Educators and administrators often use sub-scores derived from state accountability assessments to diagnose learning/instruction and inform curriculum planning. However, there are several psychometric limitations of observed sub-scores, two of which were the focus of the present study: (1) limited reliabilities due to short lengths, and (2) little distinct information in sub-scores for most existing assessments. The present study was conducted to evaluate the extent to which these limitations might be overcome by incorporating collateral information into sub-score estimation. The three sources of collateral information under investigation included (1) information from other sub-scores, (2) schools that students attended, and (3) school-level scores on the same test taken by previous cohorts of students in that school. Kelley's and Shin's methods were implemented in a fully Bayesian framework and were adapted to incorporate differing levels of collateral information. Results were evaluated in light of three comparison criteria, i.e., signal noise ratio, standard error of estimate, and sub-score separation index. The data came from state accountability assessments. Consistent with the literature, using information from other sub-scores produced sub-scores with enhanced precision but reduced profile variability. This finding suggests that using collateral information internal to the test has the capability of enhancing sub-score reliability, but at the expense of losing the distinctness of each individual sub-score. Using information indicating the schools that students attended led to a small gain in sub-score precision without losing sub-score distinctness. Furthermore, using such information was found to have the potential to improve sub-score validity by addressing Simpson's paradox when sub-score correlations were not invariant across schools. Using previous-year school-level sub-score information was found to have the potential to enhance both precision and distinctness for school-level sub-scores, although not for student-level sub-scores. School-level sub-scores were found to exhibit satisfactory psychometric properties and thus have value in evaluating school curricular effectiveness. Issues concerning validity, interpretability, suitability of using such collateral information are discussed in the context of state accountability assessments.

<p>Phosphorus load reduction and dreissenid invasion are the two most important factors that influence europhication dynamics in the Great Lakes. The 1978 amendments to the Great Lakes Water Quality Agreement (GLWQA) between the United States and Canada established target phosphorus loads for the lakes, leading to reductions in external phosphorus loading to the Great Lakes. With diminished phosphorus levels, further nutrient management was a minor concern until the proliferation of invasive dreissenid mussels. Dreissenid mussels were first documented in the Laurentian Great Lakes in the late 1980s. Zebra mussels (<italic>Dreissena polymorpha</italic>) spread quickly into shallow, hard-substrate areas; quagga mussels (<italic>Dreissena rostriformis bugensis</italic>) spread more slowly and are currently colonizing deep, offshore areas. These mussels have the potential to modify biogeochemical processes and food web structure, altering nutrient cycling and availability. Following the mussel invasion, cyanobacterial blooms and nuisance benthic algal growth have reappeared in many nearshore areas of the Great Lakes.</p><p>This dissertation characterizes long-term patterns of phosphorus loading and mussel populations for Saginaw Bay, and estimates the effects of load reductions and dreissenid invasion on several aspects of pelagic water quality, focusing on phosphorus flux and cycling in Saginaw Bay. Bayesian approaches were used to quantify the impacts of load reduction and mussel invasion, while at the same time addressing model parameter uncertainty and prediction uncertainty associated with long-term observational data. Annual total phosphorus load estimates suggest a decreasing trend until the late 1970s to early 1980s, reflecting the effectiveness of point source controls implemented pursuant to GLWQA. Despite the decrease, however, the annual loads have not likely met the 440 tonne yr-1 target established for Saginaw Bay. In 1990 zebra mussels were discovered in the bay and by 1992 they were widespread and peaked with densities of >30,000 m<super>-2</super>. Following the peak, mean densities dropped and modeling results predict that the density will reach equilibria at ~600 m<super>-2</super>. When mussels appeared, the proportion of tributary phosphorus retained in Saginaw Bay increased from ~0.5 to ~0.7, reducing phosphorus export to the main body of Lake Huron. The combined effects of increased phosphorus retention and decreased phosphorus loading have caused an ~60% decrease in phosphorus export from Saginaw Bay to Lake Huron. The analysis of long-term patterns of pelagic water quality highlights the sustained effects of mussel invasion on altering water quality parameters in Saginaw Bay; there was a consistent decrease in chlorophyll concentrations by ~46%, and total phosphorus concentrations by ~25%, and an increase in secchi depths by ~15% over ~20 year invasion of mussels. A comparison of chlorophyll-phospohrus relationship between pre- and post-invasion periods suggest the reduced chlorophyll yield for a given phosphorus concentration after the mussel invasion. Further, decreases in both total phosphorus and chlorophyll concentrations were found in the majority of 24 mussel-invaded US lakes in addition to Saginaw Bay, and modeling results predict less chlorophyll yields per unit phosphorus level that ranges from oligo- to mesotrophic conditions. All lines of evidence presented in the dissertation point to the important roles of load reductions and invasive mussels affecting eutrophication dynamics in lake ecosystems.</p> / Dissertation

