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.

Power Study on Testing Epidemic Alternatives

Detecting change points in epidemic models has been studied by many scholars. Yao (1993) summarized five existing test statistics in the literature. Out of those test statistics, it was observed that the likelihood ratio statistic showed its standout power. However, all of the existing test statistics are based on an assumption that population variance is known, which is an unrealistic assumption in practice. To avoid assuming known population variance, a new test statistic for detecting epidemic models is studied in this thesis. The new test statistic is a parameter-free test statistic which is more powerful compared to the existing test statistics. Different sample sizes and lengths of epidemic durations are used for the power comparison purpose. Monte Carlo simulation is used to find the critical values of the new test statistic and to perform the power comparison. Based on the Monte Carlo simulation result, it can be concluded that the sample size and the length of the duration have some effect on the power of the tests. It can also be observed that the new test statistic studied in this thesis has higher power than the existing test statistics do in all of cases.

Substructuring in four populations of African descent

When a suspect's DNA profile is admitted into court as a match to evidence the probability of the perpetrator being another individual must be calculated from database allele frequencies. The two methods used for this calculation are phenotypic frequency and likelihood ratio. Neither of these calculations takes into account substructuring within populations. In these substructured populations the frequency of homozygotes increases and that of heterozygotes usually decreases. The departure from Hardy- Weinberg expectation in a sample population can be estimated using Sewall Wright's Fst statistic. Fst values were calculated in four populations of African descent by comparing allele frequencies at three short tandem repeat loci. This was done by amplifying the three loci in each sample using the Polymerase Chain Reaction and separating these fragments using polyacrylamide gel electrophoresis. The gels were then silver stained and autoradiograms taken, from which allele frequencies were estimated. Fst values averaged 0.007+- 0.005 within populations of African descent and 0.02+- 0.01 between white and black populations.

Effect of performance feedback on perceived knowledge and likelihood to pursue continuing education

The purpose of this study was to assess the effect of performance feedback on Athletic Trainers’ (ATs) perceived knowledge (PK) and likelihood to pursue continuing education (CE). The investigation was grounded in the theories of “the definition of the situation” (Thomas & Thomas, 1928) and the “illusion of knowing,” (Glenberg, Wilkinson, & Epstein, 1982) suggesting that PK drives behavior. This investigation measured the degree to which knowledge gap predicted CE seeking behavior by providing performance feedback designed to change PK. A pre-test post-test control-group design was used to measure PK and likelihood to pursue CE before and after assessing actual knowledge. ATs (n=103) were randomly sampled and assigned to two groups, with and without performance feedback. Two independent samples t-tests were used to compare groups on the difference scores of the dependent variables. Likelihood to pursue CE was predicted by three variables using multiple linear regression: perceived knowledge, pre-test likelihood to pursue CE, and knowledge gap. There was a 68.4% significant difference (t101=2.72, p=0.01, ES=0.45) between groups in the change scores for likelihood to pursue CE because of the performance feedback (Experimental group=13.7% increase; Control group=4.3% increase). The strongest relationship among the dependent variables was between pre-test and post-test measures of likelihood to pursue CE (F2,102=56.80, p<0.01, r=0.73, R2=0.53). The pre- and post-test predictive relationship was enhanced when group was included in the model. In this model [YCEpost=0.76XCEpre-0.34 Xgroup+2.24+E], group accounted for a significant amount of unique variance in predicting CE while the pre-test likelihood to pursue CE variable was held constant (F3,102=40.28, p<0.01, r=0.74, R2=0.55). Pre-test knowledge gap, regardless of group allocation, was a linear predictor of the likelihood to pursue CE (F1,102=10.90, p=.01, r=.31, R2=.10). In this investigation, performance feedback significantly increased participants’ likelihood to pursue CE. Pre-test knowledge gap was a significant predictor of likelihood to pursue CE, regardless if performance feedback was provided. ATs may have self-assessed and engaged in internal feedback as a result of their test-taking experience. These findings indicate that feedback, both internal and external, may be necessary to trigger CE seeking behavior.

Effect of Performance Feedback on Perceived Knowledge and Likelihood to Pursue Continuing Education

The purpose of this study was to assess the effect of performance feedback on Athletic Trainers’ (ATs) perceived knowledge (PK) and likelihood to pursue continuing education (CE). The investigation was grounded in the theories of “the definition of the situation” (Thomas & Thomas, 1928) and the “illusion of knowing,” (Glenberg, Wilkinson, & Epstein, 1982) suggesting that PK drives behavior. This investigation measured the degree to which knowledge gap predicted CE seeking behavior by providing performance feedback designed to change PK. A pre-test post-test control-group design was used to measure PK and likelihood to pursue CE before and after assessing actual knowledge. ATs (n=103) were randomly sampled and assigned to two groups, with and without performance feedback. Two independent samples t-tests were used to compare groups on the difference scores of the dependent variables. Likelihood to pursue CE was predicted by three variables using multiple linear regression: perceived knowledge, pre-test likelihood to pursue CE, and knowledge gap. There was a 68.4% significant difference (t101= 2.72, p=0.01, ES=0.45) between groups in the change scores for likelihood to pursue CE because of the performance feedback (Experimental group=13.7% increase; Control group= 4.3% increase). The strongest relationship among the dependent variables was between pre-test and post-test measures of likelihood to pursue CE (F2,102=56.80, p<0.01, r=0.73, R2=0.53). The pre- and post-test predictive relationship was enhanced when group was included in the model. In this model [YCEpost=0.76XCEpre-0.34 Xgroup+2.24+E], group accounted for a significant amount of unique variance in predicting CE while the pre-test likelihood to pursue CE variable was held constant (F3,102=40.28, p<0.01,: r=0.74, R2=0.55). Pre-test knowledge gap, regardless of group allocation, was a linear predictor of the likelihood to pursue CE (F1,102=10.90, p=.01, r=.31, R2=.10). In this investigation, performance feedback significantly increased participants’ likelihood to pursue CE. Pre-test knowledge gap was a significant predictor of likelihood to pursue CE, regardless if performance feedback was provided. ATs may have self-assessed and engaged in internal feedback as a result of their test-taking experience. These findings indicate that feedback, both internal and external, may be necessary to trigger CE seeking behavior.

Bayesian Estimation of Small Proportions Using Binomial Group Test

Group testing has long been considered as a safe and sensible relative to one-at-a-time testing in applications where the prevalence rate p is small. In this thesis, we applied Bayes approach to estimate p using Beta-type prior distribution. First, we showed two Bayes estimators of p from prior on p derived from two different loss functions. Second, we presented two more Bayes estimators of p from prior on π according to two loss functions. We also displayed credible and HPD interval for p. In addition, we did intensive numerical studies. All results showed that the Bayes estimator was preferred over the usual maximum likelihood estimator (MLE) for small p. We also presented the optimal β for different p, m, and k.