Latent Class Analysis of Survey Error

This book concerns the error in data collected using sample surveys, the nature and magnitudes of the errors, their effects on survey estimates, how to model and estimate the errors using a variety of modeling methods, and, finally, how to interpret the estimates and make use of the results in reducing the error for future surveys. The book focuses on models that are appropriate for categorical data, although there are references to the differences and special problems that arise in the analysis and modeling of error for continuous data. Though the primary modeling method that is described is latent class analysis (LCA), a wide range of related models and applications are also discussed.

Paul P. Biemer, PhD, is Distinguished Fellow in Statistics at RTI International and Associate Director for Survey Research and Development at the Odum Institute for Research in Social Science at the University of North Carolina at Chapel Hill. An expert in the field of survey measurement error, Dr. Biemer has published extensively in his areas of research interest, which include survey design and analysis; general survey methodology; and nonsampling error modeling and evaluation. He is a coauthor of Introduction to Survey Quality and a coeditor of Telephone Survey Methodology, Survey Measurement and Process Quality, and Measurement Errors in Surveys, all published by Wiley.

Preface	p. xiii
Abbreviations	p. xvii
Survey Error Evaluation	p. 1
Survey Error	p. 1
An Overview of Surveys	p. 1
Survey Quality and Accuracy and Total Survey Error	p. 3
Nonsampling Error	p. 8
Evaluating the Mean-Squared Error	p. 14
Purposes of MSE Evaluation	p. 14
Effects of Nonsampling Errors on Analysis	p. 16
Survey Error Evaluation Methods	p. 19
Latent Class Analysis	p. 21
About This Book	p. 22
A General Model for Measurement Error	p. 25
The Response Distribution	p. 28
A Simple Model of the Response Process	p. 28
The Reliability Ratio	p. 32
Effects of Response Variance on Statistical Inference	p. 34
Variance Estimation in the Presence of Measurement Error	p. 39
Binary Response Variables	p. 41
Special Case: Two Measurements	p. 43
Extension to Polytomous Response Variables	p. 49
Repeated Measurements	p. 51
Designs for Parallel Measurements	p. 51
Nonparallel Measurements	p. 53
Example: Reliability of Marijuana Use Questions	p. 56
Designs Based on a Subsample	p. 58
Reliability of Multiitem Scales	p. 59
Scale Score Measures	p. 59
Cronbach's Alpha	p. 61
True Values, Bias, and Validity	p. 63
A True Value Model	p. 64
Obtaining True Values	p. 66
Example: Poor- or Failing-Grade Data	p. 68
Response Probability Models for Two Measurements	p. 71
Response Probability Model	p. 71
Bross' Model	p. 72
Implications for Survey Quality Investigations	p. 77
Estimating ¿, ¿, and ¿,	p. 80
Maximum-Likelihood Estimates of ¿, ¿, and ¿	p. 82
The EM Algorithm for Two Measurements	p. 88
Hui-Walter Model for Two Dichotomous Measurements	p. 93
Notation and Assumptions	p. 93
Example: Labor Force Misclassifications	p. 98
Example: Mode of Data Collection Bias	p. 101
Further Aspects of the Hui-Walter Model	p. 106
Two Polytomous Measurements	p. 106
Example: Misclassification with Three Categories	p. 107
Sensitivity of the Hui-Walter Method to Violations in the Underlying Assumptions	p. 110
Hui-Walter Estimates of Reliability	p. 111
Three or More Polytomous Measurements	p. 112
Latent Class Models for Evaluating Classification Errors	p. 115
The Standard Latent Class Model	p. 115
Latent Variable Models	p. 116
An Example from Typology Analysis	p. 119
Latent Class Analysis Software	p. 122
Latent Class Modeling Basics	p. 125
Model Assumptions	p. 125
Probability Model Parameterization of the Standard LC Model	p. 128
Estimation of the LC Model Parameters	p. 129
Loglinear Model Parameterization	p. 133
Example: Computing Probabilities Using Loglinear Parameters	p. 136
Modified Path Model Parameterization	p. 137
