Random Parameter Negative Binomial Model Research Articles

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

Unobserved heterogeneity induced by omitted variables is a major challenge in developing reliable road safety models. In recent years, the random parameters negative binomial (RPNB) model has been used frequently in crash frequency analysis to account for unobserved heterogeneity. However, the majority of past studies of the RPNB model assumed that there was no correlation between different sources of unobserved heterogeneity, which is not always true given the complex interactions of safety factors. Compared with the RPNB model, a more flexible random parameters model that is the correlated random parameters negative binomial with heterogeneity in means (CRPNBHM) model was proposed in this study. Results indicate that the CRPNBHM model could not only capture the otherwise unobserved heterogeneity, but also track the underlying correlation among different sources of unobserved heterogeneity, thus outperforming the RPNB model. In addition, new insights into the interactions of safety factors (e.g., the joint safety effects of heavy trucks and pavement rutting depth) were obtained from the CRPNBHM model and these are expected to be beneficial in developing effective safety countermeasures. Results from this study demonstrated the CRPNBHM model to be a good alternative for crash frequency analysis, particularly when unobserved heterogeneity was detected.

Public acceptance of and heterogeneity in behavioral beach trip responses to offshore wind farm development in Catalonia (Spain)

A combined travel cost – contingent behaviour survey of residents and tourists in Catalonia is conducted on-site to examine the effects on beach recreational demand of developing an offshore wind farm (OWF) project. The survey considers four potential OWF scenarios with different degrees of visual impact. We allow for heterogeneity in trip preferences among individuals and control for on-site sampling through the use of a random parameters negative binomial (RPNB) model and a Multivariate Poisson log-normal (MPLN) model, respectively. The welfare measures derived from the RPNB model relate to the current beach users only, whereas those from the MPLN model refer to the general population of residents and tourists in Catalonia. The results show the importance of the specific place of location of the OWF project and how the installation of wind turbines would significantly decrease the demand for trips, depending on their degree of visual impacts, leading to a substantial welfare loss. However, the results also show that the project mainly would cause a displacement of trips to other beaches within Catalonia rather than outside Catalonia and that the welfare per trip measures generated by the RPNB and MPLN models substantially differ. Policy implications of these findings are discussed.

Investigating the effects of monthly weather variations on Connecticut freeway crashes from 2011 to 2015

IntroductionThe objective of this research is to investigate the effects of monthly weather conditions on traffic crash experience on freeways, considering the interactions between weather, traffic volumes, and roadway conditions. Methods: Data from the state of Connecticut from 2011to 2015 were used. Random parameters negative binomial models with first-order, autoregressive covariance were estimated for representative types of freeway crashes (front-to-rear, sideswipe-same-direction, and fixed-object), most severe crashes (i.e., fatal and injury crashes), and non-injury crashes (i.e., property-damage-only crashes). Results: Major findings are that variations in monthly traffic volumes, roadway geometry, and weather conditions explain much of the variations in monthly traffic crashes. Time effects exist in the panel monthly data for all types of crashes. Taking into account this effect improves model prediction results. When the raw weather measures are highly correlated, using dimension reduction techniques helps to extract more interpretable weather factors. By considering the interaction effects between roadway condition variables, additional findings were found. In general, lower temperature, more heavy fog days, decreased precipitation, lower wind speed, higher monthly traffic volumes, and narrower inside shoulder were found to be associated with higher monthly crashes. The effects of area type and outside shoulder width change dramatically as the number of through lanes changes. Practical applications: The findings of this research could help researchers and general readers gain a better understanding of the effects of monthly weather conditions and other roadway factors on freeway crashes and give engineers practical guidelines on improving freeway safety.

Predicting downgrade crash frequency with the random-parameters negative binomial model: Insights into the impacts of geometric variables on downgrade crashes in Wyoming

