Analysis of ordinal categorical data with misclassification.

We develop a method for the analysis of multivariate ordinal categorical data with misclassification based on the latent normal variable approach. Misclassification arises if a subject has been classified into a category that does not truly reflect its actual state, and can occur with one or more variables. A basic framework is developed to enable the analysis of two types of data. The first corresponds to a single sample that is obtained from a fallible design that may lead to misclassified data. The other corresponds to data that is obtained by double sampling. Double sampling data consists of two parts: a sample that is obtained by classifying subjects using the fallible design only and a sample that is obtained by classifying subjects using both fallible and true designs, which is assumed to have no misclassification. A unified expectation-maximization approach is developed to find the maximum likelihood estimate of model parameters. Simulation studies and examples that are based on real data are used to demonstrate the applicability and practicability of the proposed methods.