Matching Items (40)
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Description
Many longitudinal studies, especially in clinical trials, suffer from missing data issues. Most estimation procedures assume that the missing values are ignorable or missing at random (MAR). However, this assumption leads to unrealistic simplification and is implausible for many cases. For example, an investigator is examining the effect of treatment

Many longitudinal studies, especially in clinical trials, suffer from missing data issues. Most estimation procedures assume that the missing values are ignorable or missing at random (MAR). However, this assumption leads to unrealistic simplification and is implausible for many cases. For example, an investigator is examining the effect of treatment on depression. Subjects are scheduled with doctors on a regular basis and asked questions about recent emotional situations. Patients who are experiencing severe depression are more likely to miss an appointment and leave the data missing for that particular visit. Data that are not missing at random may produce bias in results if the missing mechanism is not taken into account. In other words, the missing mechanism is related to the unobserved responses. Data are said to be non-ignorable missing if the probabilities of missingness depend on quantities that might not be included in the model. Classical pattern-mixture models for non-ignorable missing values are widely used for longitudinal data analysis because they do not require explicit specification of the missing mechanism, with the data stratified according to a variety of missing patterns and a model specified for each stratum. However, this usually results in under-identifiability, because of the need to estimate many stratum-specific parameters even though the eventual interest is usually on the marginal parameters. Pattern mixture models have the drawback that a large sample is usually required. In this thesis, two studies are presented. The first study is motivated by an open problem from pattern mixture models. Simulation studies from this part show that information in the missing data indicators can be well summarized by a simple continuous latent structure, indicating that a large number of missing data patterns may be accounted by a simple latent factor. Simulation findings that are obtained in the first study lead to a novel model, a continuous latent factor model (CLFM). The second study develops CLFM which is utilized for modeling the joint distribution of missing values and longitudinal outcomes. The proposed CLFM model is feasible even for small sample size applications. The detailed estimation theory, including estimating techniques from both frequentist and Bayesian perspectives is presented. Model performance and evaluation are studied through designed simulations and three applications. Simulation and application settings change from correctly-specified missing data mechanism to mis-specified mechanism and include different sample sizes from longitudinal studies. Among three applications, an AIDS study includes non-ignorable missing values; the Peabody Picture Vocabulary Test data have no indication on missing data mechanism and it will be applied to a sensitivity analysis; the Growth of Language and Early Literacy Skills in Preschoolers with Developmental Speech and Language Impairment study, however, has full complete data and will be used to conduct a robust analysis. The CLFM model is shown to provide more precise estimators, specifically on intercept and slope related parameters, compared with Roy's latent class model and the classic linear mixed model. This advantage will be more obvious when a small sample size is the case, where Roy's model experiences challenges on estimation convergence. The proposed CLFM model is also robust when missing data are ignorable as demonstrated through a study on Growth of Language and Early Literacy Skills in Preschoolers.
ContributorsZhang, Jun (Author) / Reiser, Mark R. (Thesis advisor) / Barber, Jarrett (Thesis advisor) / Kao, Ming-Hung (Committee member) / Wilson, Jeffrey (Committee member) / St Louis, Robert D. (Committee member) / Arizona State University (Publisher)
Created2013
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Description
This work presents two complementary studies that propose heuristic methods to capture characteristics of data using the ensemble learning method of random forest. The first study is motivated by the problem in education of determining teacher effectiveness in student achievement. Value-added models (VAMs), constructed as linear mixed models, use students’

