Negative Binomial Additive Models

Negative binomial additive models.

The generalized additive model is extended to handle negative binomial responses. The extension is complicated by the fact that the negative binomial distribution has two parameters and is not in the exponential family. The methodology is applied to data involving DNA adduct counts and smoking variables among ex-smokers with lung cancer. A more detailed investigation is made of the parametric r...

Estimation of Count Data using Bivariate Negative Binomial Regression Models

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 mode...

Negative Binomial Loglinear Mixed Models

Information and Estimation over Binomial and Negative Binomial Models

In recent years, a number of results have been developed which connect information measures and estimation measures under various models, including, predominently, Gaussian and Poisson models. More recent results due to Taborda and Pérez-Cruz relate the relative entropy to certain mismatched estimation errors in the context of binomial and negative binomial models, where, unlike in the case of ...

Estimation of adjusted rate differences using additive negative binomial regression.

Rate differences are an important effect measure in biostatistics and provide an alternative perspective to rate ratios. When the data are event counts observed during an exposure period, adjusted rate differences may be estimated using an identity-link Poisson generalised linear model, also known as additive Poisson regression. A problem with this approach is that the assumption of equality of...