Multivariate Pascal Mixture Regression Models for Correlated Claim Frequencies

28 Pages Posted: 17 May 2016

See all articles by Dameng Tang

Dameng Tang

University of Toronto

Andrei Badescu

University of Toronto - Department of Statistics

X. Sheldon Lin

Department of Statistical Sciences, University of Toronto

Emiliano A. Valdez

University of Connecticut - Department of Mathematics

Date Written: June 10, 2015

Abstract

In this article, we propose a multivariate Pascal mixture regression model as an alternative to understand the association between multivariate count response variables and their covariates. When compared to the copula approach, this proposed class of regression models is not only less complex but can account for more versatile dependence structures and still allow for an intuitive explanation. We examine some of the properties possessed by this class of regression models and show its connections to several other models. For fitting purposes, we use the expectation-maximization (EM) algorithm which we find to be more effective and efficient. A by-product of this algorithm is that it provides for more reliable estimated standard errors of the regression coefficients useful for inference. Four different simulation studies are conducted to examine the performance of the fitting algorithm and the versatility of the proposed model while its applicability is additionally demonstrated by fitting an automobile insurance claim count dataset. All results are satisfactory and show that the proposed model can be a promising candidate for multivariate count regression modeling.

Keywords: Pascal Distribution, Pascal Finite Mixture, Multivariate Claim Frequencies, Count Regression, Expectation-Maximization (EM) Algorithm

JEL Classification: C13, C15, C35, G22

Suggested Citation

Tang, Dameng and Badescu, Andrei and Lin, Xiaodong Sheldon and Valdez, Emiliano A., Multivariate Pascal Mixture Regression Models for Correlated Claim Frequencies (June 10, 2015). Available at SSRN: https://ssrn.com/abstract=2618265 or http://dx.doi.org/10.2139/ssrn.2618265

Dameng Tang

University of Toronto ( email )

105 St George Street
Toronto, Ontario M5S 3G8
Canada

Andrei Badescu

University of Toronto - Department of Statistics ( email )

100 St. George St.
Toronto, Ontario M5S 3G3
Canada

Xiaodong Sheldon Lin

Department of Statistical Sciences, University of Toronto ( email )

Department of Statistical Sciences
100 St George Street
Toronto, Ontario M5S 3G3
Canada

Emiliano A. Valdez (Contact Author)

University of Connecticut - Department of Mathematics ( email )

341 Mansfield Road U-1009
Storrs, CT 06269-1009
United States

HOME PAGE: http://www.math.uconn.edu/~valdez

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