This work presents two complementary studies that propose heuristic methods to capture characteristics of data using the ensemble learning method of random forest. The first study is motivated by the problem in education of determining teacher effectiveness in student achievement. Value-added models (VAMs), constructed as linear mixed models, use students’ test scores as outcome variables and teachers’ contributions as random effects to ascribe changes in student performance to the teachers who have taught them. The VAMs teacher score is the empirical best linear unbiased predictor (EBLUP). This approach is limited by the adequacy of the assumed model specification with respect to the unknown underlying model. In that regard, this study proposes alternative ways to rank teacher effects that are not dependent on a given model by introducing two variable importance measures (VIMs), the node-proportion and the covariate-proportion. These VIMs are novel because they take into account the final configuration of the terminal nodes in the constitutive trees in a random forest. In a simulation study, under a variety of conditions, true rankings of teacher effects are compared with estimated rankings obtained using three sources: the newly proposed VIMs, existing VIMs, and EBLUPs from the assumed linear model specification. The newly proposed VIMs outperform all others in various scenarios where the model was misspecified. The second study develops two novel interaction measures. These measures could be used within but are not restricted to the VAM framework. The distribution-based measure is constructed to identify interactions in a general setting where a model specification is not assumed in advance. In turn, the mean-based measure is built to estimate interactions when the model specification is assumed to be linear. Both measures are unique in their construction; they take into account not only the outcome values, but also the internal structure of the trees in a random forest. In a separate simulation study, under a variety of conditions, the proposed measures are found to identify and estimate second-order interactions.
ContributorsValdivia, Arturo (Author) / Eubank, Randall (Thesis advisor) / Young, Dennis (Committee member) / Reiser, Mark R. (Committee member) / Kao, Ming-Hung (Committee member) / Broatch, Jennifer (Committee member) / Arizona State University (Publisher)
Created2013
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Description
Parallel Monte Carlo applications require the pseudorandom numbers used on each processor to be independent in a probabilistic sense. The TestU01 software package is the standard testing suite for detecting stream dependence and other properties that make certain pseudorandom generators ineffective in parallel (as well as serial) settings. TestU01 employs

Parallel Monte Carlo applications require the pseudorandom numbers used on each processor to be independent in a probabilistic sense. The TestU01 software package is the standard testing suite for detecting stream dependence and other properties that make certain pseudorandom generators ineffective in parallel (as well as serial) settings. TestU01 employs two basic schemes for testing parallel generated streams. The first applies serial tests to the individual streams and then tests the resulting P-values for uniformity. The second turns all the parallel generated streams into one long vector and then applies serial tests to the resulting concatenated stream. Various forms of stream dependence can be missed by each approach because neither one fully addresses the multivariate nature of the accumulated data when generators are run in parallel. This dissertation identifies these potential faults in the parallel testing methodologies of TestU01 and investigates two different methods to better detect inter-stream dependencies: correlation motivated multivariate tests and vector time series based tests. These methods have been implemented in an extension to TestU01 built in C++ and the unique aspects of this extension are discussed. A variety of different generation scenarios are then examined using the TestU01 suite in concert with the extension. This enhanced software package is found to better detect certain forms of inter-stream dependencies than the original TestU01 suites of tests.
ContributorsIsmay, Chester (Author) / Eubank, Randall (Thesis advisor) / Young, Dennis (Committee member) / Kao, Ming-Hung (Committee member) / Lanchier, Nicolas (Committee member) / Reiser, Mark R. (Committee member) / Arizona State University (Publisher)
Created2013
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Description
Accelerated life testing (ALT) is the process of subjecting a product to stress conditions (temperatures, voltage, pressure etc.) in excess of its normal operating levels to accelerate failures. Product failure typically results from multiple stresses acting on it simultaneously. Multi-stress factor ALTs are challenging as they increase the number of

Accelerated life testing (ALT) is the process of subjecting a product to stress conditions (temperatures, voltage, pressure etc.) in excess of its normal operating levels to accelerate failures. Product failure typically results from multiple stresses acting on it simultaneously. Multi-stress factor ALTs are challenging as they increase the number of experiments due to the stress factor-level combinations resulting from the increased number of factors. Chapter 2 provides an approach for designing ALT plans with multiple stresses utilizing Latin hypercube designs that reduces the simulation cost without loss of statistical efficiency. A comparison to full grid and large-sample approximation methods illustrates the approach computational cost gain and flexibility in determining optimal stress settings with less assumptions and more intuitive unit allocations.

Implicit in the design criteria of current ALT designs is the assumption that the form of the acceleration model is correct. This is unrealistic assumption in many real-world problems. Chapter 3 provides an approach for ALT optimum design for model discrimination. We utilize the Hellinger distance measure between predictive distributions. The optimal ALT plan at three stress levels was determined and its performance was compared to good compromise plan, best traditional plan and well-known 4:2:1 compromise test plans. In the case of linear versus quadratic ALT models, the proposed method increased the test plan's ability to distinguish among competing models and provided better guidance as to which model is appropriate for the experiment.

