In this paper, a new bivariate negative binomial regression (BNBR) model allowing any type of correlation is defined and studied. The marginal means of the bivariate model are functions of the explanatory variables. The parameters of the bivariate regression model are estimated by using the maximum likelihood method. Some test statistics including goodness-of-fit are discussed. Two numerical da...

I consider the problem of estimating the effect of a health care reform on the frequency of individual doctor visits when the reform effect is potentially different in different parts of the outcome distribution. Quantile regression is a powerful method for studying such heterogeneous treatment effects. Only recently has this method been extended to situations where the dependent variable is a ...

The negative binomial distribution has become increasingly popular as a more flexible alternative to Poisson distribution, especially when it is questionable whether the strict requirements for Poisson distribution could be satisfied. But negative binomial distribution is better for overdispersed count data that are not necessarily heavy-tailed, for heavy tailed count data the traditional stati...

List of Tables Table Page 1. Means, standard errors and range of mean density and the negative binomial dispersion parameter, by species, and coefficients, standard errors, and 95% confidence limit from linear regression of species-specific mean abundance and negative binomial dispersion parameter .. 2. Average habitat characteristics, fish abundance, and relative sampling efficiency for monito...

In recent years, there has been an abundance of research that has used Poisson models and its variants (negative binomial and zero-inflated models) to improve our understanding of the factors that affect accident frequencies on roadway segments. This study explores the application of an alternate method, tobit regression, by viewing vehicle accident rates directly (instead of frequencies) as a ...

We propose the Weibull negative binomial distribution that is a quite flexible model to analyze positive data, and includes as special submodels the Weibull, Weibull Poisson and Weibull geometric distributions. Some of its structural properties follow from the fact that its density function can be expressed as a mixture of Weibull densities. We provide explicit expressions for moments, generati...

The zero-in ated negative binomial model is used to account for overdispersion detected in data that are initially analyzed under the zero-in ated Poisson model. We consider a frequentist analysis, a jackknife estimator and non-parametric bootstrap for parameter estimation of zero-in ated negative binomial regression models. In addition, an EM-type algorithm is developed to perform maximum like...

BACKGROUND Alcohol consumption is commonly used as a primary outcome in randomized alcohol treatment studies. The distribution of alcohol consumption is highly skewed, particularly in subjects with alcohol dependence. METHODS In this paper, we will consider the use of count models for outcomes in a randomized clinical trial setting. These include the Poisson, over-dispersed Poisson, negative ...