A latent class pattern mixture model for nonignorable nonresponses in multivariate categorical data

Survey data using categorical item variables are widely used in applied research such as psychology, education, and behavioral studies. Unfortunately, survey data are highly susceptible to nonignorable missing values that may threaten the validity of statistical inference if naively ignored or inappropriately treated. This paper proposes a novel latent pattern mixture model for nonignorable missing values in multivariate categorical outcomes. The proposed model posits the existence of two categorical latent variables; one latent variable represents a nonresponse pattern, and the other represents a response pattern conditioning on the nonresponse pattern. We propose two parameter estimation strategies: the maximum-likelihood (ML) estimation using the expectation-maximization (EM) algorithm and Bayesian estimation using the Markov-Chain Monte Carlo (MCMC) algorithm. Simulation studies revealed that the ML estimation is preferred to the Bayesian estimation with noninformative priors in terms of standardized biases given the large sample size, whereas the Bayesian estimation can be preferred when the sample size is small. Finally, our real data example analyzed a data set with parental substance use disorder and revealed six latent classes of participants that are distinguished in response and missingness patterns.