Chapter 4 extends the approach of Chapter 3 to ALT sequential model discrimination. An initial experiment is conducted to provide maximum possible information with respect to model discrimination. The follow-on experiment is planned by leveraging the most current information to allow for Bayesian model comparison through posterior model probability ratios. Results showed that performance of plan is adversely impacted by the amount of censoring in the data, in the case of linear vs. quadratic model form at three levels of constant stress, sequential testing can improve model recovery rate by approximately 8% when data is complete, but no apparent advantage in adopting sequential testing was found in the case of right-censored data when censoring is in excess of a certain amount.
ContributorsNasir, Ehab (Author) / Pan, Rong (Thesis advisor) / Runger, George C. (Committee member) / Gel, Esma (Committee member) / Kao, Ming-Hung (Committee member) / Montgomery, Douglas C. (Committee member) / Arizona State University (Publisher)
Created2014
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Description
Obtaining high-quality experimental designs to optimize statistical efficiency and data quality is quite challenging for functional magnetic resonance imaging (fMRI). The primary fMRI design issue is on the selection of the best sequence of stimuli based on a statistically meaningful optimality criterion. Some previous studies have provided some guidance and

Obtaining high-quality experimental designs to optimize statistical efficiency and data quality is quite challenging for functional magnetic resonance imaging (fMRI). The primary fMRI design issue is on the selection of the best sequence of stimuli based on a statistically meaningful optimality criterion. Some previous studies have provided some guidance and powerful computational tools for obtaining good fMRI designs. However, these results are mainly for basic experimental settings with simple statistical models. In this work, a type of modern fMRI experiments is considered, in which the design matrix of the statistical model depends not only on the selected design, but also on the experimental subject's probabilistic behavior during the experiment. The design matrix is thus uncertain at the design stage, making it diffcult to select good designs. By taking this uncertainty into account, a very efficient approach for obtaining high-quality fMRI designs is developed in this study. The proposed approach is built upon an analytical result, and an efficient computer algorithm. It is shown through case studies that the proposed approach can outperform an existing method in terms of computing time, and the quality of the obtained designs.
ContributorsZhou, Lin (Author) / Kao, Ming-Hung (Thesis advisor) / Reiser, Mark R. (Committee member) / Stufken, John (Committee member) / Welfert, Bruno (Committee member) / Arizona State University (Publisher)
Created2014
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Description
By the von Neumann min-max theorem, a two person zero sum game with finitely many pure strategies has a unique value for each player (summing to zero) and each player has a non-empty set of optimal mixed strategies. If the payoffs are independent, identically distributed (iid) uniform (0,1) random

By the von Neumann min-max theorem, a two person zero sum game with finitely many pure strategies has a unique value for each player (summing to zero) and each player has a non-empty set of optimal mixed strategies. If the payoffs are independent, identically distributed (iid) uniform (0,1) random variables, then with probability one, both players have unique optimal mixed strategies utilizing the same number of pure strategies with positive probability (Jonasson 2004). The pure strategies with positive probability in the unique optimal mixed strategies are called saddle squares. In 1957, Goldman evaluated the probability of a saddle point (a 1 by 1 saddle square), which was rediscovered by many authors including Thorp (1979). Thorp gave two proofs of the probability of a saddle point, one using combinatorics and one using a beta integral. In 1965, Falk and Thrall investigated the integrals required for the probabilities of a 2 by 2 saddle square for 2 × n and m × 2 games with iid uniform (0,1) payoffs, but they were not able to evaluate the integrals. This dissertation generalizes Thorp's beta integral proof of Goldman's probability of a saddle point, establishing an integral formula for the probability that a m × n game with iid uniform (0,1) payoffs has a k by k saddle square (k ≤ m,n). Additionally, the probabilities of a 2 by 2 and a 3 by 3 saddle square for a 3 × 3 game with iid uniform(0,1) payoffs are found. For these, the 14 integrals observed by Falk and Thrall are dissected into 38 disjoint domains, and the integrals are evaluated using the basic properties of the dilogarithm function. The final results for the probabilities of a 2 by 2 and a 3 by 3 saddle square in a 3 × 3 game are linear combinations of 1, π2, and ln(2) with rational coefficients.
ContributorsManley, Michael (Author) / Kadell, Kevin W. J. (Thesis advisor) / Kao, Ming-Hung (Committee member) / Lanchier, Nicolas (Committee member) / Lohr, Sharon (Committee member) / Reiser, Mark R. (Committee member) / Arizona State University (Publisher)
Created2011
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Description
Value-added models (VAMs) are used by many states to assess contributions of individual teachers and schools to students' academic growth. The generalized persistence VAM, one of the most flexible in the literature, estimates the ``value added'' by individual teachers to their students' current and future test scores by employing a

