The Analysis of Multivariate Misclassified Data With Special Attention to Randomized Response Data

Abstract

This article discusses log-linear analysis of misclassified categorical data when conditional misclassification probabilities are known. This kind of misclassification occurs when data are collected using a randomized response design. The authors describe the misclassification by a latent class model. Since a latent class model is a log-linear model with one or more categorical latent variables, it is possible to investigate relations between misclassified variables. Methods to fit log-linear models for the latent table are discussed, including an EM algorithm. Attention is given to problems with boundary solutions. The results can also be used in statistical disclosure control when the post-randomization method is applied to protect the privacy of respondents, in epidemiology when specificity and sensitivity are known, and in data mining when privacy is protected by intentional statistical perturbation. Examples are given using randomized response data from a research into social benefit fraud.