Development of safety performance functions for empirical Bayes estimation of crash reduction factors

Crash reduction factors (CRFs) are used to estimate the potential number of traffic crashes expected to be prevented from investment in safety improvement projects. The method used to develop CRFs in Florida has been based on the commonly used before-and-after approach. This approach suffers from a widely recognized problem known as regression-to-the-mean (RTM). The Empirical Bayes (EB) method has been introduced as a means to addressing the RTM problem. This method requires the information from both the treatment and reference sites in order to predict the expected number of crashes had the safety improvement projects at the treatment sites not been implemented. The information from the reference sites is estimated from a safety performance function (SPF), which is a mathematical relationship that links crashes to traffic exposure. The objective of this dissertation was to develop the SPFs for different functional classes of the Florida State Highway System. Crash data from years 2001 through 2003 along with traffic and geometric data were used in the SPF model development. SPFs for both rural and urban roadway categories were developed. The modeling data used were based on one-mile segments that contain homogeneous traffic and geometric conditions within each segment. Segments involving intersections were excluded. The scatter plots of data show that the relationships between crashes and traffic exposure are nonlinear, that crashes increase with traffic exposure in an increasing rate. Four regression models, namely, Poisson (PRM), Negative Binomial (NBRM), zero-inflated Poisson (ZIP), and zero-inflated Negative Binomial (ZINB), were fitted to the one-mile segment records for individual roadway categories. The best model was selected for each category based on a combination of the Likelihood Ratio test, the Vuong statistical test, and the Akaike's Information Criterion (AIC). The NBRM model was found to be appropriate for only one category and the ZINB model was found to be more appropriate for six other categories. The overall results show that the Negative Binomial distribution model generally provides a better fit for the data than the Poisson distribution model. In addition, the ZINB model was found to give the best fit when the count data exhibit excess zeros and over-dispersion for most of the roadway categories. While model validation shows that most data points fall within the 95% prediction intervals of the models developed, the Pearson goodness-of-fit measure does not show statistical significance. This is expected as traffic volume is only one of the many factors contributing to the overall crash experience, and that the SPFs are to be applied in conjunction with Accident Modification Factors (AMFs) to further account for the safety impacts of major geometric features before arriving at the final crash prediction. However, with improved traffic and crash data quality, the crash prediction power of SPF models may be further improved.

Development of safety performance functions for SafetyAnalyst applications in Florida

In 2010, the American Association of State Highway and Transportation Officials (AASHTO) released a safety analysis software system known as SafetyAnalyst. SafetyAnalyst implements the empirical Bayes (EB) method, which requires the use of Safety Performance Functions (SPFs). The system is equipped with a set of national default SPFs, and the software calibrates the default SPFs to represent the agency's safety performance. However, it is recommended that agencies generate agency-specific SPFs whenever possible. Many investigators support the view that the agency-specific SPFs represent the agency data better than the national default SPFs calibrated to agency data. Furthermore, it is believed that the crash trends in Florida are different from the states whose data were used to develop the national default SPFs. In this dissertation, Florida-specific SPFs were developed using the 2008 Roadway Characteristics Inventory (RCI) data and crash and traffic data from 2007-2010 for both total and fatal and injury (FI) crashes. The data were randomly divided into two sets, one for calibration (70% of the data) and another for validation (30% of the data). The negative binomial (NB) model was used to develop the Florida-specific SPFs for each of the subtypes of roadway segments, intersections and ramps, using the calibration data. Statistical goodness-of-fit tests were performed on the calibrated models, which were then validated using the validation data set. The results were compared in order to assess the transferability of the Florida-specific SPF models. The default SafetyAnalyst SPFs were calibrated to Florida data by adjusting the national default SPFs with local calibration factors. The performance of the Florida-specific SPFs and SafetyAnalyst default SPFs calibrated to Florida data were then compared using a number of methods, including visual plots and statistical goodness-of-fit tests. The plots of SPFs against the observed crash data were used to compare the prediction performance of the two models. Three goodness-of-fit tests, represented by the mean absolute deviance (MAD), the mean square prediction error (MSPE), and Freeman-Tukey R2 (R2FT), were also used for comparison in order to identify the better-fitting model. The results showed that Florida-specific SPFs yielded better prediction performance than the national default SPFs calibrated to Florida data. The performance of Florida-specific SPFs was further compared with that of the full SPFs, which include both traffic and geometric variables, in two major applications of SPFs, i.e., crash prediction and identification of high crash locations. The results showed that both SPF models yielded very similar performance in both applications. These empirical results support the use of the flow-only SPF models adopted in SafetyAnalyst, which require much less effort to develop compared to full SPFs.