Value-added models (VAMs) are used by many states to assess contributions of individual teachers and schools to students' academic growth. The generalized persistence VAM, one of the most flexible in the literature, estimates the ``value added'' by individual teachers to their students' current and future test scores by employing a mixed model with a longitudinal database of test scores. There is concern, however, that missing values that are common in the longitudinal student scores can bias value-added assessments, especially when the models serve as a basis for personnel decisions -- such as promoting or dismissing teachers -- as they are being used in some states. Certain types of missing data require that the VAM be modeled jointly with the missingness process in order to obtain unbiased parameter estimates. This dissertation studies two problems. First, the flexibility and multimembership random effects structure of the generalized persistence model lead to computational challenges that have limited the model's availability. To this point, no methods have been developed for scalable maximum likelihood estimation of the model. An EM algorithm to compute maximum likelihood estimates efficiently is developed, making use of the sparse structure of the random effects and error covariance matrices. The algorithm is implemented in the package GPvam in R statistical software. Illustrations of the gains in computational efficiency achieved by the estimation procedure are given. Furthermore, to address the presence of potentially nonignorable missing data, a flexible correlated random effects model is developed that extends the generalized persistence model to jointly model the test scores and the missingness process, allowing the process to depend on both students and teachers. The joint model gives the ability to test the sensitivity of the VAM to the presence of nonignorable missing data. Estimation of the model is challenging due to the non-hierarchical dependence structure and the resulting intractable high-dimensional integrals. Maximum likelihood estimation of the model is performed using an EM algorithm with fully exponential Laplace approximations for the E step. The methods are illustrated with data from university calculus classes and with data from standardized test scores from an urban school district.
ContributorsKarl, Andrew (Author) / Lohr, Sharon L (Thesis advisor) / Yang, Yan (Thesis advisor) / Kao, Ming-Hung (Committee member) / Montgomery, Douglas C. (Committee member) / Wilson, Jeffrey R (Committee member) / Arizona State University (Publisher)
Created2012
Description
When analyzing longitudinal data it is essential to account both for the correlation inherent from the repeated measures of the responses as well as the correlation realized on account of the feedback created between the responses at a particular time and the predictors at other times. A generalized method of

When analyzing longitudinal data it is essential to account both for the correlation inherent from the repeated measures of the responses as well as the correlation realized on account of the feedback created between the responses at a particular time and the predictors at other times. A generalized method of moments (GMM) for estimating the coefficients in longitudinal data is presented. The appropriate and valid estimating equations associated with the time-dependent covariates are identified, thus providing substantial gains in efficiency over generalized estimating equations (GEE) with the independent working correlation. Identifying the estimating equations for computation is of utmost importance. This paper provides a technique for identifying the relevant estimating equations through a general method of moments. I develop an approach that makes use of all the valid estimating equations necessary with each time-dependent and time-independent covariate. Moreover, my approach does not assume that feedback is always present over time, or present at the same degree. I fit the GMM correlated logistic regression model in SAS with PROC IML. I examine two datasets for illustrative purposes. I look at rehospitalization in a Medicare database. I revisit data regarding the relationship between the body mass index and future morbidity among children in the Philippines. These datasets allow us to compare my results with some earlier methods of analyses.
ContributorsYin, Jianqiong (Author) / Wilson, Jeffrey Wilson (Thesis advisor) / Reiser, Mark R. (Committee member) / Kao, Ming-Hung (Committee member) / Arizona State University (Publisher)
Created2012
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Description
A least total area of triangle method was proposed by Teissier (1948) for fitting a straight line to data from a pair of variables without treating either variable as the dependent variable while allowing each of the variables to have measurement errors. This method is commonly called Reduced Major Axis

