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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’ 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
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 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
Description
It is common in the analysis of data to provide a goodness-of-fit test to assess the performance of a model. In the analysis of contingency tables, goodness-of-fit statistics are frequently employed when modeling social science, educational or psychological data where the interest is often directed at investigating the association among multi-categorical variables. Pearson's chi-squared statistic is well-known in goodness-of-fit testing, but it is sometimes considered to produce an omnibus test as it gives little guidance to the source of poor fit once the null hypothesis is rejected. However, its components can provide powerful directional tests. In this dissertation, orthogonal components are used to develop goodness-of-fit tests for models fit to the counts obtained from the cross-classification of multi-category dependent variables. Ordinal categories are assumed. Orthogonal components defined on marginals are obtained when analyzing multi-dimensional contingency tables through the use of the QR decomposition. A subset of these orthogonal components can be used to construct limited-information tests that allow one to identify the source of lack-of-fit and provide an increase in power compared to Pearson's test. These tests can address the adverse effects presented when data are sparse. The tests rely on the set of first- and second-order marginals jointly, the set of second-order marginals only, and the random forest method, a popular algorithm for modeling large complex data sets. The performance of these tests is compared to the likelihood ratio test as well as to tests based on orthogonal polynomial components. The derived goodness-of-fit tests are evaluated with studies for detecting two- and three-way associations that are not accounted for by a categorical variable factor model with a single latent variable. In addition the tests are used to investigate the case when the model misspecification involves parameter constraints for large and sparse contingency tables. The methodology proposed here is applied to data from the 38th round of the State Survey conducted by the Institute for Public Policy and Michigan State University Social Research (2005) . The results illustrate the use of the proposed techniques in the context of a sparse data set.
ContributorsMilovanovic, Jelena (Author) / Young, Dennis (Thesis advisor) / Reiser, Mark R. (Thesis advisor) / Wilson, Jeffrey (Committee member) / Eubank, Randall (Committee member) / Yang, Yan (Committee member) / Arizona State University (Publisher)
Created2011
Some topics concerning the singular value decomposition and generalized singular value decomposition
Description
This dissertation involves three problems that are all related by the use of the singular value decomposition (SVD) or generalized singular value decomposition (GSVD). The specific problems are (i) derivation of a generalized singular value expansion (GSVE), (ii) analysis of the properties of the chi-squared method for regularization parameter selection in the case of nonnormal data and (iii) formulation of a partial canonical correlation concept for continuous time stochastic processes. The finite dimensional SVD has an infinite dimensional generalization to compact operators. However, the form of the finite dimensional GSVD developed in, e.g., Van Loan does not extend directly to infinite dimensions as a result of a key step in the proof that is specific to the matrix case. Thus, the first problem of interest is to find an infinite dimensional version of the GSVD. One such GSVE for compact operators on separable Hilbert spaces is developed. The second problem concerns regularization parameter estimation. The chi-squared method for nonnormal data is considered. A form of the optimized regularization criterion that pertains to measured data or signals with nonnormal noise is derived. Large sample theory for phi-mixing processes is used to derive a central limit theorem for the chi-squared criterion that holds under certain conditions. Departures from normality are seen to manifest in the need for a possibly different scale factor in normalization rather than what would be used under the assumption of normality. The consequences of our large sample work are illustrated by empirical experiments. For the third problem, a new approach is examined for studying the relationships between a collection of functional random variables. The idea is based on the work of Sunder that provides mappings to connect the elements of algebraic and orthogonal direct sums of subspaces in a Hilbert space. When combined with a key isometry associated with a particular Hilbert space indexed stochastic process, this leads to a useful formulation for situations that involve the study of several second order processes. In particular, using our approach with two processes provides an independent derivation of the functional canonical correlation analysis (CCA) results of Eubank and Hsing. For more than two processes, a rigorous derivation of the functional partial canonical correlation analysis (PCCA) concept that applies to both finite and infinite dimensional settings is obtained.
ContributorsHuang, Qing (Author) / Eubank, Randall (Thesis advisor) / Renaut, Rosemary (Thesis advisor) / Cochran, Douglas (Committee member) / Gelb, Anne (Committee member) / Young, Dennis (Committee member) / Arizona State University (Publisher)
Created2012
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 (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
Description
Public health surveillance is a special case of the general problem where counts (or rates) of events are monitored for changes. Modern data complements event counts with many additional measurements (such as geographic, demographic, and others) that comprise high-dimensional covariates. This leads to an important challenge to detect a change that only occurs within a region, initially unspecified, defined by these covariates. Current methods are typically limited to spatial and/or temporal covariate information and often fail to use all the information available in modern data that can be paramount in unveiling these subtle changes. Additional complexities associated with modern health data that are often not accounted for by traditional methods include: covariates of mixed type, missing values, and high-order interactions among covariates. This work proposes a transform of public health surveillance to supervised learning, so that an appropriate learner can inherently address all the complexities described previously. At the same time, quantitative measures from the learner can be used to define signal criteria to detect changes in rates of events. A Feature Selection (FS) method is used to identify covariates that contribute to a model and to generate a signal. A measure of statistical significance is included to control false alarms. An alternative Percentile method identifies the specific cases that lead to changes using class probability estimates from tree-based ensembles. This second method is intended to be less computationally intensive and significantly simpler to implement. Finally, a third method labeled Rule-Based Feature Value Selection (RBFVS) is proposed for identifying the specific regions in high-dimensional space where the changes are occurring. Results on simulated examples are used to compare the FS method and the Percentile method. Note this work emphasizes the application of the proposed methods on public health surveillance. Nonetheless, these methods can easily be extended to a variety of applications where counts (or rates) of events are monitored for changes. Such problems commonly occur in domains such as manufacturing, economics, environmental systems, engineering, as well as in public health.
