Overdispersion in modelling accidents on road sections and in Empirical Bayes estimation

The statistical analysis of crash-frequency data: A review and assessment of methodological alternatives

“…13 12 Usually the overdispersion parameter or its inverse is assumed to be fixed, but recent research in highway safety has shown that the variance structure can potentially be dependent on explanatory variables Hauer, 2001;Lord et al, 2005a;Cafiso et al, 2010b).…”

Bias properties of Bayesian statistics in finite mixture of negative binomial regression models in crash data analysis

“…Over-dispersion caused by unobserved heterogeneity in crash data is a serious problem and has been addressed in a variety of ways within the negative binomial (NB) modeling framework (Hauer, 2001;Heydecker and Wu, 2001;Miaou and Lord, 2003;Geedipally et al, 2009;Anastasopoulos and Mannering, 2009). However, the true factors that affect heterogeneity are often unknown to researchers and failure to accommodate such heterogeneity in the model can undermine the validity of the empirical results.…”

The Poisson inverse Gaussian (PIG) generalized linear regression model for analyzing motor vehicle crash data

“…Previous studies have shown that the dispersion parameter can also be modeled as a function of the explanatory variables to explain more variation. The link functional form for dispersion parameters was also investigated by authors (Hauer, 2001, Heydecker and Wu, 2001, Miaou and Lord, 2003, Mitra and Washington, 2007 . Considering that Equation (15) contains all the covariates (Mitra and Washington, 2007), we simply modeled the dispersion parameters of NB and PIG models as the function of segment length in the format recommended by Geedipally and Lord (2011) The nonlinear relationship provides more flexibility to capture the variance of the data.…”

“…The commonly used link function which associated crash with covariates such as daily traffic flow, lane width was chosen. Both models were developed using varying dispersion parameters for the flexibility of accounting for the variation and better statistical fit (Hauer, 2001, Heydecker and Wu, 2001, Miaou and Lord, 2003, Mitra and Washington, 2007, Geedipally and Lord, 2011. Models with fixed dispersion parameters were also listed for comparison purposes.…”