A derivation of prediction intervals for gamma regression

Abstract

ABSTRACTGamma regression (GR) is a member of generalized liner models and often used when the phenomenon under study is skewed and the mean is proportional to the standard deviation. It can find applications in several areas such as life-testing problems, forecasting cancer incidences, weather extremes and quality control. Also it is a natural candidate when modelling the variance and it has been increasingly used over the past decade. When appropriate, studies encouraged its use over log transformation, Lewis et al. [Examples of designed experiments with nonnormal responses. J Qual Technol. 2001;33:265–278] and Hardin and Hilbe [Generalized linear models and extensions, 2nd ed. Stata Press; 2007]. Diagnostic tools and various inferential procedures such as confidence intervals and hypothesis testing were developed for GR models. An exception is prediction intervals for a future value of the process understudy. They are rarely discussed despite of its apparent importance for a practitioner. In this study I describe a simple but yet an effective procedure to compute prediction intervals for Gamma models. Four real data sets coming from medical and industrial experiments are studied to demonstrate the implementations and the usefulness of the suggested intervals. Extensive simulations are performed to investigate their advertised coverage under a wide range of sample sizes and several model designs showing consistency and satisfactory performance even for small samples.