Matching Items (25)
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- All Subjects: Statistics
- All Subjects: spatial statistics
- Creators: Stufken, John
- Creators: Fotheringham, A. Stewart
- Creators: Zhou, Shuang
- Member of: ASU Electronic Theses and Dissertations
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 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
Description
Gerrymandering is a central problem for many representative democracies. Formally, gerrymandering is the manipulation of spatial boundaries to provide political advantage to a particular group (Warf, 2006). The term often refers to political district design, where the boundaries of political districts are “unnaturally” manipulated by redistricting officials to generate durable advantages for one group or party. Since free and fair elections are possibly the critical part of representative democracy, it is important for this cresting tide to have scientifically validated tools. This dissertation supports a current wave of reform by developing a general inferential technique to “localize” inferential bias measures, generating a new type of district-level score. The new method relies on the statistical intuition behind jackknife methods to construct relative local indicators. I find that existing statewide indicators of partisan bias can be localized using this technique, providing an estimate of how strongly a district impacts statewide partisan bias over an entire decade. When compared to measures of shape compactness (a common gerrymandering detection statistic), I find that weirdly-shaped districts have no consistent relationship with impact in many states during the 2000 and 2010 redistricting plan. To ensure that this work is valid, I examine existing seats-votes modeling strategies and develop a novel method for constructing seats-votes curves. I find that, while the empirical structure of electoral swing shows significant spatial dependence (even in the face of spatial heterogeneity), existing seats-votes specifications are more robust than anticipated to spatial dependence. Centrally, this dissertation contributes to the much larger social aim to resist electoral manipulation: that individuals & organizations suffer no undue burden on political access from partisan gerrymandering.
ContributorsWolf, Levi (Author) / Rey, Sergio J (Thesis advisor) / Anselin, Luc (Committee member) / Fotheringham, A. Stewart (Committee member) / Tam Cho, Wendy K (Committee member) / Arizona State University (Publisher)
Created2017
Description
Generalized Linear Models (GLMs) are widely used for modeling responses with non-normal error distributions. When the values of the covariates in such models are controllable, finding an optimal (or at least efficient) design could greatly facilitate the work of collecting and analyzing data. In fact, many theoretical results are obtained on a case-by-case basis, while in other situations, researchers also rely heavily on computational tools for design selection.
Three topics are investigated in this dissertation with each one focusing on one type of GLMs. Topic I considers GLMs with factorial effects and one continuous covariate. Factors can have interactions among each other and there is no restriction on the possible values of the continuous covariate. The locally D-optimal design structures for such models are identified and results for obtaining smaller optimal designs using orthogonal arrays (OAs) are presented. Topic II considers GLMs with multiple covariates under the assumptions that all but one covariate are bounded within specified intervals and interaction effects among those bounded covariates may also exist. An explicit formula for D-optimal designs is derived and OA-based smaller D-optimal designs for models with one or two two-factor interactions are also constructed. Topic III considers multiple-covariate logistic models. All covariates are nonnegative and there is no interaction among them. Two types of D-optimal design structures are identified and their global D-optimality is proved using the celebrated equivalence theorem.
Three topics are investigated in this dissertation with each one focusing on one type of GLMs. Topic I considers GLMs with factorial effects and one continuous covariate. Factors can have interactions among each other and there is no restriction on the possible values of the continuous covariate. The locally D-optimal design structures for such models are identified and results for obtaining smaller optimal designs using orthogonal arrays (OAs) are presented. Topic II considers GLMs with multiple covariates under the assumptions that all but one covariate are bounded within specified intervals and interaction effects among those bounded covariates may also exist. An explicit formula for D-optimal designs is derived and OA-based smaller D-optimal designs for models with one or two two-factor interactions are also constructed. Topic III considers multiple-covariate logistic models. All covariates are nonnegative and there is no interaction among them. Two types of D-optimal design structures are identified and their global D-optimality is proved using the celebrated equivalence theorem.
ContributorsWang, Zhongsheng (Author) / Stufken, John (Thesis advisor) / Kamarianakis, Ioannis (Committee member) / Kao, Ming-Hung (Committee member) / Reiser, Mark R. (Committee member) / Zheng, Yi (Committee member) / Arizona State University (Publisher)
Created2018
Description
In the presence of correlation, generalized linear models cannot be employed to obtain regression parameter estimates. To appropriately address the extravariation due to correlation, methods to estimate and model the additional variation are investigated. A general form of the mean-variance relationship is proposed which incorporates the canonical parameter. The two variance parameters are estimated using generalized method of moments, negating the need for a distributional assumption. The mean-variance relation estimates are applied to clustered data and implemented in an adjusted generalized quasi-likelihood approach through an adjustment to the covariance matrix. In the presence of significant correlation in hierarchical structured data, the adjusted generalized quasi-likelihood model shows improved performance for random effect estimates. In addition, submodels to address deviation in skewness and kurtosis are provided to jointly model the mean, variance, skewness, and kurtosis. The additional models identify covariates influencing the third and fourth moments. A cutoff to trim the data is provided which improves parameter estimation and model fit. For each topic, findings are demonstrated through comprehensive simulation studies and numerical examples. Examples evaluated include data on children’s morbidity in the Philippines, adolescent health from the National Longitudinal Study of Adolescent to Adult Health, as well as proteomic assays for breast cancer screening.