Road deaths, injuries and property damage place a huge burden on the economy of most nations. Wyoming has a high crash rate on mountain passes. The crash rates observed in the state is as a result of many factors mainly related to the challenging mountainous terrain in the state, which places extra burden on drivers in terms of requiring higher levels of alertness and driving skill. This study was conducted to investigate factors leading to crashes on Wyoming downgrades, with a focus on geometric variables. Traditionally, crash frequency analysis is conducted using count models such as Poisson or negative binomial models. However, factors that affect crash frequency are known to vary across observations. The use of a methodology that fails to take into account heterogeneity in observed and unobserved effects relating to roadway characteristics can lead to biased and inconsistent estimates. Inferences made from such parameter estimates may be misleading. This study employed the random-parameters negative binomial regression models to evaluate the impact of geometric variables on crash frequency. Five separate models were estimated for total, fatal/injury, property damage only (PDO), truck, and non-truck crash frequencies. Several geometric and traffic variables were found to influence the frequency of crashes on downgrades. These included segment length, vertical grade, shoulder width, lane width, presence of downgrade warning sign, vertical curve length, presence of a passing lane, percentage of trucks, number of lanes and AADT. The results suggest that segment length, lane width, presence of a passing lane, presence of a downgrade warning sign, vertical grade, and percentage of trucks are best modeled as random parameters. The findings of this study will provide transportation agencies with a better understanding of the impact of geometric variables on downgrade crashes.

Evaluating the predictive power of an SPF for two-lane rural roads with random parameters on out-of-sample observations

Negative binomial (NB) regression is among the most common statistical modeling methods used to model crash frequencies due to its simple functional form and ability to handle over-dispersion commonly found in crash data. However, a drawback of this approach is that regression parameters are assumed to be the same across observations, which could contribute to biased parameter estimates. To alleviate this concern, the random parameters negative binomial (RPNB) model was recently proposed, which allows regression parameters to differ across observations following some known distribution. The resulting coefficients should be less biased, and thus the RPNB approach is believed to provide a more accurate relationship between independent variables and expected crash frequency. However, the prediction accuracy of the RPNB model relative to the standard NB model has not been thoroughly evaluated, particularly with respect to out-of-sample observations for which unique random parameters cannot be estimated. In this paper, the predictive power of the RPNB and NB models are examined using two-lane rural highway data from three engineering Districts in Pennsylvania. Multiple evaluation metrics are applied—root-mean-square error (RMSE) and mean absolute error (MAE), coefficients from calibration functions and cumulative residual (CURE) plots—to assess each model type. The results show that the RPNB model outperforms the NB model when applied to within sample observations (i.e., those used to estimate the model) by making use of the observation-specific coefficients. However, the predictive power of the RPNB model appears to be similar to or slightly less precise than the traditional NB model when applied to out-of-sample observations. Since the RPNB model is estimated using a simulation-based approach, sensitivity tests were also performed to see how the parameter estimates change with the number of Halton draws used to perform the simulation. For the sample sizes used in this paper, the estimates were fairly insensitive when more than 50 Halton draws were used. The findings suggest that the RPNB model is more reliable when applied to the same set of sites that were used to estimate the model but might not be as robust as the traditional NB model when applied to other sites.

Application of a model-based recursive partitioning algorithm to predict crash frequency

Count regression models have been applied widely in traffic safety research to estimate expected crash frequencies on road segments. Data mining algorithms, such as classification and regression trees, have recently been introduced into the field to overcome some of the assumptions associated with statistical models. However, these data-driven algorithms usually provide non-parametric output, making it difficult to draw statistical inference or to evaluate how independent variables are associated with expected crash frequencies. In this paper, the model-based recursive partitioning (MOB) algorithm is applied in a crash frequency application. The algorithm incorporates the concept of recursive partitioning data in tree models and develops user-defined statistical models as outputs. The objective of this paper is to explore the potential of the MOB algorithm as a methodological alternative to parametric modeling methods in crash frequency analysis. To accomplish the objective, a standard negative binomial (NB) regression model, a NB model developed using the MOB algorithm, adjusted NB models which incorporate variables identified by the MOB algorithm, and a random parameters NB model are compared using 8 years of data collected from two-lane rural highways in Pennsylvania. The models are compared in terms of data fitness, sign and magnitude of statistical association between the independent and dependent variables, and predictive power. The results show that the MOB-NB model yields better data fitness than other NB models, and provides similar performance to the RPNB model, suggesting that the MOB-NB model may be capturing unobserved heterogeneity by dividing the data into subgroups. The presence of a passing zone and posted speed limit are two covariates identified by the MOB algorithm that differentiate variable effects among subgroups. In addition, the MOB-NB model provides the highest prediction accuracy based on the training and test data sets, although the difference among models is small. The comparison results reveal that the MOB algorithm is a promising alternative to identify covariates, evaluate variable associations and instability, and make predictions in a crash frequency context.

