Accounting for Dispersion and Correlation in Estimating Safety Performance Functions. An Overview Starting from a Case Study

Abstract

In statistical analysis of crash count data, as well as in estimating Safety Performance Functions (SPFs), the failure of Poisson equidispersion hypothesis and the temporal correlation in annual crash counts must be considered to improve the reliability of estimation of the parameters. After a short discussion on the statistical tools accounting for dispersion and correlation, the paper presents the methodological path followed in estimating a SPF for urban four-leg, signalized intersections. Since the case study exhibited signs of underdispersion, a Conway-Maxwell-Poisson Generalized Linear Model (GLM) was fitted to the data; then a quasi-Poisson model in the framework of Generalized Estimating Equations (GEEs) was performed in order to account for correlation.Results confirm that dispersion and correlation are phenomena that cannot be eluded in the estimation of SPFs under penalty of loss of efficiency in estimating model parameters. Generalized Estimating Equations overcome this problem allowing to incorporate together dispersion and temporal correlation when a quasi-Poisson distribution is used for modeling crash data. Moreover, whereas GEE regression is handy (many statistical software packages have already implemented GEE functions), the interest of COM-Poisson regression, because of difficulties in interpreting the model parameters and in arranging COM-Poisson codes, is still limited to the research field.

Estimating the Safety Performance Function for Urban Unsignalized Four-Legged One-Way Intersections in Palermo, Italy

“…al, [13]; Giuffrè et. al, [14]; Giuffrè at al [15]). Covariates explored in the current study are listed in Table 3; they were selected looking at safety performance function for urban unsignalized intersections referred in literature over last 10 years (e.g.…”

“…These distributions are an effective tool to address problem of dispersion and to increase estimates effi ciency (Lord [27]); these models take into account for overdispersion by means of a parameter called overdispersion parameter α (with α > 1); wider considerations are reported in the cited papers Giuffrè et. al [15]; Lord [27]). Table 5 shows coeffi cient estimates and goodness-of-fi t for the model selected.…”

Modeling traffic safety at urban four leg-signalized intersections

“…Results confirmed the potential of the COM-Poisson model to account for dispersion phenomenon and provided a good goodness-offit. However, COM-Poisson regression models, despite their benefits, have disadvantages in terms of model estimation, also as a result of difficulties in accounting for temporal correlation in the data; (see [22]). In order to incorporate the time trend in crash count data, a different approach based on GEEs was also applied in the developing of SPFs.…”

Modelos multivariados para dados de contagem com excesso de zeros

“…A distribuição de COM-Poisson é mais flexível quando comparada com as outras distribuições de contagem, pois o seu parâmetro de dispersão ν pode acomodar tanto sobredispersão (ν < 1); quanto a subdispersão (ν > 1); equidispersão (ν = 1) e quando ν = 0 e λ > 1, S(λ , ν) não converge e a distribuição não é definida ((GIUFFRÈ et al, 2013); Gupta, Sim e Ong (2014)).…”