Joint modeling for longitudinal set-inflated continuous and count responses

Abstract

A joint mixture model for analyzing mixed longitudinal continuous and count data is presented. The continuous response is inflated in a set $\mathcal{A}$, and a set-inflated normal (SIN) distribution is used as its distribution. The count response is inflated in a set $\mathcal{B}$. $\mathcal{B}$ includes one or more points of sample space and a set-inflated power series (SIPS) distribution is used as its distribution. A full likelihood-based approach is used to obtain the maximum likelihood estimates of parameters via the EM algorithm. A random effects approach is applied to investigate the correlated longitudinal responses and correlated inflation mechanisms of each subject through time. Also, to consider the correlation between the mixed continuous and count responses of each individual at each time, the correlated random effects are used. In order to assess the performance of the model, some simulation studies are performed. An application of our models is illustrated for joint analysis of (1) number of days in the last month that the individual drank alcohol, and (2) weight of respondent for the first two waves of the American’s Changing Lives survey.

Keywords:

• Bootstrap
• finite mixture distributions
• joint mixture model
• likelihood ratio test
• longitudinal studies
• mixed correlated responses

MATHEMATICS SUBJECT CLASSIFICATION:

• 62J02; 62J05; 62J12