A least total area of triangle method was proposed by Teissier (1948) for fitting a straight line to data from a pair of variables without treating either variable as the dependent variable while allowing each of the variables to have measurement errors. This method is commonly called Reduced Major Axis (RMA) regression and is often used instead of Ordinary Least Squares (OLS) regression. Results for confidence intervals, hypothesis testing and asymptotic distributions of coefficient estimates in the bivariate case are reviewed. A generalization of RMA to more than two variables for fitting a plane to data is obtained by minimizing the sum of a function of the volumes obtained by drawing, from each data point, lines parallel to each coordinate axis to the fitted plane (Draper and Yang 1997; Goodman and Tofallis 2003). Generalized RMA results for the multivariate case obtained by Draper and Yang (1997) are reviewed and some investigations of multivariate RMA are given. A linear model is proposed that does not specify a dependent variable and allows for errors in the measurement of each variable. Coefficients in the model are estimated by minimization of the function of the volumes previously mentioned. Methods for obtaining coefficient estimates are discussed and simulations are used to investigate the distribution of coefficient estimates. The effects of sample size, sampling error and correlation among variables on the estimates are studied. Bootstrap methods are used to obtain confidence intervals for model coefficients. Residual analysis is considered for assessing model assumptions. Outlier and influential case diagnostics are developed and a forward selection method is proposed for subset selection of model variables. A real data example is provided that uses the methods developed. Topics for further research are discussed.
ContributorsLi, Jingjin (Author) / Young, Dennis (Thesis advisor) / Eubank, Randall (Thesis advisor) / Reiser, Mark R. (Committee member) / Kao, Ming-Hung (Committee member) / Yang, Yan (Committee member) / Arizona State University (Publisher)
Created2012
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Description
Functional or dynamic responses are prevalent in experiments in the fields of engineering, medicine, and the sciences, but proposals for optimal designs are still sparse for this type of response. Experiments with dynamic responses result in multiple responses taken over a spectrum variable, so the design matrix for a dynamic

Functional or dynamic responses are prevalent in experiments in the fields of engineering, medicine, and the sciences, but proposals for optimal designs are still sparse for this type of response. Experiments with dynamic responses result in multiple responses taken over a spectrum variable, so the design matrix for a dynamic response have more complicated structures. In the literature, the optimal design problem for some functional responses has been solved using genetic algorithm (GA) and approximate design methods. The goal of this dissertation is to develop fast computer algorithms for calculating exact D-optimal designs.



First, we demonstrated how the traditional exchange methods could be improved to generate a computationally efficient algorithm for finding G-optimal designs. The proposed two-stage algorithm, which is called the cCEA, uses a clustering-based approach to restrict the set of possible candidates for PEA, and then improves the G-efficiency using CEA.



The second major contribution of this dissertation is the development of fast algorithms for constructing D-optimal designs that determine the optimal sequence of stimuli in fMRI studies. The update formula for the determinant of the information matrix was improved by exploiting the sparseness of the information matrix, leading to faster computation times. The proposed algorithm outperforms genetic algorithm with respect to computational efficiency and D-efficiency.



The third contribution is a study of optimal experimental designs for more general functional response models. First, the B-spline system is proposed to be used as the non-parametric smoother of response function and an algorithm is developed to determine D-optimal sampling points of a spectrum variable. Second, we proposed a two-step algorithm for finding the optimal design for both sampling points and experimental settings. In the first step, the matrix of experimental settings is held fixed while the algorithm optimizes the determinant of the information matrix for a mixed effects model to find the optimal sampling times. In the second step, the optimal sampling times obtained from the first step is held fixed while the algorithm iterates on the information matrix to find the optimal experimental settings. The designs constructed by this approach yield superior performance over other designs found in literature.
ContributorsSaleh, Moein (Author) / Pan, Rong (Thesis advisor) / Montgomery, Douglas C. (Committee member) / Runger, George C. (Committee member) / Kao, Ming-Hung (Committee member) / Arizona State University (Publisher)
Created2015