Assessing the explanatory and predictive performance of a random parameters count model with heterogeneity in means and variances.

Random parameters model has been demonstrated to be an effective method to account for unobserved heterogeneity that commonly exists in highway crash data. However, the predefined single distribution for each random parameter may limit how the unobserved heterogeneity is captured. A more flexible approach is to develop a random parameters model with heterogeneity in means and variances by allowing the mean and variance of potential each random parameter to be an estimable function of explanatory variables. This burgeoning technique for modelling unobserved heterogeneity has been increasingly applied to various safety evaluation scenarios recently. However, the predictive performance of this emerging method, which determines the practicability of the model for a specific circumstance, has never been investigated as far as our knowledge. In addition, the explanatory power by including heterogeneous means and variances of random parameters need to be further investigated to confirm the potential merits of this method in crash data analysis. In this paper, a random parameters negative binomial with heterogeneity in means and variances (RPNBHMV) model, a standard random parameters negative binomial (RPNB) model and a traditional fixed parameters negative binomial (NB) model were estimated using the same dataset. The explanatory and predictive performance of the three models were thoroughly evaluated and compared. Results showed that: 1) the RPNB model fitted the data significantly better than the NB model, and the RPNBHMV model further improved the statistical fit of the RPNB model but the improvement was slight; 2) more insights into interactions of safety factors were inferred from the RPNBHMV model, which demonstrates the explanatory benefit of this model; 3) the RPNBHMV and RPNB models had both advantages (e.g., produced overall better prediction accuracy) and disadvantages (e.g., provided reduced prediction accuracy across the range of explanatory variables) when applied to in-sample observations (i.e., observations used to estimate the model); 4) the RPNBHMV and RPNB models might be less precise than the NB model when applied to out-of-sample observations. These findings indicate that the RPNBHMV model offers more insights and may be used for explanatory safety analysis for sites where reliable data can be collected. However, the simple NB model is more reliable - at least with the dataset used in this study - than its random parameters model counterparts for other sites where the data are unavailable or unreliable, which is a common safety evaluation scenario in practice.

A correlated random parameters tobit model to analyze the safety effects and temporal instability of factors affecting crash rates.

Numerous studies have previously used a variety of count-data models to investigate factors that affect the number of crashes over a certain period of time on roadway segments. Unlike past studies which deal with crash frequency, this study views the crash rates directly as a continuous variable left-censored at zero and explores the application of an alternate approach based on tobit regression. To thoroughly investigate the factors affecting freeway crash rates and the potentially temporal instability in the effects of crash factors involving traffic volume, freeway geometries and pavement conditions, a classic uncorrelated random parameters tobit (URPT) model and a correlated random parameters tobit (CRPT) model were estimated, along with a conventional fixed parameters tobit (FPT) model. The analysis revealed a large number of safety factors, including several appealing and interesting factors rarely studied in the past, such as the safety effects of climbing lanes and distance along composite descending grade. The results also showed that the CRPT model was not only able to reflect the heterogeneous effects of various factors, but also able to estimate the underlying interactions among unobserved characteristics, and therefore provide better statistical fit and offer more insights into factors contributing to freeway crashes than its model counterparts. Additionally, the results showed significant temporal instability in CRPT models across the studied time periods indicating that crash factors (including unobserved characteristics and the underlying interactions among them) and their effects on crash rates varied over time, and more attentions should be paid when interpreting crash data-analysis findings and making safety policies. The modeling technique in this study demonstrates the potential of CRPT model as an effective approach to gain new insights into safety factors, particularly when the heterogeneous effects of factors on safety are interactive. Additionally, findings from this study are also expected to assist in developing more effective countermeasures by better understanding the safety effects of factors associated with freeway design characteristics and pavement conditions.

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.

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.