A latent variable model for mixed continuous and ordinal responses with nonignorable missing responses: Assessing the local influence via covariance structure

Abstract

A joint model for mixed ordinal and continuous responses, with missing values in both variables, and their missing mechanisms is proposed. Full likelihood-based approach that yields maximum likelihood estimates of the model parameters is used. For data with missing responses in both variables some modified Pearson residuals are also proposed. A common way to investigte if perturbations of model components influence key results of the analysis is to compare the results derived from the original and perturbed models using an influence graph. For this, influence of a small perturbation of elements of the covariance structure of the model on likelihood displacement is also studied. The model is illustrated using data from a foreign language achievement study.