From Empirical Bayes to Full Bayes: Methods for Analysing Traffice Safety Data, October 25, 2004

Traffic safety engineers are among the early adopters of Bayesian statistical tools for analyzing crash data. As in many other areas of application, empirical Bayes methods were their first choice, perhaps because they represent an intuitively appealing, yet relatively easy to implement alternative to purely classical approaches. With the enormous progress in numerical methods made in recent years and with the availability of free, easy to use software that permits implementing a fully Bayesian approach, however, there is now ample justification to progress towards fully Bayesian analyses of crash data. The fully Bayesian approach, in particular as implemented via multi-level hierarchical models, has many advantages over the empirical Bayes approach. In a full Bayesian analysis, prior information and all available data are seamlessly integrated into posterior distributions on which practitioners can base their inferences. All uncertainties are thus accounted for in the analyses and there is no need to pre-process data to obtain Safety Performance Functions and other such prior estimates of the effect of covariates on the outcome of interest. In this slight, fully Bayesian methods may well be less costly to implement and may result in safety estimates with more realistic standard errors. In this manuscript, we present the full Bayesian approach to analyzing traffic safety data and focus on highlighting the differences between the empirical Bayes and the full Bayes approaches. We use an illustrative example to discuss a step-by-step Bayesian analysis of the data and to show some of the types of inferences that are possible within the full Bayesian framework.

From Empirical Bayes to Full Bayes: Methods for Analyzubg Traffic Safey Data, October 25, 2004

Traffic safety engineers are among the early adopters of Bayesian statistical tools for analyzing crash data. As in many other areas of application, empirical Bayes methods were their first choice, perhaps because they represent an intuitively appealing, yet relatively easy to implement alternative to purely classical approaches. With the enormous progress in numerical methods made in recent years and with the availability of free, easy to use software that permits implementing a fully Bayesian approach, however, there is now ample justification to progress towards fully Bayesian analyses of crash data. The fully Bayesian approach, in particular as implemented via multi-level hierarchical models, has many advantages over the empirical Bayes approach. In a full Bayesian analysis, prior information and all available data are seamlessly integrated into posterior distributions on which practitioners can base their inferences. All uncertainties are thus accounted for in the analyses and there is no need to pre-process data to obtain Safety Performance Functions and other such prior estimates of the effect of covariates on the outcome of interest. In this light, fully Bayesian methods may well be less costly to implement and may result in safety estimates with more realistic standard errors. In this manuscript, we present the full Bayesian approach to analyzing traffic safety data and focus on highlighting the differences between the empirical Bayes and the full Bayes approaches. We use an illustrative example to discuss a step-by-step Bayesian analysis of the data and to show some of the types of inferences that are possible within the full Bayesian framework.

The Effect of Four-Lane to Three-Lane Conversion on the Number of Crashes and Crash Rates in Iowa Roads, June 2005

