A joint model for mixed longitudinal k-category inflation ordinal and continuous responses

Abstract

In this paper, a joint model is presented to analyse longitudinal continuous and ordinal mixed responses. The ordinal longitudinal response inflates in the kth category, e.g., in the first, middle, or last. A k-category-inflated proportional odds () model with the random effects vectors is applied for modelling the ordinal response. The correlation of longitudinal responses through time as well as two response variables are modelled by utilizing the random effects vectors in the joint model. Further, a full likelihood-based approach is used to obtain the maximum likelihood estimates of parameters via the EM algorithm. Then, some simulation studies are performed to assess the performance of the model. Simulations show that the model performs well in coverage rates, estimation bias, and consistency. However, there are minor restrictions on the nature of the covariates for the identifiability of the model. Additionally, an application of our model is illustrated for joint analysis of the child's reading recognition skill (read) and the child's antisocial behaviour (anti) of the Peabody Individual Achievement Test (PIAT) dataset. The four-time points of the PIAT survey are evaluated.