Modelling dependence in a ratemaking procedure with multivariate Poisson regression models

When actuaries face with the problem of pricing an insurance contract that contains different types of coverage, such as a motor insurance or homeowner's insurance policy, they usually assume that types of claim are independent. However, this assumption may not be realistic: several studies have shown that there is a positive correlation between types of claim. Here we introduce different regression models in order to relax the independence assumption, including zero-inflated models to account for excess of zeros and overdispersion. These models have been largely ignored to multivariate Poisson date, mainly because of their computational di±culties. Bayesian inference based on MCMC helps to solve this problem (and also lets us derive, for several quantities of interest, posterior summaries to account for uncertainty). Finally, these models are applied to an automobile insurance claims database with three different types of claims. We analyse the consequences for pure and loaded premiums when the independence assumption is relaxed by using different multivariate Poisson regression models and their zero-inflated versions.

Mixture of bivariate Poisson regression models with an application to insurance

In a recent paper Bermúdez [2009] used bivariate Poisson regression models for ratemaking in car insurance, and included zero-inflated models to account for the excess of zeros and the overdispersion in the data set. In the present paper, we revisit this model in order to consider alternatives. We propose a 2-finite mixture of bivariate Poisson regression models to demonstrate that the overdispersion in the data requires more structure if it is to be taken into account, and that a simple zero-inflated bivariate Poisson model does not suffice. At the same time, we show that a finite mixture of bivariate Poisson regression models embraces zero-inflated bivariate Poisson regression models as a special case. Additionally, we describe a model in which the mixing proportions are dependent on covariates when modelling the way in which each individual belongs to a separate cluster. Finally, an EM algorithm is provided in order to ensure the models’ ease-of-fit. These models are applied to the same automobile insurance claims data set as used in Bermúdez [2009] and it is shown that the modelling of the data set can be improved considerably.

Multi-level zero-inflated Poisson regression modelling of correlated count data with excess zeros

Count data with excess zeros relative to a Poisson distribution are common in many biomedical applications. A popular approach to the analysis of such data is to use a zero-inflated Poisson (ZIP) regression model. Often, because of the hierarchical Study design or the data collection procedure, zero-inflation and lack of independence may occur simultaneously, which tender the standard ZIP model inadequate. To account for the preponderance of zero counts and the inherent correlation of observations, a class of multi-level ZIP regression model with random effects is presented. Model fitting is facilitated using an expectation-maximization algorithm, whereas variance components are estimated via residual maximum likelihood estimating equations. A score test for zero-inflation is also presented. The multi-level ZIP model is then generalized to cope with a more complex correlation structure. Application to the analysis of correlated count data from a longitudinal infant feeding study illustrates the usefulness of the approach.

Predicting sprint running times from isokinetic and squat lift tests: A regression analysis

This study examined the relationship between isokinetic hip extensor/hip flexor strength, 1-RM squat strength, and sprint running performance for both a sprint-trained and non-sprint-trained group. Eleven male sprinters and 8 male controls volunteered for the study. On the same day subjects ran 20-m sprints from both a stationary start and with a 50-m acceleration distance, completed isokinetic hip extension/flexion exercises at 1.05, 4.74, and 8.42 rad.s(-1), and had their squat strength estimated. Stepwise multiple regression analysis showed that equations for predicting both 20-m maximum velocity nm time and 20-m acceleration time may be calculated with an error of less than 0.05 sec using only isokinetic and squat strength data. However, a single regression equation for predicting both 20-m acceleration and maximum velocity run times from isokinetic or squat tests was not found. The regression analysis indicated that hip flexor strength at all test velocities was a better predictor of sprint running performance than hip extensor strength.

Exploratory Approach to the use of Techniques of Regression Analysis and Pooled Analysis in Studies of Consumer Behavior

This paper is part of a large study to assess the adequacy of the use of multivariate statistical techniques in theses and dissertations of some higher education institutions in the area of marketing with theme of consumer behavior from 1997 to 2006. The regression and conjoint analysis are focused on in this paper, two techniques with great potential of use in marketing studies. The objective of this study was to analyze whether the employement of these techniques suits the needs of the research problem presented in as well as to evaluate the level of success in meeting their premisses. Overall, the results suggest the need for more involvement of researchers in the verification of all the theoretical precepts of application of the techniques classified in the category of investigation of dependence among variables.

An EM-based Semi-Parametric Mixture Model Approach to the Regression Analysis of Competing-Risks Data

We consider a mixture model approach to the regression analysis of competing-risks data. Attention is focused on inference concerning the effects of factors on both the probability of occurrence and the hazard rate conditional on each of the failure types. These two quantities are specified in the mixture model using the logistic model and the proportional hazards model, respectively. We propose a semi-parametric mixture method to estimate the logistic and regression coefficients jointly, whereby the component-baseline hazard functions are completely unspecified. Estimation is based on maximum likelihood on the basis of the full likelihood, implemented via an expectation-conditional maximization (ECM) algorithm. Simulation studies are performed to compare the performance of the proposed semi-parametric method with a fully parametric mixture approach. The results show that when the component-baseline hazard is monotonic increasing, the semi-parametric and fully parametric mixture approaches are comparable for mildly and moderately censored samples. When the component-baseline hazard is not monotonic increasing, the semi-parametric method consistently provides less biased estimates than a fully parametric approach and is comparable in efficiency in the estimation of the parameters for all levels of censoring. The methods are illustrated using a real data set of prostate cancer patients treated with different dosages of the drug diethylstilbestrol. Copyright (C) 2003 John Wiley Sons, Ltd.

