Flexible Regression Models for Count Data Based on Renewal Processes: The Countr Package

Abstract

A new alternative to the standard Poisson regression model for count data is suggested. This new family of models is based on discrete distributions derived from renewal processes, i.e., distributions of the number of events by some time t. Unlike the Poisson model, these models have, in general, time-dependent hazard functions. Any survival distribution can be used to describe the inter-arrival times between events, which gives a rich class of count processes with great flexibility for modelling both underdispersed and overdispersed data. The R package Countr provides a function, renewalCount(), for fitting renewal count regression models and methods for working with the fitted models. The interface is designed to mimic the glm() interface and standard methods for model exploration, diagnosis and prediction are implemented. Package Countr implements stateof-the-art recently developed methods for fast computation of the count probabilities. The package functionalities are illustrated using several datasets.

Keywords

• renewal process
• duration dependence
• count data
• weibull distribution
• convolution
• richardson extrapolation