A latent class selection model for nonignorably missing data

When we have data with missing values, the assumption that data are missing at random is very convenient. It is, however, sometimes questionable because some of the missing values could be strongly related to the underlying true values. We introduce methods for nonignorable multivariate missing data, which assume that missingness is related to the variables in question, and to the additional covariates, through a latent variable measured by the missingness indicators. The methodology developed here is useful for investigating the sensitivity of one’s estimates to untestable assumptions about the missing-data mechanism. A simulation study and data analysis are conducted to evaluate the performance of the proposed method and to compare to that of MAR-based alternatives.