Multivariate random parameters zero-inflated negative binomial regression for analyzing urban midblock crashes

Abstract

Urban midblock crashes are influenced mainly by traffic operation and roadway geometric features. In this paper, 10-year crash data from 1,506 directional urban midblock segments in Nebraska were analyzed using the multivariate random parameters zero-inflated negative binomial model to account for unobserved heterogeneity produced by correlations across segments, correlations across crash collision types, excessive zero crashes, and over dispersion. The multivariate random parameters zero-inflated negative binomial model was superior to many common crash frequency models in terms of both goodness of fit and prediction accuracy. Compared with the multivariate fixed parameters zero-inflated negative binomial model, the multivariate random parameters zero-inflated negative binomial model identified fewer key influencing factors and revealed segment-specific effects of these factors on different crash types. It showed that the number of lanes, annual average daily traffic per lane, and segment length might have non-positive effects on crash frequencies. Segments with a speed limit of 45 mph had fewer crashes than did those with lower speed limits, and there were fewer crashes on the segments in Omaha than on those in Lincoln. It was also found that neither the presence of a shoulder, on-street parking, or one-way traffic, nor lane width had significant influences on crash frequencies. These findings are informative for transportation agencies to take correct and efficient measures to accommodate diverse transportation demands without reducing traffic safety. By contrast, the fixed parameters model produced results consistent with intuition, but the results were insufficient to provide actionable recommendations.

Exploring the Application of the Linear Poisson Autoregressive Model for Analyzing the Dynamic Impact of Traffic Laws on Fatal Traffic Accident Frequency

“…In order to analyze the overdispersed data, many studies proposed different mixed Poisson models, such as the Poisson-gamma model (the negative binomial (NB) model) [7][8][9][10][11][12][13], Poisson-lognormal model [14][15][16], and Poissoninverse gamma model [17]. For the data with many zeros (i.e., excess zero-count data), the zero-inflated models were applied, including the zero-inflated Poisson model [18,19], zero-inflated negative binomial model [20][21][22], and their extension models (i.e., multiple random parameter zeroinflated negative binomial regression model [20] and zero expansion Poisson regression model with random parameter effect [23]). Although rare, crash data can sometimes be characterized by underdispersion.…”

A Correlated Random Parameters Model with Heterogeneity in Means to Account for Unobserved Heterogeneity in Crash Frequency Analysis

“…To track the unobserved heterogeneity, a conventional NB model can be extended to a random parameters NB (RPNB) model by rewriting the parameter as ( 9–12 ):…”

“…The absence of such unobserved factors can potentially lead to biased parameter estimates, inaccurate crash predictions and even erroneous inferences, which is typically referred to as unobserved heterogeneity (variation in the safety effect of factors across observations that are unknown to the analyst) (6)(7)(8). In light of this, many statistical techniques have been developed to account for unobserved heterogeneity and among which, the random parameters NB (RPNB) model has been frequently used for crash frequency analysis (9)(10)(11)(12). The idea behind a random parameters model is that the unobserved heterogeneity from one observation to the next can be captured by allowing each parameter in the model to vary across observations according to a pre-defined distribution (e.g., the normal distribution).…”

“…The idea behind a random parameters model is that the unobserved heterogeneity from one observation to the next can be captured by allowing each parameter in the model to vary across observations according to a pre-defined distribution (e.g., the normal distribution). The statistical fit and interpretative power of the RPNB model have been proved to be superior to that of a simple NB model and enable it to benefit from its ability to account for the overall unobserved heterogeneity (10)(11)(12).…”

Sparse group regularization for semi‐continuous transportation data

“…Many methods have been proposed to analyze crash data, such as generalized additive models and gamma model 3 . Among them, the zero‐inflated count model is one of the most ubiquitous models and has been widely used in the transportation domain to examine crash frequency 4 at intersections, 5 on roadway segments, 6 freeways, 7 and for weather‐related conditions 8 …”