Tornado intensity and impacts vary drastically across space, thus spatial and statistical analyses were used to identify patterns of tornado severity in the Southeastern United States and to assess the vulnerability and estimated recurrence of tornadic activity. Records from the Storm Prediction Center's tornado database (1950-2014) were used to estimate kernel density to identify areas of high and low tornado frequency at both the regional- and state-scales. Return periods (2-year, 5-year, 10-year, 25-year, 50-year, and 100-year) were calculated at both scales as well using a composite score that included EF-scale magnitude, injury counts, and fatality counts. Results showed that the highest density of tornadoes occur in Alabama, Mississippi, and Arkansas, while the highest return period intensities occur in Alabama and Mississippi. Scaledependent analysis revealed finer details of density and intensity for each state. Better communication of high hazard areas and integration into existing mitigation plans is suggested.

The response of a karst aquifer to storm events is often faster and more severe than that of a non-karst aquifer. This distinction is often problematic for planners and municipalities, because karst flooding does not typically occur along perennial water courses; thus, traditional flood management strategies are usually ineffective. The City of Bowling Green (CoBG), Kentucky is a representative example of an area plagued by karst flooding. The CoBG, is an urban karst area (UKA), that uses Class V Injection Wells to lessen the severity of flooding. The overall effectiveness, siting, and flooding impact of Injection Wells in UKA’s is lacking; their influence on groundwater is evident from decades of recurring problems in the form of flooding and groundwater contamination. This research examined Class V Injection Wells in the CoBG to determine how Injection Well siting, design, and performance influence urban karst hydrology. The study used high-resolution monitoring, as well as hydrologic modeling, to evaluate Injection Well and spring responses during storm and baseflow conditions. In evaluating the properties of the karst aquifer and the influences from the surrounding environment, a relationship was established between precipitation events, the drainage capacity of the Injection Wells, and the underlying karst system. Ultimately, the results from this research could be used to make sound data-driven policy recommendations and to inform stormwater management in UKAs.

The United States is in the midst of an opioid epidemic. In addition to other system level interventions, almost all states have responded to the crisis by implementing prescription drug monitoring programs (PDMPs). PDMPs are state-level interventions that track the dispensing of Controlled Substances. Data generated at the time of medication dispensing is uploaded to a central data server that may be used to assist in identifying drug diversion, medication misuse, or potentially aberrant prescribing practices. Prior studies assessing the impact of PDMPs on trends in opioid-related morbidity have often failed to take into account the wide heterogeneity of program features and how the effectiveness of these features may be mitigated by insurance status. Previous research has also failed to differentiate the effects of these programs on prescription vs. illicit opioid-related morbidity. The studies in this dissertation attempt to address these gaps using epidemiological techniques to examine the associations between specific PDMP features and trends in prescription and illicit opioid-related poisonings in populations of different insurance beneficiaries. Results of these studies demonstrate that implementation of specific PDMP features is significantly associated with differential trends in prescription and illicit-opioid related poisonings and that the effectiveness of these features vary depending on the insurance status of the population studied. These results suggest that PDMPs offer a valuable tool in addressing the United States’ opioid epidemic, and may be used as empirical evidence to support PDMP best practices in the future.

