Gaussian Copula–based Regression Models for the Analysis of Mixed Outcomes: An Application on Household's Utilization of Health Services Data

Abstract

In analyzing most correlated outcomes, the popular multivariate Gaussian distribution is very restrictive and therefore dependence modeling using copulas is nowadays very common to take into account the association among mixed outcomes. In this paper, we use Gaussian copula to construct a joint distribution for three mixed discrete and continuous responses. Our approach entails specifying marginal regression models for the outcomes, and combining them via a copula to form a joint model. Closed form for likelihood function is obtained by considering sampling weights. We also obtain the likelihood function for mixed responses where one of the responses, time to event outcome, may have censored values. Some simulation studies are performed to illustrate the performance of the model. Finally, the model is applied on data involving trivariate mixed outcomes on hospitalization of individuals, based on the survey of household's utilization of health services.

The Application of Copula Continuous Extension Technique for Bivariate Discrete Data: A Case Study on Dependence Modeling of Seismicity Data

“…The Copula model approach becomes an alternative method in statistics, which is used in constructing the joint distribution of multivariate variables wherein dependence between marginals exists. Meanwhile, an application of the Copula model arises in a wide context, and several of the most commonly used are briefly mentioned, namely financial risk assessment by Zhang and Jiang [1], environmental sciences by Bhatti and Do [2], image processing by Dong et al [3], health data by Ghahroodi et al [4], and industrial problem by Wan and Li [5]. Furthermore, the Copula models used in the aforementioned cases are for continuous variables.…”