The Utah Department of Transportation (UDOT) Traffic and Safety Division continues to advance the safety of roadway sections throughout the state. To aid UDOT in meeting their goal the Department of Civil and Environmental Engineering at Brigham Young University (BYU) has worked with the Statistics Department in developing analysis tools for safety. The most recent of these tools has been the development of a hierarchical Bayesian Poisson Mixture Model (PMM) statistical model of traffic crashes and safety on UDOT roadways statewide and the integration of the results of this model in a Geographic Information System (GIS) framework. This research focuses on the enhancement of the framework for highway safety mitigation in Utah with its six primary steps: 1) network screening, 2) diagnosis, 3) countermeasure selection, 4) economic appraisal, 5) project prioritization, and 6) effectiveness evaluation. The framework was enhanced by developing a methodology for accomplishing the steps of network screening, diagnosis, and countermeasure selection. This methodology is titled, "Hot Spot Identification and Analysis." The hot spot identification and analysis methodology consists of the following seven steps: 1) identify problematic segments with safety concern, 2) identify problem spots within the segments, 3) micro analysis of problematic segments and spots, 4) defining the segment, 5) defining the problem, 6) evaluation of possible countermeasures, and 7) selection and recommendation of feasible countermeasures. The methodology is to help in the identification of hot spots with safety concerns so that they can be analyzed and countermeasures can be identified to mitigate the safety issues. Examples of how the methodology is to function are given with specific examples from Utah's state roadway network.

The Utah Department of Transportation (UDOT) Traffic and Safety Division continues to advance the safety of roadway sections throughout the state. In an effort to aid UDOT in meeting their goal, the Department of Civil and Environmental Engineering at Brigham Young University (BYU) has worked with the Statistics Department in developing analysis tools for safety. The most recent of these tools has been the development of a hierarchical Bayesian Poisson Mixture Model (PMM) of traffic crashes known as the Utah Crash Prediction Model (UCPM), a hierarchical Bayesian Binomial statistical model known as the Utah Crash Severity Model (UCSM), and a Bayesian Horseshoe selection method. The UCPM and UCSM models helped with the analysis of safety on UDOT roadways statewide and the integration of the results of these models was applied to Geographic Information System (GIS) framework. This research focuses on the addition of roadway attributes in the selection and analysis of “hot spots.” This is in conjunction with the framework for highway safety mitigation migration in Utah with its six primary steps: network screening, diagnosis, countermeasure selection, economic appraisal, project prioritization, and effectiveness evaluation. The addition of roadway attributes was included as part of the network screening, diagnosis, and countermeasure selection, which are included in the methodology titled “Hot Spot Identification and Analysis.” Included in this research was the documentation of the steps and process for data preparation and model use for the step of network screening and the creation of one of the report forms for the steps of diagnosis and countermeasure selection. The addition of roadway attributes is required at numerous points in the process. Methods were developed to locate and evaluate the usefulness of available data. Procedures and systemization were created to convert raw data into new roadway attributes, such as grade and sag/crest curve location. For the roadway attributes to be useful in selection and analysis, methods were developed to combine and associate the attributes to crashes on problem segments and problem spots. The methodology for “Hot Spot Identification and Analysis” was enhanced to include steps for the inclusion and defining of the roadway attributes. These methods and procedures were used to help in the identification of safety hot spots so that they can be analyzed and countermeasures selected. Examples of how the methods are to function are given with sites from Utah’s state roadway network.

Generalized linear mixture models (GLMM) are widely used in statistical applications to model count and binary data. We consider the problem of nonparametric likelihood estimation of mixing distributions in GLMM's with multiple random effects. The log-likelihood to be maximized has the general form l(G)=Σi log∫f(yi,γ) dG(γ) where f(.,γ) is a parametric family of component densities, yi is the ith observed response dependent variable, and G is a mixing distribution function of the random effects vector γ defined on Ω. The literature presents many algorithms for maximum likelihood estimation (MLE) of G in the univariate random effect case such as the EM algorithm (Laird, 1978), the intra-simplex direction method, ISDM (Lesperance and Kalbfleish, 1992), and vertex exchange method, VEM (Bohning, 1985). In this dissertation, the constrained Newton method (CNM) in Wang (2007), which fits GLMM's with random intercepts only, is extended to fit clustered datasets with multiple random effects. Owing to the general equivalence theorem from the geometry of mixture likelihoods (see Lindsay, 1995), many NPMLE algorithms including CNM and ISDM maximize the directional derivative of the log-likelihood to add potential support points to the mixing distribution G. Our method, Direct Search Directional Derivative (DSDD), uses a directional search method to find local maxima of the multi-dimensional directional derivative function. The DSDD's performance is investigated in GLMM where f is a Bernoulli or Poisson distribution function. The algorithm is also extended to cover GLMM's with zero-inflated data. Goodness-of-fit (GOF) and selection methods for mixed models have been developed in the literature, however their application in models with nonparametric random effects distributions is vague and ad-hoc. Some popular measures such as the Deviance Information Criteria (DIC), conditional Akaike Information Criteria (cAIC) and R2 statistics are potentially useful in this context. Additionally, some cross-validation goodness-of-fit methods popular in Bayesian applications, such as the conditional predictive ordinate (CPO) and numerical posterior predictive checks, can be applied with some minor modifications to suit the non-Bayesian approach. / Graduate / 0463 / rabihsaab@gmail.com

Generalized linear mixture models (GLMM) are widely used in statistical applications to model count and binary data. We consider the problem of nonparametric likelihood estimation of mixing distributions in GLMM's with multiple random effects. The log-likelihood to be maximized has the general form l(G)=Σi log∫f(yi,γ) dG(γ) where f(.,γ) is a parametric family of component densities, yi is the ith observed response dependent variable, and G is a mixing distribution function of the random effects vector γ defined on Ω. The literature presents many algorithms for maximum likelihood estimation (MLE) of G in the univariate random effect case such as the EM algorithm (Laird, 1978), the intra-simplex direction method, ISDM (Lesperance and Kalbfleish, 1992), and vertex exchange method, VEM (Bohning, 1985). In this dissertation, the constrained Newton method (CNM) in Wang (2007), which fits GLMM's with random intercepts only, is extended to fit clustered datasets with multiple random effects. Owing to the general equivalence theorem from the geometry of mixture likelihoods (see Lindsay, 1995), many NPMLE algorithms including CNM and ISDM maximize the directional derivative of the log-likelihood to add potential support points to the mixing distribution G. Our method, Direct Search Directional Derivative (DSDD), uses a directional search method to find local maxima of the multi-dimensional directional derivative function. The DSDD's performance is investigated in GLMM where f is a Bernoulli or Poisson distribution function. The algorithm is also extended to cover GLMM's with zero-inflated data. Goodness-of-fit (GOF) and selection methods for mixed models have been developed in the literature, however their application in models with nonparametric random effects distributions is vague and ad-hoc. Some popular measures such as the Deviance Information Criteria (DIC), conditional Akaike Information Criteria (cAIC) and R2 statistics are potentially useful in this context. Additionally, some cross-validation goodness-of-fit methods popular in Bayesian applications, such as the conditional predictive ordinate (CPO) and numerical posterior predictive checks, can be applied with some minor modifications to suit the non-Bayesian approach. / Graduate / 0463 / rabihsaab@gmail.com