Generalized Linier Autoregressive Moving Average (GLARMA) Negative Binomial Regression Models with Metropolis Hasting Algorithm

Abstract

This paper discusses regression models when the variance in count data is not equal to the mean. It happens in mortality cause of traffic accident data in jurisdiction's territory of Dharmasraya's Police Resort, where the variance is larger than the mean, which is called overdispersion. In this case we used negative binomial regression in time series with generalized linier autoregressive moving average (GLARMA) models. The parameters were estimated using maximum likelihood estimation (MLE) method and metropolis hasting algorithm at 100th burn - in period and 150000 iteration. The prior distribution and the number of iteration in metropolis hasting algorithm had less Mean Square Error (MSE) than MLE method. Prediction for next period using model metropolis hasting algorithm.