Using Tail Dependence on Copula-based Regression Models in Mixed Data | ||
| The Egyptian Statistical Journal | ||
| Article 4, Volume 68, Issue 2, December 2024, Pages 65-85 PDF (1.05 M) | ||
| Document Type: Original Article | ||
| DOI: 10.21608/esju.2024.311618.1039 | ||
| Author | ||
| Fatma Alshenawy* | ||
| Faculty of Commerce, Mansoura University, Egypt | ||
| Abstract | ||
| This paper explores the efficacy of incorporating tail dependence into copula-based regression models applied to mixed health insurance data. Recognizing the limitations of traditional Generalized Linear Models (GLMs) in capturing the nuanced relationships within mixed data types, we extend the GLM framework to include bivariate and multivariate structures with gamma and negative binomial distributions. We apply a comprehensive suite of copula families—Gaussian, Clayton, Gumbel, Frank, and Student's-t to model the dependencies between variables, focusing on capturing tail dependence, a critical aspect in the context of insurance claim sizes and frequencies. Our methodology involves fitting bivariate GLMs for each pair of variables to understand pairwise dependencies and then extending the analysis to multivariate GLMs to capture the complex interplay between multiple predictors and the response variable. The analysis is performed on a rich dataset of health insurance claims, to identify the copula family that best represents the dependence structure. The results demonstrate that copulas with heavier tails, such as the Gumbel and Student's t copulas, provide superior fit and predictive performance for extreme claim amounts, outperforming those with lighter tails, such as the Gaussian and Frank copulas. The Clayton copula also shows promise in modeling lower tail dependence. Our findings suggest that tail dependence is a significant factor in accurately modeling health insurance claims data, and that the choice of copula family has a profound impact on the model's effectiveness. We conclude that copula-based regression models, with a focus on tail dependence, offer a robust alternative to conventional regression techniques, enabling actuaries and data analysts in health insurance to better understand risk and price policies more accurately. Our research contributes to the actuarial field by providing a systematic comparison of copula families in the context of health insurance data and by underscoring the importance of tail dependence in actuarial modeling | ||
| Keywords | ||
| Tail Dependence; Copula-Based Regression Models; Health Insurance Data; Mixed Data; Gaussian Copula; Clayton Copula; Gumbel Copula | ||
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