Copula-based bivariate count data regression models for simultaneous estimation of crash counts based on severity and number of vehicles

•Simultaneous estimation of crash frequency by either type or severity considered.•Univariate and bivariate (without and with copulas) negative binomial regression models compared.•Bivariate models with copulas shown to outperform traditional bivariate and univariate models.•Bivariate model with normal copulas outperforms other copulas tested.