Journal of Data Science

Abstract: This paper extends the analysis of the bivariate Seemingly Unrelated (SUR) Tobit by modeling its nonlinear dependence structure through copula and assuming non-normal marginal error distributions. For model estimation, the use of copula methods enables the use of the (classical) Inference Function for Margins (IFM) method by Joe and Xu (1996), which is more computationally attractive (feasible) than the full maximum likelihood approach. However, our simulation study shows that the IFM method provides a biased estimate of the copula parameter in the presence of censored observations in both margins. In order to obtain an unbiased estimate of the copula association parameter, we propose/develop a modified version of the IFM method, which we refer to as Inference Function for Augmented Margins (IFAM). Since the usual asymptotic approach, that is the computation of the asymptotic covariance matrix of the parameter estimates, is troublesome, we propose the use of resampling procedures (bootstrap methods) to obtain confidence intervals for the copula-based SUR Tobit model parameters. The satisfactory results from the simulation and empirical studies indicate the adequate performance of our proposed model and methods. We illustrate our procedure using bivariate data on consumption of salad dressings and lettuce by U.S. individuals.

Abstract: The association between bivariate binary responses has been studied using Pearson’s correlation coefficient, odds ratio, and tetrachoric correlation coefficient. This paper introduces a copula to model the association. Numerical comparisons between the proposed method and the existing methods are presented. Results show that these methods are comparative. However, the copula method has a clearer interpretation and is easier to extend to bivariate responses with three or more ordinal categories. In addition, a goodness-of-fit test for the selection of a model is performed. Applications of the method on two real data sets are also presented.