ContributorsDavila, Saylisse (Author) / Runger, George C. (Thesis advisor) / Montgomery, Douglas C. (Committee member) / Young, Dennis (Committee member) / Gel, Esma (Committee member) / Arizona State University (Publisher)
Created2010
Description
Analytics has transformed many of the core principles of sports journalism, forcing journalists to work smarter, harder and more creatively than ever before. Yet reporters today are uniquely prepared to navigate the constantly evolving world of journalism, as they now find themselves armed with a plethora of statistics and data that allow storytelling at depths never previously imagined. In interviews with those at the cutting edge of the industry, journalists from around the country imparted insight into how they work to blend new age thinking with time-tested methods of journalism. This thesis expands on those insights and examines the strategies employed to best attack questions of how to best integrate analytics into writing, what role analytics should play in interviews, how to find stories using analytics and others.
The process to answer these questions began by compiling a list of 166 journalists who could provide valuable insight into the current state of sports journalism. Targeted specifically were those journalists who were either currently or had spent extensive time as a beat reporter, as a crucial aspect of the study hinged on the exploration of the role of analytics in day-to-day coverage. Of those 166 journalists, 93 made themselves available through either Twitter direct message or email. Once contacted, 47 of those journalists responded, eventually leading to 27 phone interviews and 7 email interviews.
Each interview began with the journalist establishing a baseline for what they thought the role of analytics should be in the coverage of their respective sports. From there, the conversation often took a linear turn as journalists talked about the experiences in their career that led them to that conclusion, what moments had shifted their overall opinions of analytics, their best approaches for utilizing analytics in both articles and interviews, their favorite and least favorite analytical measures, the gaps that remain in analytics, and the future of the industry as a whole.
Each interview was transcribed, and a number of compelling themes emerged. The many different themes were organized into three different groups, past, present and future, where they were further expanded on to best display the many concepts illustrated in this thesis. Among the themes explored include how journalists use coaches and players to validate statistics, what strategies work best when including analytics in conversations with athletes, how to find story ideas through analytics and the issues plaguing the analytics community. Once themes had been identified, the percentage of journalists who had indicated agreement with the themes were calculated. Thus, themes investigated were represented statistically as well as by a quote from a journalist addressing the idea.
Across 34 interviews with some of the country’s most established and well-respected voices, many of the pressing issues facing analytics in sports journalism today were explored, including the melding of analytical and narrative writing, how best to use analytics in question asking, and the “holy grail” of analytical data. Across interviews, a host of interesting strategies and ideas emerged as journalists examined how the industry reached its current point, what practices are currently most effective, and where the industry is headed. The perspective gained from this thesis gives insight into many of the lesser-discussed elements of journalism, imparting a deeper understanding of the challenges that lay ahead for sports journalism through an examination for how far the industry has come. While analytics and their usage in sports journalism remains a difficult concept to fully encapsulate, this thesis hopefully gives a better look at their complex and ever-evolving relationship.
The process to answer these questions began by compiling a list of 166 journalists who could provide valuable insight into the current state of sports journalism. Targeted specifically were those journalists who were either currently or had spent extensive time as a beat reporter, as a crucial aspect of the study hinged on the exploration of the role of analytics in day-to-day coverage. Of those 166 journalists, 93 made themselves available through either Twitter direct message or email. Once contacted, 47 of those journalists responded, eventually leading to 27 phone interviews and 7 email interviews.
Each interview began with the journalist establishing a baseline for what they thought the role of analytics should be in the coverage of their respective sports. From there, the conversation often took a linear turn as journalists talked about the experiences in their career that led them to that conclusion, what moments had shifted their overall opinions of analytics, their best approaches for utilizing analytics in both articles and interviews, their favorite and least favorite analytical measures, the gaps that remain in analytics, and the future of the industry as a whole.
Each interview was transcribed, and a number of compelling themes emerged. The many different themes were organized into three different groups, past, present and future, where they were further expanded on to best display the many concepts illustrated in this thesis. Among the themes explored include how journalists use coaches and players to validate statistics, what strategies work best when including analytics in conversations with athletes, how to find story ideas through analytics and the issues plaguing the analytics community. Once themes had been identified, the percentage of journalists who had indicated agreement with the themes were calculated. Thus, themes investigated were represented statistically as well as by a quote from a journalist addressing the idea.
Across 34 interviews with some of the country’s most established and well-respected voices, many of the pressing issues facing analytics in sports journalism today were explored, including the melding of analytical and narrative writing, how best to use analytics in question asking, and the “holy grail” of analytical data. Across interviews, a host of interesting strategies and ideas emerged as journalists examined how the industry reached its current point, what practices are currently most effective, and where the industry is headed. The perspective gained from this thesis gives insight into many of the lesser-discussed elements of journalism, imparting a deeper understanding of the challenges that lay ahead for sports journalism through an examination for how far the industry has come. While analytics and their usage in sports journalism remains a difficult concept to fully encapsulate, this thesis hopefully gives a better look at their complex and ever-evolving relationship.
ContributorsRosenfarb, Jacob Alexander (Author) / Boivin, Paola (Thesis director) / Reed, Sada (Committee member) / Walter Cronkite School of Journalism & Mass Comm (Contributor) / Barrett, The Honors College (Contributor)
Created2020-05