Journal of Data Science

There is growing interest in accommodating network structure in panel data models. We consider dynamic network Poisson autoregressive (DN-PAR) models for panel count data, enabling their use in regard to a time-varying network structure. We develop a Bayesian Markov chain Monte Carlo technique for estimating the DN-PAR model, and conduct Monte Carlo experiments to examine the properties of the posterior quantities and compare dynamic and constant network models. The Monte Carlo results indicate that the bias in the DN-PAR models is negligible, while the constant network model suffers from bias when the true network is dynamic. We also suggest an approach for extracting the time-varying network from the data. The empirical results for the count data for confirmed cases of COVID-19 in the United States indicate that the extracted dynamic network models outperform the constant network models in regard to the deviance information criterion and out-of-sample forecasting.

Abstract:In medical literature, researchers suggested various statistical procedures to estimate the parameters in claim count or frequency model. In the recent years, the Poisson regression model has been widely used particularly. However, it is also recognized that the count or frequency data in medical practice often display over-dispersion, i.e., a situation where the variance of the response variable exceeds the mean. Inappropriate imposition of the Poisson may underestimate the standart errors and overstate the significance of the regression parameters, and consequently, giving misleading inference about the regression parameters. This article suggests the Negative Binomial (NB) and Conway-Maxwell-Poisson (COM-Poisson) regression models as an alternatives for handling overdispersion. All mentioned regression models are applied to simulation data and dataset of hospitalization number of people with schizophrenia, the results are compared.