Residuals in Bell-Touchard regression models
Residual Analysis. Regression Model. Generalized Linear Models. Count Data.
Pearson Residual.
The Bell-Touchard distribution and its regression model, are a promising alternative
to the statistical models that are already established in the count data modelling, as Poisson
and Negative Binomial models. Count data are observations such that the variable assumes
non-negative integer values and are useful, for example, to modelling the number of claims
that happened in a given period of time, which are of interest to insurance companies, for
example. The Poisson model, for this purpose, is not a model that does work well with the
overdispersion problem, a situation in which the variance is greater than the expectation.
Alternatives to deal with this kind of problem emerged, being proposed the zero-inflated
models and the Negative Binomial model. The Bell-Touchard model, that is a generalization of
Bell model, is a recent alternative that tries to solve this kind of problem. In this master’s
dissertation, a deeper research is made about residuals in the Bell-Touchard regression model
and the main goal is to improve the academic literature about count data.