Modelling the US Diabetes Mortality Rates via Generalized Linear Model with the Tweedie Distribution

Oznur Ozaltin, Neslihan Iyit

Abstract: In this study, we are interested in modelling the response variable as the US diabetes mortality rate in the aspect of different types of neoplasms, endocrine, nutritional and metabolic diseases, musculoskeletal system diseases, obesity, sugar intake, and alcohol use disorder via generalized linear model (GLM) with the Tweedie distribution. In this study, firstly, we will focus on the effects of changing the variance power parameter and the index of the power link function on the AIC goodness-of-fit test statistic and also Pearson chi-square and deviance statistics for the dispersion parameter and the residuals in the GLMs with the Tweedie distribution for the US diabetes mortality data. The best link function is determined as identity with the variance power parameter 1.9 and the link function power 1 belonging to the Tweedie distribution in the GLM for the US diabetes mortality data. Secondly, the importance of model diagnostic plots based on the residuals, Cooks distance and leverage is emphasized to determine the extreme observations that may cause some problems for parameter estimations, hypothesis tests, and statistical inferences in the GLM for the US diabetes mortality data from the Tweedie distribution.

Keywords: Diabetes mortality, generalized linear model, Tweedie distribution, link function