Bayesian approach to errors-in-variables in count data regression models / Nur Aainaa Rozliman - Nur Aainaa , Rozliman (2018)
In most practical applications, data sets are often contaminated with error or mismeasured covariates. When these errors-in-variables or measurement errors are not corrected, they will cause misleading statistical inferences and analysis. Therefore, we will focus on addressing errors-in-variables problems in count data regression models, specifically Poisson regression and negative binomial regression models. To remain useful in realistic situations, we utilize the Bayesian approach where the variance is estimated instead of assumed as known. We relax the distributional assumption of the exposure model by intentionally misspecifying the model with a flexible distribution. Following this, we shall also compare the performance between two different flexible distributions in modelling the exposure, namely the flexible generalized skew-normal distribution and flexible skewgeneralized normal distribution. We also conduct simulation studies on synthetic data sets using Markov Chain Monte Carlo simulation techniques to investigate the performance of the flexible Bayesian approach. The results of our findings show that the flexible Bayesian approach is able to estimate the values of the true regression parameters consistently and accurately with a significant bias reduction.