Joint model for longitudinal mixture of normal and zero-inflated power series correlated responses Abbreviated title:mixture of normal and zero-inflated power series random-effects model

ABSTRACT

In this paper, a joint model is presented for analyzing longitudinal continuous and count mixed responses. The frequency distribution of continuous longitudinal response variable for each subject at any time has a skewed and or multi-modal form. Then, a suitable finite mixture of normals is used as its distribution. It seems that the continuous response comes from several distinct sub-populations. The number of zeros of the count response is inflated. Also, a zero-inflated power series (ZIPS) distribution is applied as its distribution in order to model the count response. The correlation of longitudinal responses through time and that of mixed continuous and count responses are modeled by utilizing the random-effects vectors in the finite mixtures of regression (FMR) models. 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 for assessing the performance of the model. Additionally, an application is illustrated for joint analysis of the number of days during the last month that the individual drank alcohol, as well as the respondents’ weight. Finally, the two first times of the Americans Changing Lives survey are evaluated.

KEYWORDS:

• Mixed correlated responses
• finite mixture distributions
• joint model
• the finite mixture of normals
• zero-inflated
• longitudinal studies
• random effect
• the EM algorithm

Notes

1. Time 1 represents the first wave in 1986 and Time 2 as the second wave in 1988.