Analysis of Rural Interstate Fatality Rates in Consideration of Recent Increases in Maximum Statutory Speed Limits

The relationship between traffic safety and speed limits has been an area of significant research. Since the repeal of the National Maximum Speed Law in 1995, states have full autonomy in establishing maximum statutory speed limits. Since 2001, at least 25 states have increased their maximum limits to speeds as high as 85 mph. This study examines changes in rural interstate fatalities from 2001 to 2016 in consideration of such increases. Speed limit policy data include the maximum speed limit for each state–year combination, as well as the proportion of rural interstate mileage posted at each speed limit in each state. Random parameter negative binomial models are estimated to control for unobserved heterogeneity, as well as time-invariant effects unique to each state. The results show that increasing the mileage of rural interstates posted at 70, 75, or 80 mph by 1% is associated with fatality increases of 0.2%, 0.5%, and 0.6%, respectively. These increases are more pronounced than when considering only the maximum statutory limits in each state. The study also examines the influence between these higher limits and the frequency of fatal crashes involving speeding and driver distraction. At the highest limits of 75 and 80 mph, the increases among these subsets of crashes are greater than the increases in total fatalities. Ultimately, this study provides important empirical evidence in support of continuing speed limit policy discussions, in addition to identifying salient analytical concerns that should be considered as a part of longitudinal analyses of state-level fatality data.

Exposure to pedestrian crash based on household survey data: Effect of trip purpose

Pedestrian are vulnerable to severe injury and mortality in the road crashes. Understanding the essence of the pedestrian crash is important to the development of effective safety countermeasures and improvement of social well-being. It is necessary to measure the exposure for the quantification of pedestrian crash risk. The primary goals of this study are to explore the efficient exposure measure for pedestrian crash, and identify the possible factors contributing to the incidence of pedestrian crash. In this study, amount of travel was estimated based on the Travel Characteristic Survey (TCS) data in 2011, and the crash data were obtained from the Transport Information System (TIS) of the Hong Kong Transport Department during the period from 2011 to 2015. Total population, walking frequency and walking time were adopted to represent the pedestrian exposure to road crash. The effect of trip purpose on pedestrian crash was evaluated by disaggregating the pedestrian exposure proxies by purpose. Three random-parameter negative binomial regression models were developed to compare the performances of the three pedestrian exposure proxies. It was found that the model in which walking frequency was used as the exposure proxy provided the best goodness-of-fit. Frequency of walking back home, among other trip purposes, was the most sensitive to the increase in pedestrian crash risk. Additionally, increase in the frequency of pedestrian crash was correlated to the increases in the proportions of children and elderly people. Furthermore, household size, median household income, road density, number of non-signalized intersection as well as number of zebra crossings also significantly affected the pedestrian crash frequency. Findings of this study should be indicative to the development and implementation of effective traffic control and management measures that can improve the pedestrian safety in the long run.

Safety effects of street lighting on roadway segments: Development of a crash modification function

Objective: Nighttime crashes are overrepresented on the U.S. highway system. Roadway lighting, which provides additional visibility by supplementing vehicle headlights, has been identified as an effective countermeasure to improve nighttime safety. However, the existing literature does not provide a thorough understanding of the effects of street lighting photometric characteristics on nighttime crash occurrence on roadway segments. This study aimed to investigate the relationship between lighting photometric measures and nighttime crash risk on roadway segments and develop a crash modification function/factor (CMF).Methods: The research team collected horizontal illuminance data on 440 roadway segments between 2 successive signalized intersections in Florida for 2012–2014 and matched 4 years of nighttime and daylight crash data (2011–2014). Random parameter negative binomial models were estimated for both nighttime and daylight crash frequencies. The expected night-to-day crash odds ratio, as an equivalent of CMF, was derived from the fitted models with the correction of estimation variances. The confidence intervals (CIs) of the developed CMF were estimated using the Cox method.Results: The coefficient of the mean of horizontal illuminance is significantly negative in the nighttime model. The coefficients of the standard deviation of horizontal illuminance are significantly positive and normally distributed in both the nighttime and daylight models. The significance of the standard deviation in the daylight model captures the confounding effects—a high standard deviation correlates with high traffic exposures, poor safety design standards, and low maintenance quality. The CMF based on the expected daylight-to-day odds ratio was developed as an exponential function of the increments and the increment squares of the mean and the standard deviation of horizontal illuminance. Its 95% CIs indicate that the CMF is almost significant over the whole range. Other significant variables contributing to nighttime crash risk include annual average daily traffic, truck percentage, segment length, access density, undivided roads, and urban/city limits.Conclusions: Horizontal illuminance characteristics have a significant impact on nighttime crash risk on roadway segments. An increase in the mean of horizontal illuminance, indicating an improvement in average lighting level, tends to decrease nighttime crash risk; an increase in the standard deviation, representing a poor uniformity of lighting pattern on a roadway segment, is more likely to raise nighttime crash risk. Because the 2 measures are strongly correlated in a low mean range (<0.44 fc), the 2 photometric measures need to be considered together to interpret the safety effects of lighting patterns. The standard deviation shows better performance in measuring lighting uniformity on a roadway segment than the traditional ratios (max-to-min and mean-to-min). However, a new photometric measure is needed to capture the true lighting pattern influencing driver vision at night.

