Modeling clustered count data using mixed effect discrete Weibull regression model with cubic splines

This paper investigates the use of mixed-effect discrete Weibull (DW) regression model with cubic splines for clustered count data. DW regression model can be used for both over and under-dispersed data thus, it can be an appropriate choice for researchers to use without having the risk to violate assumptions for using a particular model distribution. We used a cubic spline function to model the non-linear relationship between the outcome variable and the covariate. The proposed model is applied to a clustered dataset from the eighth Korean National Health and Nutrition Examination Survey (KNHANES VIII) from 2019 to assess the factors influencing the amount of alcohol drink in 17 different regions. We compared the results with our proposed model with those of Poisson, negative binomial, zero-inflated Poisson and zero-inflated negative binomial regression models in the presence of spline function. The results show that using DW regression model with cubic spline gives the best fit. We also held a simulation study to investigate the performance and the robustness of DW with a spline function. It turns out that DW regression model with a spline function can flexibly model clustered count data with various dispersion and data with many zeros.