Discipline: Mathematics and Statistics
Subcategory: Mathematics and Statistics
Ciara Allen - North Carolina Central University
The Poisson distribution is a well-known, discrete probability distribution that is commonly used to model count data. When using the Poisson distribution, one assumes equi-dispersion; that is, the mean and variance of the distribution of the data are equal. However, count data often exhibit over-dispersion, such that the variance is greater than the mean. To model over-dispersed count data, Poisson mixed models are commonly used where the mean is a random variable that follows a probability distribution, such as inverse-Gaussian, gamma, or lognormal, which is known as the mixing distribution. This project considers the Poisson-Inverse Gaussian (PIG) regression model, and the purpose is to test the sensitivity of maximum likelihood estimators (MLEs) of the PIG model parameters when the inverse Gaussian (or mixing) distribution is misspecified completely. We simulate Poisson-Gamma and Poisson-Lognormal data and compute MLEs for the regression parameters and the variance of the mixing distribution under an assumed PIG model. The simulation results suggests that the regression parameter estimates are less sensitive to mixing distribution misspecification than the variance component. The results are consistent with those of Weems and Smith (2018) which show that the MLEs are robust to small perturbations of the mixing distribution. Future work will consist of the application of a PIG model to real data.
Funder Acknowledgement(s): HBCU-UP
Faculty Advisor: Dr. Kimberly Weems, firstname.lastname@example.org
Role: Using R software, I simulated Poisson-Gamma and Poisson-Lognormal data and generated visualizations. I estimated the Poisson Inverse-Gaussian parameters using maximum likelihood estimation.