Highlights Multiple safety performance functions (SPFs) by crash severity are developed for urban intersections  Various functional forms of the negative binomial (NB) regression and a generalized Poisson (GP) regression model are applied to develop the SPFs  All the NB models and a GP model show promising results when estimating the SPFs  On the basis of goodness of fit and predictive performance measures, the developed models are compared to choose a better model  The performance of the NB-P model is better than the competing models for signalized intersections while the GP model outperforms other models for unsignalized intersections

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