We analyze crash data collected by the Iowa Department of Transportation using Bayesian methods. The data set includes monthly crash numbers, estimated monthly traffic volumes, site length and other information collected at 30 paired sites in Iowa over more than 20 years during which an intervention experiment was set up. The intervention consisted in transforming 15 undivided road segments from four-lane to three lanes, while an additional 15 segments, thought to be comparable in terms of traffic safety-related characteristics were not converted. The main objective of this work is to find out whether the intervention reduces the number of crashes and the crash rates at the treated sites. We fitted a hierarchical Poisson regression model with a change-point to the number of monthly crashes per mile at each of the sites. Explanatory variables in the model included estimated monthly traffic volume, time, an indicator for intervention reflecting whether the site was a “treatment” or a “control” site, and various interactions. We accounted for seasonal effects in the number of crashes at a site by including smooth trigonometric functions with three different periods to reflect the four seasons of the year. A change-point at the month and year in which the intervention was completed for treated sites was also included. The number of crashes at a site can be thought to follow a Poisson distribution. To estimate the association between crashes and the explanatory variables, we used a log link function and added a random effect to account for overdispersion and for autocorrelation among observations obtained at the same site. We used proper but non-informative priors for all parameters in the model, and carried out all calculations using Markov chain Monte Carlo methods implemented in WinBUGS. We evaluated the effect of the four to three-lane conversion by comparing the expected number of crashes per year per mile during the years preceding the conversion and following the conversion for treatment and control sites. We estimated this difference using the observed traffic volumes at each site and also on a per 100,000,000 vehicles. We also conducted a prospective analysis to forecast the expected number of crashes per mile at each site in the study one year, three years and five years following the four to three-lane conversion. Posterior predictive distributions of the number of crashes, the crash rate and the percent reduction in crashes per mile were obtained for each site for the months of January and June one, three and five years after completion of the intervention. The model appears to fit the data well. We found that in most sites, the intervention was effective and reduced the number of crashes. Overall, and for the observed traffic volumes, the reduction in the expected number of crashes per year and mile at converted sites was 32.3% (31.4% to 33.5% with 95% probability) while at the control sites, the reduction was estimated to be 7.1% (5.7% to 8.2% with 95% probability). When the reduction in the expected number of crashes per year, mile and 100,000,000 AADT was computed, the estimates were 44.3% (43.9% to 44.6%) and 25.5% (24.6% to 26.0%) for converted and control sites, respectively. In both cases, the difference in the percent reduction in the expected number of crashes during the years following the conversion was significantly larger at converted sites than at control sites, even though the number of crashes appears to decline over time at all sites. Results indicate that the reduction in the expected number of sites per mile has a steeper negative slope at converted than at control sites. Consistent with this, the forecasted reduction in the number of crashes per year and mile during the years after completion of the conversion at converted sites is more pronounced than at control sites. Seasonal effects on the number of crashes have been well-documented. In this dataset, we found that, as expected, the expected number of monthly crashes per mile tends to be higher during winter months than during the rest of the year. Perhaps more interestingly, we found that there is an interaction between the four to three-lane conversion and season; the reduction in the number of crashes appears to be more pronounced during months, when the weather is nice than during other times of the year, even though a reduction was estimated for the entire year. Thus, it appears that the four to three-lane conversion, while effective year-round, is particularly effective in reducing the expected number of crashes in nice weather.

Methods for Estimating Annual Exceedance-Probability Discharges for Streams in Iowa, Based on Data through Water Year 2010, TR-519, 2013

A statewide study was performed to develop regional regression equations for estimating selected annual exceedance- probability statistics for ungaged stream sites in Iowa. The study area comprises streamgages located within Iowa and 50 miles beyond the State’s borders. Annual exceedanceprobability estimates were computed for 518 streamgages by using the expected moments algorithm to fit a Pearson Type III distribution to the logarithms of annual peak discharges for each streamgage using annual peak-discharge data through 2010. The estimation of the selected statistics included a Bayesian weighted least-squares/generalized least-squares regression analysis to update regional skew coefficients for the 518 streamgages. Low-outlier and historic information were incorporated into the annual exceedance-probability analyses, and a generalized Grubbs-Beck test was used to detect multiple potentially influential low flows. Also, geographic information system software was used to measure 59 selected basin characteristics for each streamgage. Regional regression analysis, using generalized leastsquares regression, was used to develop a set of equations for each flood region in Iowa for estimating discharges for ungaged stream sites with 50-, 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent annual exceedance probabilities, which are equivalent to annual flood-frequency recurrence intervals of 2, 5, 10, 25, 50, 100, 200, and 500 years, respectively. A total of 394 streamgages were included in the development of regional regression equations for three flood regions (regions 1, 2, and 3) that were defined for Iowa based on landform regions and soil regions. Average standard errors of prediction range from 31.8 to 45.2 percent for flood region 1, 19.4 to 46.8 percent for flood region 2, and 26.5 to 43.1 percent for flood region 3. The pseudo coefficients of determination for the generalized leastsquares equations range from 90.8 to 96.2 percent for flood region 1, 91.5 to 97.9 percent for flood region 2, and 92.4 to 96.0 percent for flood region 3. The regression equations are applicable only to stream sites in Iowa with flows not significantly affected by regulation, diversion, channelization, backwater, or urbanization and with basin characteristics within the range of those used to develop the equations. These regression equations will be implemented within the U.S. Geological Survey StreamStats Web-based geographic information system tool. StreamStats allows users to click on any ungaged site on a river and compute estimates of the eight selected statistics; in addition, 90-percent prediction intervals and the measured basin characteristics for the ungaged sites also are provided by the Web-based tool. StreamStats also allows users to click on any streamgage in Iowa and estimates computed for these eight selected statistics are provided for the streamgage.