Increased opioid analgesic (OA) prescribing has been associated with increased risk of prescription opioid diversion, misuse, and abuse. States established prescription drug monitoring programs (PDMPs) to collect and analyze electronic records for dispensed controlled substances to reduce prescription drug abuse and diversion. PDMP data can be used by prescribers for tracking patient’s history of controlled substance prescribing to inform clinical decisions. The studies in this dissertation are focused on the less utilized potential of the PDMP data to enhance public health surveillance to monitor OA prescribing and co-prescribing and association with opioid overdose mortality and morbidity. Longitudinal analysis of OA prescribing and evaluation of the effect of recent policies and opioid prescribing guidelines require consensus measures for OA utilization and computational tools for uniform operationalization by researchers and agencies. Statistical macros and computational tools for OA utilization measures were developed and tested with Kentucky PDMP data. A set of covariate measures using mortality and morbidity surveillance data were also developed as proxy measures for prevalence of painful conditions justifying OA utilization, and availability of heroin and medication treatment for opioid use disorder. A series of epidemiological studies used the developed OA measures as outcomes, and adjusted for time-varying socio-demographic and health care utilization covariates in population-averaged statistical models to assess longitudinal trend and pattern changes in OA utilization in Kentucky in recent years. The first study, “Trends and Patterns of OA Prescribing: Regional and Rural-Urban Variations in Kentucky from 2012 to 2015,” shows significant downward trends in rates of residents with OA prescriptions. Despite the significant decline over time, and after accounting for prevalence of injuries and cancer, the rate of dispensed OA prescriptions among residents in Kentucky Appalachian counties remained significantly higher than the rest of the state. The second study, “Population-Level Measures for High-Risk OA Prescribing: Longitudinal Trends and Relationships with Pain-Associated Conditions,” shows significant reduction in high-risk OA prescribing (e.g., high daily dosage, long-term use, concurrent prescriptions for OA and benzodiazepines) from 2012 to 2016, significantly positive associations between high-risk OA prescribing and cancer mortality rates with no substantial change in the association magnitude over time, and declining strengths of positive associations between high-risk OA prescribing and acute traumatic injuries or chronic non-cancer pain over the study period. The third study, “A Reciprocal Association between Longitudinal Trends of Buprenorphine/Naloxone Prescribing and High-Dose OA Prescribing,” indicates a significant reciprocal relationship between high-dose OA prescribing and buprenorphine/ naloxone prescribing, and a clinically meaningful effect of buprenorphine/naloxone prescribing on reducing OA utilization. The results from the studies advanced the understanding of the epidemiology of opioid use and misuse in Kentucky, and identified actionable risk and protective factors that can inform policy, education, and drug overdose prevention interventions. The developed operational definition inventory and computational tools could stimulate further research in Kentucky and comparative studies in other states.

This thesis explores the problems of fitting antedependence (AD) models and partial antecorrelation (PAC) models to continuous non-Gaussian longitudinal data. AD models impose certain conditional independence relations among the measurements within each subject, while PAC models characterize the partial correlation relations. The models are parsimonious and useful for data exhibiting time-dependent correlations. Since the relation of conditional independence among variables is rather restrictive, we first consider an autoregressively characterized PAC model with independent asymmetric Laplace (ALD) innovations and prove that this model is an AD model. The ALD distribution previously has been applied to quantile regression and has shown promise for modeling asymmetrically distributed ecological data. In addition, the double exponential distribution, a special case of the ALD, has played an important role in fitting symmetric finance and hydrology data. We give the distribution of a linear combination of independent standard ALD variables in order to derive marginal distributions for the model. For the model estimation problem, we propose an iterative algorithm for the maximum likelihood estimation. The estimation accuracy is illustrated by some numerical examples as well as some longitudinal data sets. The second component of this dissertation focuses on AD multivariate skew normal models. The multivariate skew normal distribution not only shares some nice properties with multivariate normal distributions but also allows for any value of skewness. We derive necessary and sufficient conditions on the shape and covariance parameters for multivariate skew normal variables to be AD(p) for some p. Likelihood-based estimation for balanced and monotone missing data as well as likelihood ratio hypothesis tests for the order of antedependence and for zero skewness under the models are presented. Since the class of skew normal random variables is closed under the addition of independent standard normal random variables, we then consider an autoregressively characterized PAC model with a combination of independent skew normal and normal innovations. Explicit expressions for the marginals, which all have skew normal distributions, and maximum likelihood estimates of model parameters, are given. Numerical results show that these three proposed models may provide reasonable fits to some continuous non-Gaussian longitudinal data sets. Furthermore, we compare the fits of these models to the Treatment A cattle growth data using penalized likelihood criteria, and demonstrate that the AD(2) multivariate skew normal model fits the data best among those proposed models.

Doctor of Philosophy(PhD) / This research develops a theory to explain the pathways taken by students through higher education in Australia. From a socio-ecological perspective, pathways are conceptualised as a diverse series of choices within learning contexts. In relation to Australian higher education, the model of pathways through undergraduate courses emphasises contexts in which personal and social factors contribute to the choices students make over time. A new method identifies and documents longitudinal pathways of progression through university degree courses. Higher education population data was examined over time to test the Pathways Theory of student progression. This unique detailed longitudinal approach documented all the pathway choices made by a cohort of students as they progressed in and out of their courses over time. Pathways were documented to the point of departure from a course and beyond, to include the extended pathways of students who returned to their courses following stop-outs and transfers. The results highlight the importance of a longitudinal approach in explaining pathways through specific course contexts. This research underlines the importance of considering context and diversity in student behaviours when using indicators of performance, retention and completion. Understanding the relationship between the personal and social characteristics of students and their specific learning contexts contributed to an understanding of the choice behaviour of students as they negotiated pathways through courses within the broader context of higher education. [Information on pages 271-275 has been removed from the digital version of this thesis for copyright reasons. The full print version of this thesis is available in The University of Sydney Library: Robinson, R. A. (2006). Pathways in Context: Background Characteristics and Demographics in Student Progression through Higher Education. PhD Thesis. The University of Sydney, Sydney.]

