Random parameters multivariate tobit and zero-inflated count data models: Addressing unobserved and zero-state heterogeneity in accident injury-severity rate and frequency analysis

• Accident injury-severity rates and frequencies are modeled.
• Random parameters tobit and zero-inflated count data models are estimated, and unobserved and zero-state heterogeneity are addressed.
• Forecasts are compared with mean-predicted and individual βs for the random parameters.
• The random parameters multivariate models are statistically superior.
• The forecasts with the individual βs for the random parameters are more accurate.

This paper uses data collected over a five-year period between 2005 and 2009 in Indiana to estimate random parameters multivariate tobit and zero-inflated count data models of accident injury-severity rates and frequencies, respectively. The proposed modeling approach accounts for unobserved factors that may vary systematically across segments with and without observed or reported accident injury-severities, thus addressing unobserved, zero-accident state and non-zero-accident state heterogeneity. Moreover, the multivariate setting allows accounting for contemporaneous cross-equation error correlation for modeling accident injury-severity rates and frequencies as systems of seemingly unrelated equations. The tobit and zero-inflated count data modeling approaches address the excessive amount of zeros inherent in the two sets of dependent variables (accident injury-severity rates and frequencies, respectively), which are – in nature – continuous and discrete count data, respectively, that are left-censored with a clustering at zero. The random parameters multivariate tobit and zero-inflated count data models are counter-imposed with their equivalent fixed parameters and lower order models, and the results illustrate the statistical superiority of the presented models. Finally, the relative benefits of random parameters modeling are explored by demonstrating the forecasting accuracy of the random parameters multivariate models with the software-generated mean ββs of the random parameters, and with the observation-specific ββs of the random parameters.