Sensitivity analysis for nonignorable missing responses with application to multivariate Random effect model

A joint model with random effects for longitudinal mixed ordinal and continuous responses, with potentially non-random missing values in both types of responses is proposed. The presented model simultaneously considers a multivariate probit regression model for the missing mechanisms, which provides the ability of examining the missing data assumptions, and a multivariate mixed model for the responses. Random effects are used to take into account the correlation between longitudinal responses of the same individual. A full likelihood-based approach that allows yielding maximum likelihood estimates of the model parameters is used. The joint modeling of responses with the possibility of missing values requires caution since the interpretation of the fitted model highly depends on the assumptions that are unexaminable in a fundamental sense. A sensitivity of the results to the assumptions is also investigated. To illustrate the application of such modeling the longitudinal data of PIAT (Peabody Individual Achievement Test) is analyzed.