Calderón Cartagena, Hilda Inés

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    An assessment of copula-based regression models for bivariate count data
    (2018) Calderón Cartagena, Hilda Inés; Torres Saavedra, Pedro A.; College of Arts and Sciences - Sciences; Santana Morant, Dámaris; Macchiavelli, Raúl E.; Department of Mathematics; Ferrer Alameda, Mercedes S.
    It is known that analyzing correlated bivariate count data as independent in a regression context can lead to inefficient coefficients estimates. However, the number of parametric bivariate distributions that can be found in the literature to model bivariate counts are limited and not flexible enough to account for general correla- tion structures and different marginal distributions. Copula-based regression models provide a more flexible way of generating joint distributions for bivariate data by admitting different marginal distributions and various dependence structures. The purpose of this work was to evaluate the performance of copula-based regression models for bivariate counts under different scenarios, and to apply this approach to bivariate crash data in Puerto Rico highways. Scenarios with low, medium and high degrees of dependence were considered, as well as different sample sizes. In particular, the application of copulas when one of the marginal means was small was examined. Overall, if appropriate copulas are fitted, copula-based regression models provide more efficient estimators for the regression parameters when com- pared to modeling the counts independently, even when the data exhibits a degree of association as low as a Kendall’s τ = 0.3, though we recommend a sample size of N = 300 or higher to assure an unbiased estimation of the copula parameter. The gain in efficiency increases with the degree of association. Also, traditional penalized likelihood-based criteria, such as AIC and BIC, seem to have a fairly good performance in selecting the best model among a set of candidate copula models. As a last note, interpretation of the copula parameter about the dependence structure is possible but should be made carefully since the range of its transformation to a dependence measure is narrower than [−1, 1].