Development of Safety Performance Functions for SafetyAnalyst Applications in Florida

In 2010, the American Association of State Highway and Transportation Officials (AASHTO) released a safety analysis software system known as SafetyAnalyst. SafetyAnalyst implements the empirical Bayes (EB) method, which requires the use of Safety Performance Functions (SPFs). The system is equipped with a set of national default SPFs, and the software calibrates the default SPFs to represent the agency’s safety performance. However, it is recommended that agencies generate agency-specific SPFs whenever possible. Many investigators support the view that the agency-specific SPFs represent the agency data better than the national default SPFs calibrated to agency data. Furthermore, it is believed that the crash trends in Florida are different from the states whose data were used to develop the national default SPFs. In this dissertation, Florida-specific SPFs were developed using the 2008 Roadway Characteristics Inventory (RCI) data and crash and traffic data from 2007-2010 for both total and fatal and injury (FI) crashes. The data were randomly divided into two sets, one for calibration (70% of the data) and another for validation (30% of the data). The negative binomial (NB) model was used to develop the Florida-specific SPFs for each of the subtypes of roadway segments, intersections and ramps, using the calibration data. Statistical goodness-of-fit tests were performed on the calibrated models, which were then validated using the validation data set. The results were compared in order to assess the transferability of the Florida-specific SPF models. The default SafetyAnalyst SPFs were calibrated to Florida data by adjusting the national default SPFs with local calibration factors. The performance of the Florida-specific SPFs and SafetyAnalyst default SPFs calibrated to Florida data were then compared using a number of methods, including visual plots and statistical goodness-of-fit tests. The plots of SPFs against the observed crash data were used to compare the prediction performance of the two models. Three goodness-of-fit tests, represented by the mean absolute deviance (MAD), the mean square prediction error (MSPE), and Freeman-Tukey R2 (R2FT), were also used for comparison in order to identify the better-fitting model. The results showed that Florida-specific SPFs yielded better prediction performance than the national default SPFs calibrated to Florida data. The performance of Florida-specific SPFs was further compared with that of the full SPFs, which include both traffic and geometric variables, in two major applications of SPFs, i.e., crash prediction and identification of high crash locations. The results showed that both SPF models yielded very similar performance in both applications. These empirical results support the use of the flow-only SPF models adopted in SafetyAnalyst, which require much less effort to develop compared to full SPFs.

Contemporary aspects of dividends: Before and during the financial crisis

The number of dividend paying firms has been on the decline since the popularity of stock repurchases in the 1980s, and the recent financial crisis has brought about a wave of dividend reductions and omissions. This dissertation examined the U.S. firms and American Depository Receipts that are listed on the U.S. equity exchanges according to their dividend paying history in the previous twelve quarters. While accounting for the state of the economy, the firm’s size, profitability, earned equity, and growth opportunities, it determines whether or not the firm will pay a dividend in the next quarter. It also examined the likelihood of a dividend change. Further, returns of firms were examined according to their dividend paying history and the state of the economy using the Fama-French three-factor model. Using forward, backward, and step-wise selection logistic regressions, the results show that firms with a history of regular and uninterrupted dividend payments are likely to continue to pay dividends, while firms that do not have a history of regular dividend payments are not likely to begin to pay dividends or continue to do so. The results of a set of generalized polytomous logistic regressions imply that dividend paying firms are more likely to reduce dividend payments during economic expansions, as opposed to recessions. Also the analysis of returns using the Fama-French three factor model reveals that dividend paying firms are earning significant abnormal positive returns. As a special case, a similar analysis of dividend payment and dividend change was applied to American Depository Receipts that trade on the NYSE, NASDAQ, and AMEX exchanges and are issued by the Bank of New York Mellon. Returns of American Depository Receipts were examined using the Fama-French two-factor model for international firms. The results of the generalized polytomous logistic regression analyses indicate that dividend paying status and economic conditions are also important for dividend level change of American Depository Receipts, and Fama-French two-factor regressions alone do not adequately explain returns for these securities.

The White Ibis and Wood Stork as indicators for restoration of the everglades ecosystem