Evaluation of Different Methods to Calculate Heavy-Truck VMT, Final Report, December 2004

Reliable estimates of heavy-truck volumes are important in a number of transportation applications. Estimates of truck volumes are necessary for pavement design and pavement management. Truck volumes are important in traffic safety. The number of trucks on the road also influences roadway capacity and traffic operations. Additionally, heavy vehicles pollute at higher rates than passenger vehicles. Consequently, reliable estimates of heavy-truck vehicle miles traveled (VMT) are important in creating accurate inventories of on-road emissions. This research evaluated three different methods to calculate heavy-truck annual average daily traffic (AADT) which can subsequently be used to estimate vehicle miles traveled (VMT). Traffic data from continuous count stations provided by the Iowa DOT were used to estimate AADT for two different truck groups (single-unit and multi-unit) using the three methods. The first method developed monthly and daily expansion factors for each truck group. The second and third methods created general expansion factors for all vehicles. Accuracy of the three methods was compared using n-fold cross-validation. In n-fold cross-validation, data are split into n partitions, and data from the nth partition are used to validate the remaining data. A comparison of the accuracy of the three methods was made using the estimates of prediction error obtained from cross-validation. The prediction error was determined by averaging the squared error between the estimated AADT and the actual AADT. Overall, the prediction error was the lowest for the method that developed expansion factors separately for the different truck groups for both single- and multi-unit trucks. This indicates that use of expansion factors specific to heavy trucks results in better estimates of AADT, and, subsequently, VMT, than using aggregate expansion factors and applying a percentage of trucks. Monthly, daily, and weekly traffic patterns were also evaluated. Significant variation exists in the temporal and seasonal patterns of heavy trucks as compared to passenger vehicles. This suggests that the use of aggregate expansion factors fails to adequately describe truck travel patterns.

Determination and Evaluation of Alternative Methods for Managing and Controlling Highway-Related Dust Phase II—Demonstration Project, June 2005

The State of Iowa currently has approximately 69,000 miles of unpaved secondary roads. Due to the low traffic count on these unpaved o nts as ng e two dust ed d roads, paving with asphalt or Portland cement concrete is not economical. Therefore to reduce dust production, the use of dust suppressants has been utilized for decades. This study was conducted to evaluate the effectiveness of several widely used dust suppressants through quantitative field testing on two of Iowa’s most widely used secondary road surface treatments: crushed limestone rock and alluvial sand/gravel. These commercially available dust suppressants included: lignin sulfonate, calcium chloride, and soybean oil soapstock. These suppressants were applied to 1000 ft test sections on four unpaved roads in Story County, Iowa. Tduplicate field conditions, the suppressants were applied as a surface spray once in early June and again in late August or early September. The four unpaved roads included two with crushed limestone rock and two with alluvial sand/gravel surface treatmewell as high and low traffic counts. The effectiveness of the dust suppressants was evaluated by comparing the dust produced on treated and untreated test sections. Dust collection was scheduled for 1, 2, 4, 6, and 8 weeks after each application, for a total testiperiod of 16 weeks. Results of a cost analysis between annual dust suppressant application and biennial aggregate replacement indicated that the cost of the dust suppressant, its transportation, and application were relatively high when compared to that of thaggregate types. Therefore, the biennial aggregate replacement is considered more economical than annual dust suppressant application, although the application of annual dust suppressant reduced the cost of road maintenance by 75 %. Results of thecollection indicated that the lignin sulfonate suppressant outperformed calcium chloride and soybean oil soapstock on all four unpavroads, the effect of the suppressants on the alluvial sand/gravel surface treatment was less than that on the crushed limestone rock, the residual effects of all the products seem reasonably well after blading, and the combination of alluvial sand/gravel surface treatment anhigh traffic count caused dust reduction to decrease dramatically.

Development of In-Situ Detection Methods for Materials-Related Distress (MRD) in Concrete Pavements, July 2003

