Better performance for right-skewed data using an alternative gamma model

Abstract

Abstract Background The Maximum Likelihood Estimator (MLE) for parameters of the gamma distribution is commonly used to estimate models of right-skewed variables such as costs, hospital length of stay, and appointment wait times in Economics and Healthcare research. The common specification for this estimator assumes the variance is proportional to the square of the mean, which underlies estimation and specification tests. We present a specification in which the variance is directly proportional to the mean. Methods We used simulation experiments to investigate finite sample results, and we used United States Department of Veterans Affairs (VA) healthcare cost data as an empirical example comparing the fit and predictive ability of the models. Results Simulation showed the MLE based on a correctly specified alternative has less parameter bias, lower standard errors, and less skewness in distribution than a misspecified standard model. The application to VA healthcare cost data showed the alternative specification can have better R square, smaller root mean squared error, and smaller mean residuals within deciles of predicted values. Conclusions The alternative gamma specification can be a useful alternative to the standard specification for estimating models of right-skewed continuous variables.

Keywords

• Gamma distribution
• Generalized Linear models
• Maximum likelihood estimation
• Right-skewed variables