Large numbers of colonially nesting herons, egrets, ibises, storks and spoonbills were one of the defining natural phenomena of the historical Everglades. Reproduction of these species has been tracked over at least a century, and some clear responses to dramatic anthropogenic hydrological alterations have been established. These include a marked decline in nesting populations of several species, and a movement of colonies away from the over-drained estuarine region. Ponding in a large portion of the freshwater marsh has favored species that hunt by sight in deep water (egrets, cf. 25–45 cm), while tactile feeders (ibises and storks) that depend on concentrated prey in shallow water (5–25 cm) have become proportionately much less common. There has been a marked increase in the interval between exceptionally large breeding aggregations of White Ibises (Eudocimus albus). Loss of short hydroperiod wetlands on the margins of the Everglades have delayed nest initiations 1–2 months by Wood Storks (Mycteria americana) resulting in poor nesting success. These responses are consistent with mechanisms that involve foraging, and the availability and production of prey animals, and each of the relationships is highly dependent on hydrology. Here, we define a group of characteristics about wading bird dynamics (= indicators) that collectively track the specific ecological relationships that supported ibises and storks in the past. We suggest four metrics as indicators of restoration success: timing of nesting by storks, the ratio of nesting ibises + storks to Great Egrets, the proportion of all nests located in the estuarine/freshwater ecotone, and the interval between years with exceptionally large ibis nestings. Each of these metrics has historical (e.g., predrainage) data upon which to base expectations for restoration, and the metrics have little measurement error relative to the large annual variation in numbers of nests. In addition to the strong scientific basis for the use of these indicators, wading birds are also a powerful tool for public communication because they have strong aesthetic appeal, and their ecological relationships with water are intuitively understandable. In the interests of communicating with the public and decision-makers, we integrate these metrics into a single-page annual “traffic-light” report card for wading bird responses. Collectively, we believe these metrics offer an excellent chance of detecting restoration of the ecosystem functions that supported historical wading bird nesting patterns.

Non -traded goods, product differentiation and integration of factor markets

This research sought to determine the implications of a non-traded differentiated commodity produced with increasing returns to scale, for the welfare of countries that allowed free international migration. We developed two- and three-country Ricardian models in which labor was the only factor of production. The countries traded freely in homogeneous goods produced with constant returns to scale. Each also had a non-traded differentiated good sector where production took place using increasing returns to scale technology. Then we allowed for free international migration between two of the countries and observed what happened to welfare in both countries as indicated by their per capita utilities in the new equilibrium relative to their pre-migration utilities. ^ Preferences of consumers were represented by a two-tier utility function [Dixit and Stiglitz 1977]. As migration took place it impacted utility in two ways. The expanding country enjoyed the positive effect of increased product diversity in the non-traded good sector. However, it also suffered adverse terms-of-trade as its production cost declined. The converse was true for the contracting country. To determine the net impact on welfare we derived indirect per capita utility functions of the countries algebraically and graphically. Then we juxtaposed the graphs of the utility functions to obtain possible general equilibria. These we used to observe the welfare outcomes. ^ We found that the most likely outcomes were either that both countries gained, or one country lost while the other gained. We were, however, able to generate cases where both countries lost as a result of allowing free inter-country migration. This was most likely to happen when the shares of income spent on each country's export good differed significantly. In the three country world when we allowed two of the countries to engage in preferential trading arrangements while imposing a prohibitive tariff on imports from the third country welfare of the partner countries declined. When inter-union migration was permitted welfare declined even further. This we showed was due to the presence of the non-traded good sector. ^

Incorporating variable peak -to -daily ratios in the equilibrium traffic assignment procedure of the Florida Standard Urban Transportation Modeling Structure (FSUTMS)

The standard highway assignment model in the Florida Standard Urban Transportation Modeling Structure (FSUTMS) is based on the equilibrium traffic assignment method. This method involves running several iterations of all-or-nothing capacity-restraint assignment with an adjustment of travel time to reflect delays encountered in the associated iteration. The iterative link time adjustment process is accomplished through the Bureau of Public Roads (BPR) volume-delay equation. Since FSUTMS' traffic assignment procedure outputs daily volumes, and the input capacities are given in hourly volumes, it is necessary to convert the hourly capacities to their daily equivalents when computing the volume-to-capacity ratios used in the BPR function. The conversion is accomplished by dividing the hourly capacity by a factor called the peak-to-daily ratio, or referred to as CONFAC in FSUTMS. The ratio is computed as the highest hourly volume of a day divided by the corresponding total daily volume. ^ While several studies have indicated that CONFAC is a decreasing function of the level of congestion, a constant value is used for each facility type in the current version of FSUTMS. This ignores the different congestion level associated with each roadway and is believed to be one of the culprits of traffic assignment errors. Traffic counts data from across the state of Florida were used to calibrate CONFACs as a function of a congestion measure using the weighted least squares method. The calibrated functions were then implemented in FSUTMS through a procedure that takes advantage of the iterative nature of FSUTMS' equilibrium assignment method. ^ The assignment results based on constant and variable CONFACs were then compared against the ground counts for three selected networks. It was found that the accuracy from the two assignments was not significantly different, that the hypothesized improvement in assignment results from the variable CONFAC model was not empirically evident. It was recognized that many other factors beyond the scope and control of this study could contribute to this finding. It was recommended that further studies focus on the use of the variable CONFAC model with recalibrated parameters for the BPR function and/or with other forms of volume-delay functions. ^