Financial failure is an important subject for both the economical development of the country and for the self - evaluation of individual companies. Increase in the number of financially failed companies points out the misuse of the country resources. Recently, financial failure threatens both small and large companies in Turkey. It is important to determine factors that affect the financial failure by analyzing models and to use these models for auditing the financial situation. In today&rsquo / s Turkey, the statistical methods that are used for this purpose involve single level models applied to cross-sectional data. However, multilevel models applied to panel data are more preferable as they gather more information, and also, enable the calculated financial success probabilities to be more trustworthy. In this thesis, publicly available panel data that are collected from The Istanbul Stock Exchange are investigated. Mainly, financial success of companies from two sectors, namely industry and services, are investigated. For the analysis of this panel data, data exploration methods, missing data imputation, possible solutions to multicollinearity problem, single level logistic regression models and multilevel models are used. By these models, financial success probabilities for each company are calculated / the factors related to the financial failure are determined, and changes in time are observed. Models and early warning systems resulted in correct classification rates of up to 100%. In the services sector, a small number of companies having publicly available data result in a decline in the success of models. It is concluded that sharing data with more subjects observed in a longer time period collected in the same format with academicians, will result in better justified outputs, which are useful for both academicians and managers.

A recent advancement in statistical methodology, Integrative Data Analyses (IDA Curran & Hussong, 2009) has led researchers to employ a calibration technique as to not violate an independence assumption. This technique uses a randomly selected, simplified correlational structured subset, or calibration, of a whole data set in a preliminary stage of analysis. However, a single calibration estimator suffers from instability, low precision and loss of power. To overcome this limitation, a multiple calibration (MC; Greenbaum et al., 2013; Wang et al., 2013) approach has been developed to produce better estimators, while still removing a level of dependency in the data as to not violate independence assumption. The MC method is conceptually similar to multiple imputation (MI; Rubin, 1987; Schafer, 1997), so MI estimators were borrowed for comparison. A simulation study was conducted to compare the MC and MI estimators, as well as to evaluate the performance of the operating characteristics of the methods in a cross classified data characteristic design. The estimators were tested in the context of assessing change over time in a longitudinal data set. Multiple calibrations consisting of a single measurement occasion per subject were drawn from a repeated measures data set, analyzed separately, and then combined by the rules set forth by each method to produce the final results. The data characteristics investigated were effect size, sample size, and the number of repeated measures per subject. Additionally, a real data application of an MC approach in an IDA framework was conducted on data from three completed, randomized controlled trials studying the treatment effects of Multidimensional Family Therapy (MDFT; Liddle et al., 2002) on substance use trajectories for adolescents at a one year follow-up. The simulation study provided empirical evidence of how the MC method preforms, as well as how it compares to the MI method in a total of 27 hypothetical scenarios. There were strong asymptotic tendencies observed for the bias, standard error, mean square error and relative efficiency of an MC estimator to approach the whole set estimators as the number of calibrations approached 100. The MI combination rules proved not appropriate to borrow for the MC case because the standard error formulas were too conservative and performance with respect to power was not robust. As a general suggestion, 5 calibrations are sufficient to produce an estimator with about half the bias of a single calibration estimator and at least some indication of significance, while 20 calibrations are ideal. After 20 calibrations, the contribution of an additional calibration to the combined estimator greatly diminished. The MDFT application demonstrated a successful implementation of 5 calibration approach in an IDA on real data, as well as the risk of missing treatment effects when analysis is limited to a single calibration's results. Additionally, results from the application provided evidence that MDFT interventions reduced the trajectories of substance use involvement at a 1-year follow-up to a greater extent than any of the active control treatment groups, overall and across all gender and ethnicity subgroups. This paper will aid researchers interested in employing a MC approach in an IDA framework or whenever a level of dependency in a data set needs to be removed for an independence assumption to hold.