Recruitment Probabilities	p. 140
Example: Computing Probabilities Using Modified Path Model Parameters	p. 142
Incorporating Grouping Variables	p. 144
Example: Loglinear Parameterization of the Hui-Walter Model	p. 147
Example: Analysis of Past-Year Marijuana Use with Grouping Variables	p. 150
Model Estimation and Evaluation	p. 155
EM Algorithm for the LL Parameterization	p. 156
Assessing Model Fit	p. 158
Model Selection	p. 161
Model-Building Strategies	p. 163
Model Restrictions	p. 166
Example: Continuation of Marijuana Use Analysis	p. 168
Further Aspects of Latent Class Modeling	p. 181
Parameter Estimation	p. 181
Simulation and "Expeculation"	p. 181
Model Identifiability	p. 183
Checking Identifiability with Expeculation	p. 185
Data Sparseness	p. 188
Boundary Estimates	p. 191
Local Maxima	p. 192
Latent Class Flippage	p. 194
Local Dependence Models	p. 196
Unexplained Heterogeneity	p. 197
Correlated Errors	p. 199
Bivocality	p. 200
A Strategy for Modeling Local Dependence	p. 203
Example: Locally Dependent Measures of Sexual Assault	p. 205
Modeling Complex Survey Data	p. 209
Objectives of Survey Weighting	p. 210
LCA with Complex Survey Data	p. 215
Including Design Variables in the Fitted Model	p. 217
Weighted and Rescaled Frequencies	p. 218
Pseudo-Maximum-Likelihood Estimation	p. 220
Treating the Average Cell Weight as an Offset Parameter	p. 223
Two-Step Estimation	p. 225
Illustration of Weighted and Unweighted Analyses	p. 227
Conclusions and Recommendations	p. 229
Latent Class Models for Special Applications	p. 231
Models for Ordinal Data	p. 231
A Latent Class Model for Reliability	p. 235
Generalized Kappa Statistics	p. 236
Comparison of Error Model and Agreement Model Concepts of Reliability	p. 240
Reliability of Self-Reports of Race	p. 243
Capture-Recapture Models	p. 249
Latent Class Capture-Recapture Models	p. 251
Modeling Erroneous Enumerations	p. 252
Parameter Estimation	p. 253
Example: Evaluating the Census Undercount	p. 254
Example: Classification Error in a PES	p. 258
Latent Class Models for Panel Data	p. 263
Markov Latent Class Models	p. 264
Manifest Markov Models	p. 265
Example: Application of the MM Model to Labor Force Data	p. 268
Markov Latent Class Models	p. 270
Example: Application of the MLC Model to Labor Force Data	p. 274
The EM Algorithm for MLC Models	p. 275
MLC Model with Grouping Variables	p. 278
Example: CPS Labor Force Status Classification Error	p. 280
Example: Underreporting in Consumer Expenditure Survey	p. 284
Some Nonstandard Markov Models	p. 291
Manifest Mover-Stayer Model	p. 291
Latent Class Mover-Stayer Model	p. 295
Second-Order MLC Model	p. 297
Example: CEIS Analysis with Four Timepoints	p. 298
MLC Model with Time-Varying Grouping Variables	p. 301
Example: Assessment of Subject Interests	p. 304
Multiple Indicators at One or More Waves	p. 306
Further Aspects of Markov Latent Class Analysis	p. 308
Estimation Issues with MLCA	p. 308
Methods for Panel Nonresponse	p. 310
Example: Assessment of Subject Interests with Nonresponse	p. 314
Survey Error Evaluation: Past, Present, and Future	p. 317
History of Survey Error Evaluation Methodology	p. 317
The US Census Bureau Model for Survey Error	p. 317
From Bross' Model to the Standard LC and MLC Models	p. 320
Loglinear Models with Latent Variables	p. 322
Current State of the Art	p. 323
Criticisms of LCA for Survey Error Evaluation	p. 324
General Strategy for Applying LC and MLC Models	p. 328
Some Ideas for Future Directions	p. 331
Conclusions	p. 335
Two-Stage Sampling Formulas	p. 337
Loglinear Modeling Essentials	p. 339
Loglinear versus ANOVA Models: Similarities and Differences	p. 339
Modeling Cell and Other Conditional Probabilities	p. 345
Generalization to Three Variables	p. 347
Estimation of Loglinear and Logit Models	p. 350
References	p. 353
Index	p. 369
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Latent Class Analysis of Survey Error

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