Investigating factors of crash frequency with random effects and random parameters models: New insights from Chinese freeway study

In response to the rapid economic growth in China, its freeway system has become the longest in the world and likely will continue to expand. Unfortunately, the safety issues on freeways in China have grown as well and are of great concern to Chinese transportation authorities and drivers. While many proven safety countermeasures developed and implemented by other countries are available for reference, they may be not fully transferrable to China due to the differences in driving cultures and conditions. As a result, an investigation of China’s unique safety factors and effective relevant countermeasures are urgently needed.The study presented in this paper thoroughly investigated the factors contributing to freeway crashes in China based on detailed crash data, traffic characteristics, freeway geometry, pavement conditions, and weather conditions. To properly account for the over-dispersion of data and unobserved heterogeneity, a random effects negative binomial (RENB) model and a random parameters negative binomial (RPNB) model were applied, along with a negative binomial (NB) model. The analysis revealed a large number of crash frequency factors, including several interesting and important factors rarely studied in the past, such as the safety effects of climbing lanes. Moreover, the RENB and RPNB models were found to considerably outperform the NB model; however, although the RPNB exhibited better goodness-of-fit than the RENB model, the difference was rather small. The findings of this study shed more light on the factors influencing freeway crashes in China. The results will be useful to highway designers and engineers for creating, building, and operating safe freeways as well as to safety management departments for developing effective safety countermeasures. The study presented in this paper also provides additional guidance for choosing relevant methods to analyze safety and to identify safety factors.

Comparison of modelling methods accounting for temporal correlation in crash counts

ABSTRACTTemporal correlation in crash counts is an important issue that road safety researchers face when developing crash prediction models. Several modelling methods have been proposed to date to address this issue. Random effects negative binomial (RENB) model, random parameters negative binomial (RPNB) model, multilevel negative binomial (MLNB) model, negative multinomial (NM) model, and generalized estimating equation (GEE) model are the most frequently used ones. Although those models have been applied successfully, it is not clear to researchers what their differences are and how to make a choice among them. This study attempts to answer these questions through describing the main features of the five models, showing their connections, illustrating their applications to predict the crash frequency on basic freeway segments, and discussing their differences that can guide the choice making. The application results show that the RENB, MLNB, and RPNB models are superior to others in terms of predictability (for the current data set), capability, usability, and interpretability. Three fundamental differences, including the ways to handle temporal correlation, whether to account for other heterogeneities, and the interpretation of estimated coefficients, provide some guidance on the model choice.

A joint econometric approach for modeling crash counts by collision type

In recent years, there is growing recognition that common unobserved factors that influence crash frequency by one attribute level are also likely to influence crash frequency by other attribute levels. The most common approach employed to address the potential unobserved heterogeneity in safety literature is the development of multivariate crash frequency models. The current study proposes an alternative joint econometric framework to accommodate for the presence of unobserved heterogeneity – referred to as joint negative binomial-multinomial logit fractional split (NB-MNLFS) model. Furthermore, the study undertakes a first of its kind comparison exercise between the most commonly used multivariate model (multivariate random parameter negative binomial model) and the proposed joint approach by generating an equivalent log-likelihood measure. The empirical analysis is based on the zonal level crash count data for different collision types from the state of Florida for the year 2015. The model results highlight the presence of common unobserved effects affecting the two components of the joint model as well as the presence of parameter heterogeneity. The equivalent log-likelihood and goodness of fit measures clearly highlight the comparable performance offered by the proposed joint model relative to the commonly used multivariate approach. Overall, the model interpretations and fit measures clearly highlight the potential complementary role of the proposed approach for crash frequency analyses.

