estimates......Page 213
5.1.6 Local Maxima......Page 214
5.1.7 Latent Class Flippage......Page 216
5.2 LOCAL DEPENDENCE MODELS......Page 218
5.2.1 Unexplained Heterogeneity......Page 219
5.2.2 Correlated Errors......Page 221
5.2.3 Bivocality......Page 222
5.2.4 A Strategy for Modeling Local Dependence......Page 225
5.2.5 Example: Locally Dependent Measures of Sexual Assault......Page 227
5.3 MODELING COMPLEX SURVEY DATA......Page 231
5.3.1 Objectives of Survey Weighting......Page 232
5.3.2 LCA with Complex Survey Data......Page 237
5.3.3 Including Design Variables in the Fitted Model......Page 239
5.3.4 Weighted and Rescaled Frequencies......Page 240
5.3.5 Pseudo-Maximum-Likelihood Estimation......Page 242
5.3.6 Treating the Average Cell Weight as an Offset Parameter......Page 245
5.3.7 Two-Step Estimation......Page 247
5.3.8 Illustration of Weighted and Unweighted Analyses......Page 249
5.3.9 Conclusions and Recommendations......Page 251
6.1 MODELS FOR ORDINAL DATA......Page 253
6.2 A LATENT CLASS MODEL FOR RELIABILITY......Page 257
6.2.1 Generalized Kappa Statistics......Page 258
6.2.2 Comparison of Error Model and Agreement Model Concepts of Reliability......Page 262
6.2.3 Reliability of Self-Reports of Race......Page 265
6.3 CAPTURE–RECAPTURE MODELS......Page 271
6.3.1 Latent Class Capture–Recapture Models......Page 273
6.3.2 Modeling Erroneous Enumerations......Page 274
6.3.3 Parameter Estimation......Page 275
6.3.4 Example: Evaluating the Census Undercount......Page 276
6.3.5 Example: Classification Error in a PES......Page 280
CHAPTER 7: Latent Class Models for Panel Data......Page 285
7.1 MARKOV LATENT CLASS MODELS......Page 286
7.1.1 Manifest Markov Models......Page 287
7.1.2 Example: Application of the MM Model to Labor Force Data......Page 290
7.1.3 Markov Latent Class Models......Page 292
7.1.4 Example: Application of the MLC Model to Labor Force Data......Page 296
7.1.5 The EM Algorithm for MLC Models......Page 297
7.1.6 MLC Model with Grouping Variables......Page 300
7.1.7 Example: CPS Labor Force Status Classification Error......Page 302
7.1.8 Example: Underreporting in U. S. Consumer Expenditure Survey......Page 306
7.2.1 Manifest Mover–Stayer Model......Page 313
7.2.2 Latent Class Mover–Stayer Model......Page 317
7.2.3 Second-Order MLC Model......Page 319
7.2.4 Example: CEIS Analysis with Four Timepoints......Page 320
7.2.5 MLC Model with Time-Varying Grouping Variables......Page 323
7.2.6 Example: Assessment of Subject Interests......Page 326
7.2.7 Multiple Indicators at One or More Waves......Page 328
7.3.1 Estimation Issues with MLCA......Page 330
7.3.2 Methods for Panel Nonresponse......Page 332
7.3.3 Example: Assessment of Subject Interests with Nonresponse......Page 336
8.1.1 The US Census Bureau Model for Survey Error......Page 339
8.1.2 From Bross’ Model to the Standard LC and MLC Models......Page 342
8.1.3 Loglinear Models with Latent Variables......Page 344
8.2 CURRENT STATE OF THE ART......Page 345
8.2.1 Criticisms of LCA for Survey Error Evaluation......Page 346
8.2.2 General Strategy for Applying LC and MLC Models......Page 350
8.3 SOME IDEAS FOR FUTURE DIRECTIONS......Page 353
8.4 CONCLUSION......Page 357
APPENDIX A: Two-Stage Sampling Formulas......Page 359
B.1 LOGLINEAR VERSUS ANOVA MODELS: SIMILARITIES AND DIFFERENCES......Page 361
B.2 MODELING CELL AND OTHER CONDITIONAL PROBABILITIES......Page 367
B.3 GENERALIZATION TO THREE VARIABLES......Page 369
B.4 ESTIMATION OF LOGLINEAR AND LOGIT MODELS......Page 372
References......Page 375
Index......Page 391