Optimal designs for mixed effects poisson regression models

Magdeburg, Univ., Fak. für Mathematik, Diss., 2010

Innovation sources and productivity in Catalonian firms: a quantile regression analysis

This paper explores the effects of two main sources of innovation -intramural and external R&D- on the productivity level in a sample of 3,267 Catalonian firms. The data set used is based on the official innovation survey of Catalonia which was a part of the Spanish sample of CIS4, covering the years 2002-2004. We compare empirical results by applying usual OLS and quantile regression techniques both in manufacturing and services industries. In quantile regression, results suggest different patterns at both innovation sources as we move across conditional quantiles. The elasticity of intramural R&D activities on productivity decreased when we move up the high productivity levels both in manufacturing and services sectors, while the effects of external R&D rise in high-technology industries but are more ambiguous in low-technology and knowledge-intensive services. JEL codes: O300, C100, O140. Keywords: Innovation sources, R&D, Productivity, Quantile regression

A priori ratemaking using bivariate poisson regression models

In automobile insurance, it is useful to achieve a priori ratemaking by resorting to gene- ralized linear models, and here the Poisson regression model constitutes the most widely accepted basis. However, insurance companies distinguish between claims with or without bodily injuries, or claims with full or partial liability of the insured driver. This paper exa- mines an a priori ratemaking procedure when including two di®erent types of claim. When assuming independence between claim types, the premium can be obtained by summing the premiums for each type of guarantee and is dependent on the rating factors chosen. If the independence assumption is relaxed, then it is unclear as to how the tari® system might be a®ected. In order to answer this question, bivariate Poisson regression models, suitable for paired count data exhibiting correlation, are introduced. It is shown that the usual independence assumption is unrealistic here. These models are applied to an automobile insurance claims database containing 80,994 contracts belonging to a Spanish insurance company. Finally, the consequences for pure and loaded premiums when the independence assumption is relaxed by using a bivariate Poisson regression model are analysed.

Innovation sources and productivity: a quantile regression analysis

This paper explores the effects of two main sources of innovation —intramural and external R&D— on the productivity level in a sample of 3,267 Catalan firms. The data set used is based on the official innovation survey of Catalonia which was a part of the Spanish sample of CIS4, covering the years 2002-2004. We compare empirical results by applying usual OLS and quantile regression techniques both in manufacturing and services industries. In quantile regression, results suggest different patterns at both innovation sources as we move across conditional quantiles. The elasticity of intramural R&D activities on productivity decreased when we move up the high productivity levels both in manufacturing and services sectors, while the effects of external R&D rise in high-technology industries but are more ambiguous in low-technology and services industries.

Factors explaining local privatization: A meta-regression analysis

Privatization of local public services has been implemented worldwide in the last decades. Why local governments privatize has been the subject of much discussion, and many empirical works have been devoted to analyzing the factors that explain local privatization. Such works have found a great diversity of motivations, and the variation among reported empirical results is large. To investigate this diversity we undertake a meta-regression analysis of the factors explaining the decision to privatize local services. Overall, our results indicate that significant relationships are very dependent upon the characteristics of the studies. Indeed, fiscal stress and political considerations have been found to contribute to local privatization specially in the studies of US cases published in the eighties that consider a broad range of services. Studies that focus on one service capture more accurately the influence of scale economies on privatization. Finally, governments of small towns are more affected by fiscal stress, political considerations and economic efficiency, while ideology seems to play a major role for large cities.

Innovation sources and productivity in Catalonian firms: a quantile regression analysis

This paper explores the effects of two main sources of innovation - intramural and external R&D— on the productivity level in a sample of 3,267 Catalonian firms. The data set used is based on the official innovation survey of Catalonia which was a part of the Spanish sample of CIS4, covering the years 2002-2004. We compare empirical results by applying usual OLS and quantile regression techniques both in manufacturing and services industries. In quantile regression, results suggest different patterns at both innovation sources as we move across conditional quantiles. The elasticity of intramural R&D activities on productivity decreased when we move up the high productivity levels both in manufacturing and services sectors, while the effects of external R&D rise in high-technology industries but are more ambiguous in low-technology and knowledge-intensive services. JEL codes: O300, C100, O140 Keywords: Innovation sources, R&D, Productivity, Quantile Regression

U.S. Universities’ Net Returns from Patenting and Licensing: A Quantile Regression Analysis, September 2006

In line with the rights and incentives provided by the Bayh-Dole Act of 1980, U.S. universities have increased their involvement in patenting and licensing activities through their own technology transfer offices. Only a few U.S. universities are obtaining large returns, however, whereas others are continuing with these activities despite negligible or negative returns. We assess the U.S. universities’ potential to generate returns from licensing activities by modeling and estimating quantiles of the distribution of net licensing returns conditional on some of their structural characteristics. We find limited prospects for public universities without a medical school everywhere in their distribution. Other groups of universities (private, and public with a medical school) can expect significant but still fairly modest returns only beyond the 0.9th quantile. These findings call into question the appropriateness of the revenue-generating motive for the aggressive rate of patenting and licensing by U.S. universities.