We propose classification models for binary and multicategory data where the predictor is a random function. The functional predictor could be irregularly and sparsely sampled or characterized by high dimension and sharp localized changes. In the former case, we employ Bayesian modeling utilizing flexible spline basis which is widely used for functional regression. In the latter case, we use Bayesian modeling with wavelet basis functions which have nice approximation properties over a large class of functional spaces and can accommodate varieties of functional forms observed in real life applications. We develop an unified hierarchical model which accommodates both the adaptive spline or wavelet based function estimation model as well as the logistic classification model. These two models are coupled together to borrow strengths from each other in this unified hierarchical framework. The use of Gibbs sampling with conjugate priors for posterior inference makes the method computationally feasible. We compare the performance of the proposed models with the naive models as well as existing alternatives by analyzing simulated as well as real data. We also propose a Bayesian unified hierarchical model based on a proportional hazards model and generalized linear model for survival analysis with irregular longitudinal covariates. This relatively simple joint model has two advantages. One is that using spline basis simplifies the parameterizations while a flexible non-linear pattern of the function is captured. The other is that joint modeling framework allows sharing of the information between the regression of functional predictors and proportional hazards modeling of survival data to improve the efficiency of estimation. The novel method can be used not only for one functional predictor case, but also for multiple functional predictors case. Our methods are applied to analyze real data sets and compared with a parameterized regression method.

BACKGROUND: Adolescent idiopathic scoliosis (AIS) surgery is the most common reason for elective pediatric orthopaedic surgery. Minimization of adverse events is an important goal. Institute of Medicine (IOM) outlined 6 facets of healthcare quality improvement within the acronym STEEEP. Two of these facets, Safety and Timeliness for AIS surgery in Canada, are examined in this thesis. METHODS: A three - part study, using clinical records at the largest Canadian pediatric hospital and CIHI national administrative data, determined i) the relationship between surgical wait times and rates of adverse events, along with determination of an empirically derived access target, ii) accuracy of ICD-10 coding of surgical AIS cases along with an optimal search strategy to identify surgical AIS cases, and iii) the volume – outcome relationships for scoliosis surgery using hierarchical and conventional single level multi-variate regression analysis. RESULTS: Access target of 3 months minimized the adverse events related to waiting. Optimal search strategy for AIS surgical cases using ICD-10 coding required combination of codes as each code in isolation was inaccurate due to limitations in coding definitions. There was no significant volume – outcome relationship using appropriate modeling strategies. CONCLUSIONS: Ensuring timeliness of surgical treatment of less than 3 months is important in surgical cases of AIS given the potential for curve progression in higher risk individuals who are skeletally immature with large magnitude curves at time of surgical consent. At the administrative database level, knowledge of coding accuracy and optimal search strategies are needed to capture a complete cohort for analysis. In AIS, several ICD-10 codes need to be combined. AIS surgery cases captured through this optimal search strategy, revealed no significant volume-outcome relationships with appropriate modeling. Based on these results, minimum volume thresholds and regionalization of care for AIS surgery does not appear to be justified. However, a larger sample size was needed to determine whether there was a clinically significant difference in wound infection and blood transfusion rates. Furthermore, clinical variables, not part of an administrative database such as curve pattern were not included.

<p>The first part of the thesis focuses on the development of Bayesian modeling motivated by geophysics applications. In Chapter 2, we model the frequency of pyroclastic flows collected from the Soufriere Hills volcano. Multiple change points within the dataset reveal several limitations of existing methods in literature. We propose Bayesian hierarchical models (BBH) by introducing an extra level of hierarchy with hyper parameters, adding a penalty term to constrain close consecutive rates, and using a mixture prior distribution to more accurately match certain circumstances in reality. We end the chapter with a description of the prediction procedure, which is the biggest advantage of the BBH in comparison with other existing methods. In Chapter 3, we develop new statistical techniques to model and relate three complex processes and datasets: the process of extrusion of magma into the lava dome, the growth of the dome as measured by its height, and the rockfalls as an indication of the dome's instability. First, we study the dynamic Negative Binomial branching process and use it to model the rockfalls. Moreover, a generalized regression model is proposed to regress daily rockfall numbers on the extrusion rate and dome height. Furthermore, we solve an inverse problem from the regression model and predict extrusion rate based on rockfalls and dome height.</p><p>The other focus of the thesis is adaptive Markov chain Monte Carlo (MCMC) method. In Chapter 4, we improve upon the Wang-Landau (WL) algorithm. The WL algorithm is an adaptive sampling scheme that modifies the target distribution to enable the chain to visit low-density regions of the state space. However, the approach relies heavily on a partition of the state space that is left to the user to specify. As a result, the implementation and the use of the algorithm are time-consuming and less automatic. We propose an automatic, adaptive partitioning scheme which continually refines the initial partition as needed during sampling. We show that this overcomes the limitations of the input user-specified partition, making the algorithm significantly more automatic and user-friendly while also making the performance dramatically more reliable and robust. In Chapter 5, we consider the convergence and autocorrelation aspects of MCMC. We propose an Exploration/Exploitation (XX) approach to constructing adaptive MCMC algorithms, which combines adaptation schemes of distinct types. The exploration piece uses adaptation strategies aiming at exploring new regions of the target distribution and thus improving the rate of convergence to equilibrium. The exploitation piece involves an adaptation component which decreases autocorrelation for sampling among regions already discovered. We demonstrate that the combined XX algorithm significantly outperforms either original algorithm on difficult multimodal sampling problems.</p> / Dissertation

