Multivariate Poisson Lognormal Research Articles

Safety Evaluation of Discontinuing Late Nighttime Flash Operations at Signalized Intersections

This study examined the safety impacts of converting late nighttime flash operation to normal phasing operation at signalized intersections by using the empirical Bayes, the univariate full Bayes, and multivariate full Bayes before-and-after methods. Data were obtained from the North Carolina Department of Transportation for 61 treatment sites and 395 reference intersections that remained on late nighttime flash operation from 2000 to 2007. The results from the empirical Bayes method are almost identical to those of the univariate full Bayes. The full Bayes method offered more flexibility in selecting the functional form of expected crashes at similar sites (similar to the safety performance function in the empirical Bayes) and in addressing uncertainty in the data. Compared with the univariate full Bayes, the multivariate full Bayes with the multivariate Poisson lognormal (MVPLN) model provided better results based on much lower deviance information criterion values. The MVPLN model was favored and the recommended crash reduction factors are 48% (±6%), 53% (±8%), and 57% (±7%) for nighttime total, injury and fatal, and frontal impact crashes, respectively.

Multivariate poisson-lognormal model for modeling related factors in crash frequency by severity

Aims: Traditionally, roadway safety analyses have used univariate distributions to model crash data for each level of severity separately. This paper uses the multivariate Poisson lognormal (MVPLN) models to estimate the expected crash frequency by two levels of severity and then compares those estimates with the univariate Poisson-lognormal (UVPLN) and the univariate Poisson (UVP) models. Materials and Methods: The parameters estimation is done by Bayesian method for crash data at two levels of severity at the intersection of Isfahan city for 6 months. Results: The results showed that there was over-dispersion issue in data. The UVP model is not able to overcome this problem while the MVPLN model can account for over-dispersion. Also, the estimates of the extra Poisson variation parameters in the MVPLN model were smaller than the UVPLN model that causes improvement in the precision of the MNPLN model. Hence, the MVPLN model is better fitted to the data set. Also, results showed effect of the total Average annual daily traffic (AADT) on the property damage only crash was significant in the all of models but effect of the total left turn AADT on the injuries and fatalities crash was significant just in the UVP model. Hence, holding all other factors fixed more property damage only crashes were expected on more the total AADT. For example, under MVPLN model an increase of 1000 vehicles in (average) the total AADT was predicted to result in 31% more property damage only crash. Conclusion: Hence, reduction of total AADT was predicted to be highly cost-effective, in terms of the crash cost reductions over the long run.

Depth-based hotspot identification and multivariate ranking using the full Bayes approach

Although the multivariate structure of traffic accidents has been recognized in the safety literature for over a decade now, univariate identification and ranking of hotspots is still dominant. The present paper advocates the use of multivariate identification and ranking of hotspots based on statistical depth functions, which are useful tools for non-parametric multivariate analysis as they provide center-out ordering of multivariate data. Thus, a depth-based multivariate method is proposed for the identification and ranking of hotspots using the full Bayes (FB) approach. The proposed method is applied to a sample of 236 signalized intersections in the Greater Vancouver Area. Various multivariate Poisson log-normal (MVPLN) models were used for data analysis. For each model, the FB posterior estimates were obtained using the Markov Chains Monte Carlo (MCMC) techniques and several goodness-of-fit measures were used for model selection. Using a depth threshold of 0.025, the proposed method identified 26 intersections (11%) as potential hotspots. The choice of a depth threshold is a delicate decision and it is suggested to determine the threshold according to the amount of funding available for safety improvement, which is the usual practice in univariate hotspot identification (HSID). Also, the results show that the performance of the proposed multivariate depth-based FB HSID method is superior to that of an analogous method based on the depths of accident frequency (AF) in terms of sensitivity, specificity and the sum of norms (lengths) of Poisson mean vectors.

Evaluation of Multivariate Poisson Log Normal Bayesian Methods for Before-After Road Safety Evaluations

The multivariate Poisson log normal (MVPLN) Bayesian method has recently been introduced in road safety analysis mainly for network screening and using different crash severity levels. However, there is little or no research applying MVPLN to different crash types. Besides, only one model structure for the expected crashes of a given severity was investigated in previous MVPLN studies. Another knowledge gap is that this method has not yet been evaluated for before–after treatment effect analysis. The objective of this study was to evaluate the application of MVPLN Bayesian method for before–after road safety evaluation studies. Two groups of unsignalized California intersections, for which a naive before–after comparison shows a significant change in the crash frequency after a hypothetical treatment was assigned, were used to conduct the study. It was found that the crash reduction rates are sensitive to the function form of expected crashes. For each model structure, MVPLN, univariate Poisson log normal (PLN) and Poisson-gamma models provided comparable results while PLN was seen to be superior. Finally, models that consider temporal effects of unobserved latent variables were found to be superior to those that don’t.

Increasing Beach Recreation Benefits by Using Wetlands to Reduce Contamination

The public swimming beach at Maumee Bay State Park (MBSP) on Lake Erie is often posted for occurrences of unsafe levels of bacteria. The main source of bacteria derives from a drainage ditch that discharges near the beach. We have conducted a comprehensive study to determine the feasibility of using a constructed wetland to filter the ditch water, prior to its entry into Maumee Bay. As part of this study, we administered an on-site non-market valuation survey of beach visitors, in which observed and contingent trips to the beach were used to estimate the potential welfare benefits of the restored wetlands. The data were analyzed using three ver - sions of the multivariate Poisson-lognormal (MPLN) model, a random effects count data model. We conclude version one, with flexible covariance structure and vehicle costs of $0.25 per mile, is the preferred version and use it to estimate an average annual willingness to pay (WTP) of $166 to construct wetlands and improve water quality. The aggregate annual benefit to an estimated 37,300 annual beach visitors is estimated as $6.19 million. The robustness of this estimate to a variety of alternative assumptions is examined.

