Random Parameters Model Applications

In the area of transportation, the first study on the random parameters model was undertaken by Milton et al. (2008). In this study mixed logit was used instead of NB models. Mannering and Bhat (2014), in a summary, show several studies undertaken in the area of accident

prediction models on road segments, some of which are presented below. Lord and Mannering (2010) state that random parameters models are statistically better than traditional fixed parameters. However, there is a criticism of the estimation of random parameters models, because when the parameter is random each observation has its ownࢼ(the estimated coefficient of the independent random parameter) so it is difficult to transfer to another location. But in case when the SD of the variable is statistically different from zero this means that on individual road sections or at intersections including roundabouts, unobserved heterogeneity exists. Unobserved heterogeneity still exists in case of using fixed parameters models for estimating such data. Consequently, using and transferring a fixed parameters model that determined to have bias leads to problems as this bias is due to unobserved heterogeneity.

Some of the studies undertaken using random-parameter count data models, for instance Anastasopoulos and Mannering (2009), in a study on road segment compared the random to fixed parameters model, and found that the efficiency and overall fit of the random parameters model is better than the fixed parameters NB model. They studied the influence of a number of geometric and traffic variables, as well as road surface conditions on the number of accidents and found that “AADT, the roughness index reading, rutting indicator reading (1 if five year average rutting readings are below 0.2 in: 0 otherwise), road segment length, median barrier presence indicator (1 if present; 0 otherwise), inside shoulder width indicator

(1 if ≥5 ft; 0 otherwise), and horizontal curvature” (p.156) to be randomly distributed across

the road segment. In this study they used 200 Halton draws to estimate the maximum likelihood function.

Another study applying this model by El-Basyouny and Sayed (2009) observed “392 urban arterials clustered in to ‘58 corridors’ in the city of Vancouver, BC”. They found that length of the segment, AADT, density of crosswalks, land use regarding business locations, density of un-signalised intersection, and the numbers of lanes between signals have a significant influence on accident frequencies and their effect was found to vary across the investigated corridors. In addition, Garnowski and Manner (2011) stated that the random parameters NB model was an appropriate model for their data in estimating factors that influence accident rates on German Autobahn connectors. Geometric variables such as steeper curve indicator, length of deceleration lane, and position of the steepest curve on the ramp were found to vary across the observations, the influence of AADT and percentage of truck traffic was fixed across the observations.

In another study on random parameter application, Ukkusuri et al. (2011) addressed the issue of “unobserved heterogeneity for modelling pedestrian crash frequencies” for “New York City at the census tract level” using random parameters NB model for the rate of pedestrian accident. They studied variables describing the “socio-demographic” and “built-environment characteristics” of the tracts. A number of variables in this study were found to vary across the observations, which shows their heterogeneous effects on the pedestrian accident numbers across the observed locations. In addition, Venkataraman et al. (2014), in an accident study on 1,153 directional road segments in the state of Washington, US, found that in 19 models out of 21 log-likelihood was significantly improved when they used random parameters NB models relative to the fixed parameter NB model. They stated that the improved log- likelihood is due to the parameters being random across the observations.

In other research areas (i.e., not transportation and safety) Rigby et al. (2003) in the UK used a random parameter logit model of the demand for the genetically modified (GM) food. They stated that the random parameters model better fits the data when they compared to the fixed parameters model. In another research area Carlsson and Martinsson (2007) applied random parameter Tobit approach to identify “willingness to pay among Swedish households to avoid power outages”. And Flannery et al. (2009) in Ireland have used random parameter logit model to explore the participation of young people in higher education. These studies used Halton draws for the estimation of maximum likelihood, and they found that when they used random parameter models, the effect of some variables varied across the observations due to unobserved heterogeneity.

These studies illustrate the effect of random parameters count data models on accident data across the roadway segments. Previous studies mentioned in this section found that random parameters models account for unobserved heterogeneity, and statistically provide better overall fit and efficiency than the fixed parameters NB model. Thus this study (thesis) used the same approach for the prediction of total accidents, truck accidents, and HBIs at roundabouts with respect to different roundabout categories. According to previous literature, no studies on the effect of the random parameters model on total and truck accidents at roundabouts and on HBI in all type of road segments and at intersections including roundabouts have been undertaken. Thus this study represents a novel approach of the application of random parameters NB models to the prediction of accidents and HBIs at roundabouts.