In this thesis, we address issues of model estimation for longitudinal categorical data and of model selection for these data with missing covariates. Longitudinal survey data capture the responses of each subject repeatedly through time, allowing for the separation of variation in the measured variable of interest across time for one subject from the variation in that variable among all subjects. Questions concerning persistence, patterns of structure, interaction of events and stability of multivariate relationships can be answered through longitudinal data analysis. Longitudinal data require special statistical methods because they must take into account the correlation between observations recorded on one subject. A further complication in analysing longitudinal data is accounting for the non- response or drop-out process. Potentially, the missing values are correlated with variables under study and hence cannot be totally excluded. Firstly, we investigate a Bayesian hierarchical model for the analysis of categorical longitudinal data from the Longitudinal Survey of Immigrants to Australia. Data for each subject is observed on three separate occasions, or waves, of the survey. One of the features of the data set is that observations for some variables are missing for at least one wave. A model for the employment status of immigrants is developed by introducing, at the first stage of a hierarchical model, a multinomial model for the response and then subsequent terms are introduced to explain wave and subject effects. To estimate the model, we use the Gibbs sampler, which allows missing data for both the response and explanatory variables to be imputed at each iteration of the algorithm, given some appropriate prior distributions. After accounting for significant covariate effects in the model, results show that the relative probability of remaining unemployed diminished with time following arrival in Australia. Secondly, we examine the Bayesian model selection techniques of the Bayes factor and Deviance Information Criterion for our regression models with miss- ing covariates. Computing Bayes factors involve computing the often complex marginal likelihood p(y|model) and various authors have presented methods to estimate this quantity. Here, we take the approach of path sampling via power posteriors (Friel and Pettitt, 2006). The appeal of this method is that for hierarchical regression models with missing covariates, a common occurrence in longitudinal data analysis, it is straightforward to calculate and interpret since integration over all parameters, including the imputed missing covariates and the random effects, is carried out automatically with minimal added complexi- ties of modelling or computation. We apply this technique to compare models for the employment status of immigrants to Australia. Finally, we also develop a model choice criterion based on the Deviance In- formation Criterion (DIC), similar to Celeux et al. (2006), but which is suitable for use with generalized linear models (GLMs) when covariates are missing at random. We define three different DICs: the marginal, where the missing data are averaged out of the likelihood; the complete, where the joint likelihood for response and covariates is considered; and the naive, where the likelihood is found assuming the missing values are parameters. These three versions have different computational complexities. We investigate through simulation the performance of these three different DICs for GLMs consisting of normally, binomially and multinomially distributed data with missing covariates having a normal distribution. We find that the marginal DIC and the estimate of the effective number of parameters, pD, have desirable properties appropriately indicating the true model for the response under differing amounts of missingness of the covariates. We find that the complete DIC is inappropriate generally in this context as it is extremely sensitive to the degree of missingness of the covariate model. Our new methodology is illustrated by analysing the results of a community survey.

Doctor of Philosophy(PhD) / This research develops a theory to explain the pathways taken by students through higher education in Australia. From a socio-ecological perspective, pathways are conceptualised as a diverse series of choices within learning contexts. In relation to Australian higher education, the model of pathways through undergraduate courses emphasises contexts in which personal and social factors contribute to the choices students make over time. A new method identifies and documents longitudinal pathways of progression through university degree courses. Higher education population data was examined over time to test the Pathways Theory of student progression. This unique detailed longitudinal approach documented all the pathway choices made by a cohort of students as they progressed in and out of their courses over time. Pathways were documented to the point of departure from a course and beyond, to include the extended pathways of students who returned to their courses following stop-outs and transfers. The results highlight the importance of a longitudinal approach in explaining pathways through specific course contexts. This research underlines the importance of considering context and diversity in student behaviours when using indicators of performance, retention and completion. Understanding the relationship between the personal and social characteristics of students and their specific learning contexts contributed to an understanding of the choice behaviour of students as they negotiated pathways through courses within the broader context of higher education. [Information on pages 271-275 has been removed from the digital version of this thesis for copyright reasons. The full print version of this thesis is available in The University of Sydney Library: Robinson, R. A. (2006). Pathways in Context: Background Characteristics and Demographics in Student Progression through Higher Education. PhD Thesis. The University of Sydney, Sydney.]