A Parametric Model for Cluster Correlated Categorical Data

Meester, S. G.; MacKay, Jock

doi:10.2307/2533435

Cited by 62 publications

(48 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Copulas have been applied with GLMs in the biomedical literature since the mid-1990s ( [16][17][18]). In the actuarial literature, the t-copula and the Gaussian copula with GLMs as marginal distributions were used to develop credibility predictions in [19].…”

Section: Copula Regressionmentioning

confidence: 99%

Multivariate Frequency-Severity Regression Models in Insurance

Frees

Lee

Yang

2016

Risks

110

View full text Add to dashboard Cite

Abstract:In insurance and related industries including healthcare, it is common to have several outcome measures that the analyst wishes to understand using explanatory variables. For example, in automobile insurance, an accident may result in payments for damage to one's own vehicle, damage to another party's vehicle, or personal injury. It is also common to be interested in the frequency of accidents in addition to the severity of the claim amounts. This paper synthesizes and extends the literature on multivariate frequency-severity regression modeling with a focus on insurance industry applications. Regression models for understanding the distribution of each outcome continue to be developed yet there now exists a solid body of literature for the marginal outcomes. This paper contributes to this body of literature by focusing on the use of a copula for modeling the dependence among these outcomes; a major advantage of this tool is that it preserves the body of work established for marginal models. We illustrate this approach using data from the Wisconsin Local Government Property Insurance Fund. This fund offers insurance protection for (i) property; (ii) motor vehicle; and (iii) contractors' equipment claims. In addition to several claim types and frequency-severity components, outcomes can be further categorized by time and space, requiring complex dependency modeling. We find significant dependencies for these data; specifically, we find that dependencies among lines are stronger than the dependencies between the frequency and average severity within each line.

show abstract

Section: Copula Regressionmentioning

confidence: 99%

Multivariate Frequency-Severity Regression Models in Insurance

Frees

Lee

Yang

2016

Risks

110

View full text Add to dashboard Cite

show abstract

“…Thus, the Frank copula is suited for very strong central dependency with very weak tail dependency. The Frank copula has been used quite extensively in empirical applications (see Meester and MacKay, 1994;Micocci and Masala, 2003).…”

Section: The Frank Copulamentioning

confidence: 99%

A copula-based approach to accommodate residential self-selection effects in travel behavior modeling

Bhat

Eluru

2009

Transportation Research Part B: Methodological

249

141

View full text Add to dashboard Cite

The dominant approach in the literature to dealing with sample selection is to assume a bivariate normality assumption directly on the error terms, or on transformed error terms, in the discrete and continuous equations. Such an assumption can be restrictive and inappropriate, since the implication is a linear and symmetrical dependency structure between the error terms. In this paper, we introduce and apply a flexible approach to sample selection in the context of built environment effects on travel behavior. The approach is based on the concept of a "copula", which is a multivariate functional form for the joint distribution of random variables derived purely from pre-specified parametric marginal distributions of each random variable. The copula concept has been recognized in the statistics field for several decades now, but it is only recently that it has been explicitly recognized and employed in the econometrics field. The copula-based approach retains a parametric specification for the bivariate dependency, but allows testing of several parametric structures to characterize the dependency. The empirical context in the current paper is a model of residential neighborhood choice and daily household vehicle miles of travel (VMT), using the 2000 San Francisco Bay Area Household Travel Survey (BATS). The sample selection hypothesis is that households select their residence locations based on their travel needs, which implies that observed VMT differences between households residing in neo-urbanist and conventional neighborhoods cannot be attributed entirely to the built environment variations between the two neighborhoods types. The results indicate that, in the empirical context of the current study, the VMT differences between households in different neighborhood types may be attributed to both built environment effects and residential self-selection effects. As importantly, the study indicates that use of a traditional Gaussian bivariate distribution to characterize the relationship in errors between residential choice and VMT can lead to misleading implications about built environment effects.1

show abstract

“…These include a fully parametric copula model for symmetric dependent clustered categorical data that involves the estimation of a parameter to estimate association between raters' classifications for a subject (Meester & MacKay 1994), several generalized estimating equation approaches, many involving kappa (Williamson, Manatunga & Lipsitz 2000;Klar, Lipsitz & Ibrahim 2000;Lipsitz & Fitzmaurice 1996), and the use of the beta-binomial distribution to account for intra-class correlation among binary responses in cluster sampling (Moore 1987;Lui, Cumberland & Kuo 1996). These marginal approaches provide inference that is population-based, rather than related to the individual raters and subjects, which is the focus of the current paper which uses a modeling approach that conditions on the random effects (Breslow & Clayton 1993).…”

Section: Discussionmentioning

confidence: 99%

On population‐based measures of agreement for binary classifications

Nelson

Edwards

2008

Can J Statistics

View full text Add to dashboard Cite

Abstract:The authors describe a model-based kappa statistic for binary classifications which is interpretable in the same manner as Scott's pi and Cohen's kappa, yet does not suffer from the same flaws. They compare this statistic with the data-driven and population-based forms of Scott's pi in a population-based setting where many raters and subjects are involved, and inference regarding the underlying diagnostic procedure is of interest. The authors show that Cohen's kappa and Scott's pi seriously underestimate agreement between experts classifying subjects for a rare disease; in contrast, the new statistic is robust to changes in prevalence. The performance of the three statistics is illustrated with simulations and prostate cancer data. Sur les mesures théoriques d'accord pour les classements binairesRésumé : Partant d'un modèle de classification binaire, les auteurs proposent une statistique kappa qui s'interprète comme le pi de Scott et le kappa de Cohen, mais qui ne souffre pas des mêmes défauts. Ils comparent cette statistique aux versions théorique et expérimentale du pi de Scott dans le cas où l'inférence sur une procédure diagnostic est faiteà partir de données issues de plusieursévaluateurs et de plusieurs sujets. Les auteurs montrent que le kappa de Cohen et le pi de Scott sous-estiment considérablement l'accord entre les experts lorsque ceux-ci sont appelésà classer des sujets comme atteints ou non d'une maladie rare ; en revanche, la nouvelle statistique est robuste aux changements de prévalence. La performance des trois statistiques est illustrée au moyen de simulations et de données sur le cancer de la prostate.

show abstract

A Parametric Model for Cluster Correlated Categorical Data

Cited by 62 publications

References 30 publications

Multivariate Frequency-Severity Regression Models in Insurance

Multivariate Frequency-Severity Regression Models in Insurance

A copula-based approach to accommodate residential self-selection effects in travel behavior modeling

On population‐based measures of agreement for binary classifications

Contact Info

Product

Resources

About