Developing a Random Parameters Negative Binomial-Lindley Model to analyze highly over-dispersed crash count data

The existence of preponderant zero crash sites and/or sites with large crash counts can present challenges during the statistical analysis of crash count data. Additionally, unobserved heterogeneity in crash data due to the absence of important variables could negatively impact the estimated model parameters. The traditional negative binomial (NB) model with fixed parameters might not adequately handle highly over-dispersed data or unobserved heterogeneity. Many research efforts that have involved the negative binomial–Lindley (NB-L) model or the random parameters negative binomial (RPNB) model, for example, have attempted to improve the inference of estimated coefficients by explicitly accounting for extra variation in crash data. The NB-L is a mixed modeling approach which provides flexibility to account for additional dispersion in data. The RP modeling approach accommodates the effect of unobserved variables by allowing the model parameters to vary from one observation to another. The following study proposes a combination of these models – the random parameters NB-L (RPNB-L) generalized linear model (GLM) – to account for underlying heterogeneity and address excess over-dispersion. The results show that the RPNB-L model not only provides a superior goodness-of-fit (GOF) with the sample data, but also offers a better understanding about the effects of potential contributing factors. The paper uses the Bayesian framework to provide a strategy for eliminating the potential for poor mixing in the Markov Chain Monte Carlo (MCMC) chains during the estimation of the RPNB-L model.

Traffic Accident Models using a Random Parameters Negative Binomial Model at Signalized Intersections: A Case of Daejeon Metropolitan Area

Traffic Accident Models using a Random Parameters Negative Binomial Model at Signalized Intersections: A Case of Daejeon Metropolitan Area

Estimating Lost Recreational Use Values of Visitors to Northwest Florida due to the Deepwater Horizon Oil Spill Using Cancelled Trip Data

AbstractThe lost recreational use values from the BP/Deepwater Horizon oil spill in the Gulf of Mexico were estimated from cancelled recreational trips to Northwest Florida. The impacts were calculated using the travel cost method for a single site with primary data collected from an online survey conducted after the spill. The data were collected in August and September 2011 with respondents residing in 13 US states that constitute the primary domestic market for coastal tourism to Northwest Florida. The survey gathered information from respondents on their recreational visits, including detailed information on their past trips and the number of trips cancelled to the study region due to the oil spill. The empirical analysis involves the estimation of a random parameter negative binomial count data demand model. Using this model we find significant preference heterogeneity surrounding the effects of the oil spill. Aggregate damages are estimated to be $207 million.

Analyzing crash frequency in freeway tunnels: A correlated random parameters approach

The majority of past road safety studies focused on open road segments while only a few focused on tunnels. Moreover, the past tunnel studies produced some inconsistent results about the safety effects of the traffic patterns, the tunnel design, and the pavement conditions. The effects of these conditions therefore remain unknown, especially for freeway tunnels in China. The study presented in this paper investigated the safety effects of these various factors utilizing a four-year period (2009–2012) of data as well as three models: 1) a random effects negative binomial model (RENB), 2) an uncorrelated random parameters negative binomial model (URPNB), and 3) a correlated random parameters negative binomial model (CRPNB). Of these three, the results showed that the CRPNB model provided better goodness-of-fit and offered more insights into the factors that contribute to tunnel safety. The CRPNB was not only able to allocate the part of the otherwise unobserved heterogeneity to the individual model parameters but also was able to estimate the cross-correlations between these parameters. Furthermore, the study results showed that traffic volume, tunnel length, proportion of heavy trucks, curvature, and pavement rutting were associated with higher frequencies of traffic crashes, while the distance to the tunnel wall, distance to the adjacent tunnel, distress ratio, International Roughness Index (IRI), and friction coefficient were associated with lower crash frequencies. In addition, the effects of the heterogeneity of the proportion of heavy trucks, the curvature, the rutting depth, and the friction coefficient were identified and their inter-correlations were analyzed.

Gas dynamic analogous exposure approach to interaction intensity in multiple-vehicle crash analysis: Case study of crashes involving taxis

Exposure is a frequency measure of being in situations in which crashes could occur. In modeling multiple-vehicle crash frequency, traditional exposure measures, such as vehicle kilometrage and travel time, may not be sufficiently representative because they may include situations in which vehicles rarely meet each other and multiple-vehicle crashes can never happen. The meeting frequency of vehicles should be a better exposure measure in such cases. This study aims to propose a novel Gas Dynamic Analogous Exposure (GDAE) to model multiple-vehicle crash frequency. We analogize the meeting frequency of vehicles with the meeting frequency of gas molecules because both systems consider the numbers of the meetings of discrete entities. A meeting frequency function of vehicles is derived based on the central idea of the classical collision theory in physical chemistry with consideration of constrained vehicular movement by the road alignments. The GDAE is then formulated on the basis of the major factors that contribute to the meeting frequency of vehicles. The proposed GDAE is a more representative proxy exposure measure in modeling of multiple-vehicle crash frequency because it further investigates and provides insight into the physics of the vehicle meeting mechanism. To demonstrate the applicability of the GDAE, zonal crash frequency models are constructed on the basis of multiple-vehicle crashes involving taxis in 398 zones of Hong Kong in 2011. The GDAE outperforms the conventional time exposure in multiple-vehicle crash modeling. To account for any unobservable heterogeneity and to cope with the over-dispersed count data, a random-parameter negative binomial model is established. Explanatory factors that contribute to the zonal multiple-vehicle crash risk involving taxis are identified. The proposed GDAE is a promising exposure measure for modeling multiple-vehicle crash frequency.