A method to account for outliers in the development of safety performance functions

Accident data sets can include some unusual data points that are not typical of the rest of the data. The presence of these data points (usually termed outliers) can have a significant impact on the estimates of the parameters of safety performance functions (SPFs). Few studies have considered outliers analysis in the development of SPFs. In these studies, the practice has been to identify and then exclude outliers from further analysis. This paper introduces alternative mixture models based on the multivariate Poisson lognormal (MVPLN) regression. The proposed approach presents outlier resistance modeling techniques that provide robust safety inferences by down-weighting the outlying observations rather than rejecting them. The first proposed model is a scale-mixture model that is obtained by replacing the normal distribution in the Poisson-lognormal hierarchy by the Student t distribution, which has heavier tails. The second model is a two-component mixture (contaminated normal model) where it is assumed that most of the observations come from a basic distribution, whereas the remaining few outliers arise from an alternative distribution that has a larger variance. The results indicate that the estimates of the extra-Poisson variation parameters were considerably smaller under the mixture models leading to higher precision. Also, both mixture models have identified the same set of outliers. In terms of goodness-of-fit, both mixture models have outperformed the MVPLN. The outlier rejecting MVPLN model provided a superior fit in terms of a much smaller DIC and standard deviations for the parameter estimates. However, this approach tends to underestimate uncertainty by producing too small standard deviations for the parameter estimates, which may lead to incorrect conclusions. It is recommended that the proposed outlier resistance modeling techniques be used unless the exclusion of the outlying observations can be justified because of data related reasons (e.g., data collection errors).

Collision prediction models using multivariate Poisson-lognormal regression

This paper advocates the use of multivariate Poisson-lognormal (MVPLN) regression to develop models for collision count data. The MVPLN approach presents an opportunity to incorporate the correlations across collision severity levels and their influence on safety analyses. The paper introduces a new multivariate hazardous location identification technique, which generalizes the univariate posterior probability of excess that has been commonly proposed and applied in the literature. In addition, the paper presents an alternative approach for quantifying the effect of the multivariate structure on the precision of expected collision frequency. The MVPLN approach is compared with the independent (separate) univariate Poisson-lognormal (PLN) models with respect to model inference, goodness-of-fit, identification of hot spots and precision of expected collision frequency. The MVPLN is modeled using the WinBUGS platform which facilitates computation of posterior distributions as well as providing a goodness-of-fit measure for model comparisons. The results indicate that the estimates of the extra Poisson variation parameters were considerably smaller under MVPLN leading to higher precision. The improvement in precision is due mainly to the fact that MVPLN accounts for the correlation between the latent variables representing property damage only ( PDO) and injuries plus fatalities ( I + F). This correlation was estimated at 0.758, which is highly significant, suggesting that higher PDO rates are associated with higher I + F rates, as the collision likelihood for both types is likely to rise due to similar deficiencies in roadway design and/or other unobserved factors. In terms of goodness-of-fit, the MVPLN model provided a superior fit than the independent univariate models. The multivariate hazardous location identification results demonstrated that some hazardous locations could be overlooked if the analysis was restricted to the univariate models.

A multivariate Poisson-lognormal regression model for prediction of crash counts by severity, using Bayesian methods

Numerous efforts have been devoted to investigating crash occurrence as related to roadway design features, environmental factors and traffic conditions. However, most of the research has relied on univariate count models; that is, traffic crash counts at different levels of severity are estimated separately, which may neglect shared information in unobserved error terms, reduce efficiency in parameter estimates, and lead to potential biases in sample databases. This paper offers a multivariate Poisson-lognormal (MVPLN) specification that simultaneously models crash counts by injury severity. The MVPLN specification allows for a more general correlation structure as well as overdispersion. This approach addresses several questions that are difficult to answer when estimating crash counts separately. Thanks to recent advances in crash modeling and Bayesian statistics, parameter estimation is done within the Bayesian paradigm, using a Gibbs Sampler and the Metropolis–Hastings (M–H) algorithms for crashes on Washington State rural two-lane highways. Estimation results from the MVPLN approach show statistically significant correlations between crash counts at different levels of injury severity. The non-zero diagonal elements suggest overdispersion in crash counts at all levels of severity. The results lend themselves to several recommendations for highway safety treatments and design policies. For example, wide lanes and shoulders are key for reducing crash frequencies, as are longer vertical curves.

Multivariate count data regression models with individual panel data from an on-site sample

The purpose of this paper is to consider the problem of controlling for on-site sampling in the context of a system (or panel) of demand equations. Specifically, in the context of recreation demand, we are concerned with the situation in which survey respondents are asked to provide information not only about the actual trips to a specific site (observed behavior), but also their anticipated trips (either under current conditions or given price and quality changes). A Multivariate Poisson-log normal (MPLN) model and a seemingly unrelated negative binomial (SUNB) model are used to jointly model the observed and contingent behavior data and to correct for on-site sampling.