The purpose of this research was to summarize existing nondestructive test methods that have the potential to be used to detect materials-related distress (MRD) in concrete pavements. The various nondestructive test methods were then subjected to selection criteria that helped to reduce the size of the list so that specific techniques could be investigated in more detail. The main test methods that were determined to be applicable to this study included two stress-wave propagation techniques (impact-echo and spectral analysis of surface waves techniques), infrared thermography, ground penetrating radar (GPR), and visual inspection. The GPR technique was selected for a preliminary round of “proof of concept” trials. GPR surveys were carried out over a variety of portland cement concrete pavements for this study using two different systems. One of the systems was a state-of-the-art GPR system that allowed data to be collected at highway speeds. The other system was a less sophisticated system that was commercially available. Surveys conducted with both sets of equipment have produced test results capable of identifying subsurface distress in two of the three sites that exhibited internal cracking due to MRD. Both systems failed to detect distress in a single pavement that exhibited extensive cracking. Both systems correctly indicated that the control pavement exhibited negligible evidence of distress. The initial positive results presented here indicate that a more thorough study (incorporating refinements to the system, data collection, and analysis) is needed. Improvements in the results will be dependent upon defining the optimum number and arrangement of GPR antennas to detect the most common problems in Iowa pavements. In addition, refining highfrequency antenna response characteristics will be a crucial step toward providing an optimum GPR system for detecting materialsrelated distress.

Rehabilitation of Concrete Pavements Utilizing Rebblization and Crack and Seat Methods, June 2005

Deterioration in portland cement concrete (PCC) pavements can occur due to distresses caused by a combination of traffic loads and weather conditions. Hot mix asphalt (HMA) overlay is the most commonly used rehabilitation technique for such deteriorated PCC pavements. However, the performance of these HMA overlaid pavements is hindered due to the occurrence of reflective cracking, resulting in significant reduction of pavement serviceability. Various fractured slab techniques, including rubblization, crack and seat, and break and seat are used to minimize reflective cracking by reducing the slab action. However, the design of structural overlay thickness for cracked and seated and rubblized pavements is difficult as the resulting structure is neither a “true” rigid pavement nor a “true” flexible pavement. Existing design methodologies use the empirical procedures based on the AASHO Road Test conducted in 1961. But, the AASHO Road Test did not employ any fractured slab technique, and there are numerous limitations associated with extrapolating its results to HMA overlay thickness design for fractured PCC pavements. The main objective of this project is to develop a mechanistic-empirical (ME) design approach for the HMA overlay thickness design for fractured PCC pavements. In this design procedure, failure criteria such as the tensile strain at the bottom of HMA layer and the vertical compressive strain on the surface of subgrade are used to consider HMA fatigue and subgrade rutting, respectively. The developed ME design system is also implemented in a Visual Basic computer program. A partial validation of the design method with reference to an instrumented trial project (IA-141, Polk County) in Iowa is provided in this report. Tensile strain values at the bottom of the HMA layer collected from the FWD testing at this project site are in agreement with the results obtained from the developed computer program.

Evaluation of Transverse Joint Forming Methods for PCC Pavement, January 2006

The members of the Iowa Concrete Paving Association, the National Concrete Pavement Technology Center Research Committee, and the Iowa Highway Research Board commissioned a study to examine alternative ways of developing transverse joints in portland cement concrete pavements. The present study investigated six separate variations of vertical metal strips placed above and below the dowels in conventional baskets. In addition, the study investigated existing patented assemblies and a new assembly developed in Spain and used in Australia. The metal assemblies were placed in a new pavement and allowed to stay in place for 30 days before the Iowa Department of Transportation staff terminated the test by directing the contractor to saw and seal the joints. This report describes the design, construction, testing, and conclusions of the project.

Evaluation of U.S. and European Concrete Pavement Noise Reduction Methods, July 2006

Highway noise is one of the most pressing of the surface characteristics issues facing the concrete paving industry. This is particularly true in urban areas, where not only is there a higher population density near major thoroughfares, but also a greater volume of commuter traffic (Sandberg and Ejsmont 2002; van Keulen 2004). To help address this issue, the National Concrete Pavement Technology Center (CP Tech Center) at Iowa State University (ISU), Federal Highway Administration (FHWA), American Concrete Pavement Association (ACPA), and other organizations have partnered to conduct a multi-part, seven-year Concrete Pavement Surface Characteristics Project. This document contains the results of Part 1, Task 2, of the ISU-FHWA project, addressing the noise issue by evaluating conventional and innovative concrete pavement noise reduction methods. The first objective of this task was to determine what if any concrete surface textures currently constructed in the United States or Europe were considered quiet, had long-term friction characteristics, could be consistently built, and were cost effective. Any specifications of such concrete textures would be included in this report. The second objective was to determine whether any promising new concrete pavement surfaces to control tire-pavement noise and friction were in the development stage and, if so, what further research was necessary. The final objective was to identify measurement techniques used in the evaluation.