Single-vehicle crashes along rural mountainous highways in Malaysia: An application of random parameters negative binomial model

Mountainous highways generally associate with complex driving environment because of constrained road geometries, limited cross-section elements, inappropriate roadside features, and adverse weather conditions. As a result, single-vehicle (SV) crashes are overrepresented along mountainous roads, particularly in developing countries, but little attention is known about the roadway geometric, traffic and weather factors contributing to these SV crashes. As such, the main objective of the present study is to investigate SV crashes using detailed data obtained from a rigorous site survey and existing databases. The final dataset included a total of 56 variables representing road geometries including horizontal and vertical alignment, traffic characteristics, real-time weather condition, cross-sectional elements, roadside features, and spatial characteristics. To account for structured heterogeneities resulting from multiple observations within a site and other unobserved heterogeneities, the study applied a random parameters negative binomial model. Results suggest that rainfall during the crash is positively associated with SV crashes, but real-time visibility is negatively associated. The presence of a road shoulder, particularly a bitumen shoulder or wider shoulders, along mountainous highways is associated with less SV crashes. While speeding along downgrade slopes increases the likelihood of SV crashes, proper delineation decreases the likelihood. Findings of this study have significant implications for designing safer highways in mountainous areas, particularly in the context of a developing country.

A preliminary investigation of the relationships between historical crash and naturalistic driving

This paper describes a project that was undertaken using naturalistic driving data collected via Global Positioning System (GPS) devices to demonstrate a proof-of-concept for proactive safety assessments of crash-prone locations. The main hypothesis for the study is that the segments where drivers have to apply hard braking (higher jerks) more frequently might be the “unsafe” segments with more crashes over a long-term. The linear referencing methodology in ArcMap was used to link the GPS data with roadway characteristic data of US Highway 101 northbound (NB) and southbound (SB) in San Luis Obispo, California. The process used to merge GPS data with quarter-mile freeway segments for traditional crash frequency analysis is also discussed in the paper. A negative binomial regression analyses showed that proportion of high magnitude jerks while decelerating on freeway segments (from the driving data) was significantly related with the long-term crash frequency of those segments. A random parameter negative binomial model with uniformly distributed parameter for ADT and a fixed parameter for jerk provided a statistically significant estimate for quarter-mile segments. The results also indicated that roadway curvature and the presence of auxiliary lane are not significantly related with crash frequency for the highway segments under consideration. The results from this exploration are promising since the data used to derive the explanatory variable(s) can be collected using most off-the-shelf GPS devices, including many smartphones.

The effect of variations in spatial units on unobserved heterogeneity in macroscopic crash models

Macroscopic safety models establish a relationship between crashes and the contributing factors in a defined spatial unit. Negative binomial (NB) and Bayesian negative binomial models with conditional autoregressive prior (CAR) are techniques widely used to establish this relationship. However, these models do not account for unobserved heterogeneity and their output is global and fixed irrespective of the spatial unit of the analysis. There is a timely need to understand how variations in spatial units affect unobserved heterogeneity. This study uses two advanced modeling techniques, the random parameter negative binomial (RPNB) and the semi-parametric geographically weighted Poisson regression (S-GWPR), to investigate whether explanatory variables found to be significant and random in one spatial aggregation will remain significant and random when another spatial aggregation is used. The key finding is that variations in spatial units do have an impact on unobserved heterogeneity. We also found that variations in spatial units have a greater impact on unobserved heterogeneity in the RPNB models compared to the S-GWPR models. We found that the S-GWPR model performs better than the RPNB model with the lowest value of mean absolute deviation (MAD) and Akaiki information criterion (AIC) but the two modeling techniques produce similar results in terms of the sign of the coefficients across the selected spatial units of analysis. Overall, the study provides a methodological basis for assessing the impact of spatial units on unobserved heterogeneity.