BACKGROUND: Adolescent idiopathic scoliosis (AIS) surgery is the most common reason for elective pediatric orthopaedic surgery. Minimization of adverse events is an important goal. Institute of Medicine (IOM) outlined 6 facets of healthcare quality improvement within the acronym STEEEP. Two of these facets, Safety and Timeliness for AIS surgery in Canada, are examined in this thesis. METHODS: A three - part study, using clinical records at the largest Canadian pediatric hospital and CIHI national administrative data, determined i) the relationship between surgical wait times and rates of adverse events, along with determination of an empirically derived access target, ii) accuracy of ICD-10 coding of surgical AIS cases along with an optimal search strategy to identify surgical AIS cases, and iii) the volume – outcome relationships for scoliosis surgery using hierarchical and conventional single level multi-variate regression analysis. RESULTS: Access target of 3 months minimized the adverse events related to waiting. Optimal search strategy for AIS surgical cases using ICD-10 coding required combination of codes as each code in isolation was inaccurate due to limitations in coding definitions. There was no significant volume – outcome relationship using appropriate modeling strategies. CONCLUSIONS: Ensuring timeliness of surgical treatment of less than 3 months is important in surgical cases of AIS given the potential for curve progression in higher risk individuals who are skeletally immature with large magnitude curves at time of surgical consent. At the administrative database level, knowledge of coding accuracy and optimal search strategies are needed to capture a complete cohort for analysis. In AIS, several ICD-10 codes need to be combined. AIS surgery cases captured through this optimal search strategy, revealed no significant volume-outcome relationships with appropriate modeling. Based on these results, minimum volume thresholds and regionalization of care for AIS surgery does not appear to be justified. However, a larger sample size was needed to determine whether there was a clinically significant difference in wound infection and blood transfusion rates. Furthermore, clinical variables, not part of an administrative database such as curve pattern were not included.

abstract: Researchers are often interested in estimating interactions in multilevel models, but many researchers assume that the same procedures and interpretations for interactions in single-level models apply to multilevel models. However, estimating interactions in multilevel models is much more complex than in single-level models. Because uncentered (RAS) or grand mean centered (CGM) level-1 predictors in two-level models contain two sources of variability (i.e., within-cluster variability and between-cluster variability), interactions involving RAS or CGM level-1 predictors also contain more than one source of variability. In this Master’s thesis, I use simulations to demonstrate that ignoring the four sources of variability in a total level-1 interaction effect can lead to erroneous conclusions. I explain how to parse a total level-1 interaction effect into four specific interaction effects, derive equivalencies between CGM and centering within context (CWC) for this model, and describe how the interpretations of the fixed effects change under CGM and CWC. Finally, I provide an empirical example using diary data collected from working adults with chronic pain. / Dissertation/Thesis / Masters Thesis Psychology 2015

In this paper, we provide a parsimonious means of estimating panel VARs with stochastic volatility. We assume that coefficients associated with domestic lagged endogenous variables arise from a finite mixture of Gaussian distribution. Shrinkage on the cluster size is introduced through suitable priors on the component weights and cluster-relevant quantities are identified through novel normal-gamma shrinkage priors. To assess whether dynamic interdependencies between units are needed, we moreover impose shrinkage priors on the coefficients related to other countries' endogenous variables. Finally, our model controls for static interdependencies by assuming that the reduced form shocks of the model feature a factor stochastic volatility structure. We assess the merits of the proposed approach by using synthetic data as well as a real data application. In the empirical application, we forecast Eurozone unemployment rates and show that our proposed approach works well in terms of predictions. / Series: Department of Economics Working Paper Series

Context: A common way to represent product lines is with variability modeling. Yet, there are different ways to extract and organize relevant characteristics of variability. Comprehensibility of these models and the ease of creating models are important for the efficiency of any variability management approach. Objective: The goal of this paper is to investigate the comprehensibility of two common styles to organize variability into models - hierarchical and constrained - where the dependencies between choices are specified either through the hierarchy of the model or as cross-cutting constraints, respectively. Method: We conducted a controlled experiment with a sample of 90 participants who were students with prior training in modeling. Each participant was provided with two variability models specified in Common Variability Language (CVL) and was asked to answer questions requiring interpretation of provided models. The models included 9 to 20 nodes and 8 to 19 edges and used the main variability elements. After answering the questions, the participants were asked to create a model based on a textual description. Results: The results indicate that the hierarchical modeling style was easier to comprehend from a subjective point of view, but there was also a significant interaction effect with the degree of dependency in the models, that influenced objective comprehension. With respect to model creation, we found that the use of a constrained modeling style resulted in higher correctness of variability models. Conclusions: Prior exposure to modeling style and the degree of dependency among elements in the model determine what modeling style a participant chose when creating the model from natural language descriptions. Participants tended to choose a hierarchical style for modeling situations with high dependency and a constrained style for situations with low dependency. Furthermore, the degree of dependency also influences the comprehension of the variability model.

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