چکیده:
Abstract Negative binomial regression model (NBR) is a popular approach for modeling overdispersed count data with covariates. Several parameterizations have been performed for NBR, and the two well-known models, negative binomial-1 regression model (NBR-1) and negative binomial-2 regression model (NBR-2), have been applied. Another parameterization of NBR is negative binomial-P regression model (NBR-P), which has an additional parameter and the ability to nest both NBR-1 and NBR-2. This paper introduces several forms of bivariate negative binomial regression model (BNBR) which can be fitted to bivariate count data with covariates. The main advantages of having several forms of BNBR are that they are nested and allow likelihood ratio test to be performed for choosing the best model, they have flexible forms of mean-variance relationship, they can be fitted to bivariate count data with positive, zero or negative correlations, and they allow overdispersion of the two dependent variables. Applications of several forms of BNBR are illustrated on two sets of count data; Australian health care and Malaysian motor insurance.
خلاصه ماشینی:
"However, to handle over-dispersed count data, a situation where the variance exceeds the mean, negative binomial regression model (NBR) has been used as an alternative.
Besides NBR, the generalized Poisson regression model (GPR) has also been suggested for handling under- or over-dispersed count data (Zamani and Ismail 2012; Karimi et al.
The limitations of bivariate models from the trivariate reduction method can be found in several studies in which a few models were suggested, such as modelling dependence through correlated random effects (Berkhout and Plug 2004), fitting bivariate data using bivariate generalized negative binomial regression model (Gurmu and Elder 2000), modelling bivariate data with bivariate negative binomial distribution (BNBD) that allows a restricted range of negative correlations (Mitchell and Paulson 1981), and modelling dependence through copula functions (Cameron et al.
The main advantages of having several forms of BNB regression are that they are nested and allow likelihood ratio test to be performed for choosing the best model, they have flexible forms of mean-variance relationship, they can be fitted to bivariate count data with positive, zero or negative correlations, and they allow over-dispersion of the two dependent variables.
The same data was also used by Cameron and Johansson (1997) for fitting several univariate models, by Gurmu and Elder (2000) who fitted bivariate generalized negative binomial regression model and by Famoye (2010) who fitted BNBR-2.
The new forms of BNBR have flexible mean-variance relationship, can be fitted to bivariate count data with positive, zero or negative correlations, and allow over-dispersion of the two response variables."