A latent class selection model for categorical response variables with nonignorably missing data

We develop a new selection model for nonignorable missing values in multivariate categorical response variables by assuming that the response variables and their missingness can be summarized into categorical latent variables. Our proposed model contains two categorical latent variables. One latent variable summarizes the response patterns while the other describes the response variables’ missingness. Our selection model is an alternative method to other incomplete data methods when the incomplete data mechanism is nonignorable. We implement simulation studies to evaluate the performance of the proposed method and analyze the General Social Survey 2018 data to demonstrate its performance.