Bias Properties of Bayesian Statistics in Finite Mixture of Negative Binomial Regression Models

Factors that cause heterogeneity in crash data are often unknown to researchers and unaccommodating such heterogeneity in statistical models can undermine the validity of empirical results. A recently proposed finite mixture for the negative binomial regression model has shown a potential advantage in addressing the unobserved heterogeneity as well as providing useful information about the features of the population under study. Despite its usefulness, however, no study has been found to examine its performance under various conditions of sample sizes and sample-mean values, which are very common in crash data analysis. This study investigated the bias associated with the Bayesian summary statistics (posterior mean and median) of dispersion parameters in the two-component finite mixture of negative binomial regression models. A simulation study was conducted using various sample sizes under different sample-mean values. Two prior specifications (non-informative and weakly-informative) on the dispersion parameter were also compared. The results showed that the posterior mean using the non-informative prior exhibited a high bias for the dispersion parameter and should be avoided in all cases. The posterior median showed much better bias properties, particularly at small sample sizes and small sample means. However, as the sample size increases, the posterior median using the non-informative prior also began to exhibit an upward bias trend. In such case, the posterior mean or median with the weakly-informative prior provided a smaller bias. Based on simulation results, guidelines about the choice of priors and the summary statistics to use are presented for different sample sizes and sample mean values.

• Corporate Authors:

  Transportation Research Board

  500 Fifth Street, NW
  Washington, DC  United States  20001
• Authors:
  • Park, Byung-Jung
  • Lord, Dominique
  • Hart, Jeff
• Conference:
  • Transportation Research Board 89th Annual Meeting
  • Location: Washington DC, United States
  • Date: 2010-1-10 to 2010-1-14
• Date: 2010

Language

• English

Media Info

• Media Type: DVD
• Features: Figures; References; Tables;
• Pagination: 24p
• Monograph Title: TRB 89th Annual Meeting Compendium of Papers DVD

Subject/Index Terms

• TRT Terms: Algorithms; Bayes' theorem; Crashes; Data collection; Data quality; Highway safety; Information processing; Representative samples (Statistics); Traffic crashes; Traffic models
• Uncontrolled Terms: Negative binomial regression analysis
• Subject Areas: Data and Information Technology; Highways; Safety and Human Factors; I81: Accident Statistics;

Filing Info

• Accession Number: 01153420
• Record Type: Publication
• Report/Paper Numbers: 10-0787
• Files: TRIS, TRB
• Created Date: Mar 31 2010 7:45AM