ContributorsIrimata, Katherine E (Author) / Wilson, Jeffrey R (Thesis advisor) / Kamarianakis, Ioannis (Committee member) / Kao, Ming-Hung (Committee member) / Reiser, Mark R. (Committee member) / Stufken, John (Committee member) / Arizona State University (Publisher)
Created2018
Description
In the study of regional economic growth and convergence, the distribution dynamics approach which interrogates the evolution of the cross-sectional distribution as a whole and is concerned with both the external and internal dynamics of the distribution has received wide usage. However, many methodological issues remain to be resolved before valid inferences and conclusions can be drawn from empirical research. Among them, spatial effects including spatial heterogeneity and spatial dependence invalidate the assumption of independent and identical distributions underlying the conventional maximum likelihood techniques while the availability of small samples in regional settings questions the usage of the asymptotic properties. This dissertation is comprised of three papers targeted at addressing these two issues. The first paper investigates whether the conventional regional income mobility estimators are still suitable in the presence of spatial dependence and/or a small sample. It is approached through a series of Monte Carlo experiments which require the proposal of a novel data generating process (DGP) capable of generating spatially dependent time series. The second paper moves to the statistical tests for detecting specific forms of spatial (spatiotemporal) effects in the discrete Markov chain model, investigating their robustness to the alternative spatial effect, sensitivity to discretization granularity, and properties in small sample settings. The third paper proposes discrete kernel estimators with cross-validated bandwidths as an alternative to maximum likelihood estimators in small sample settings. It is demonstrated that the performance of discrete kernel estimators offers improvement when the sample size is small. Taken together, the three papers constitute an endeavor to relax the restrictive assumptions of spatial independence and spatial homogeneity, as well as demonstrating the difference between the small sample and asymptotic properties for conventionally adopted maximum likelihood estimators towards a more valid inferential framework for the distribution dynamics approach to the study of regional economic growth and convergence.
ContributorsKang, Wei (Author) / Rey, Sergio (Thesis advisor) / Fotheringham, A. Stewart (Committee member) / Ye, Xinyue (Committee member) / Arizona State University (Publisher)
Created2018
Description
Large-scale cultivation of perennial bioenergy crops (e.g., miscanthus and switch-
grass) offers unique opportunities to mitigate climate change through avoided fossil fuel use and associated greenhouse gas reduction. Although conversion of existing agriculturally intensive lands (e.g., maize and soy) to perennial bioenergy cropping systems has been shown to reduce near-surface temperatures, unintended consequences on natural water resources via depletion of soil moisture may offset these benefits. In the effort of the cross-fertilization across the disciplines of physics-based modeling and spatio-temporal statistics, three topics are investigated in this dissertation aiming to provide a novel quantification and robust justifications of the hydroclimate impacts associated with bioenergy crop expansion. Topic 1 quantifies the hydroclimatic impacts associated with perennial bioenergy crop expansion over the contiguous United States using the Weather Research and Forecasting Model (WRF) dynamically coupled to a land surface model (LSM). A suite of continuous (2000–09) medium-range resolution (20-km grid spacing) ensemble-based simulations is conducted. Hovmöller and Taylor diagrams are utilized to evaluate simulated temperature and precipitation. In addition, Mann-Kendall modified trend tests and Sieve-bootstrap trend tests are performed to evaluate the statistical significance of trends in soil moisture differences. Finally, this research reveals potential hot spots of suitable deployment and regions to avoid. Topic 2 presents spatio-temporal Bayesian models which quantify the robustness of control simulation bias, as well as biofuel impacts, using three spatio-temporal correlation structures. A hierarchical model with spatially varying intercepts and slopes display satisfactory performance in capturing spatio-temporal associations. Simulated temperature impacts due to perennial bioenergy crop expansion are robust to physics parameterization schemes. Topic 3 further focuses on the accuracy and efficiency of spatial-temporal statistical modeling for large datasets. An ensemble of spatio-temporal eigenvector filtering algorithms (hereafter: STEF) is proposed to account for the spatio-temporal autocorrelation structure of the data while taking into account spatial confounding. Monte Carlo experiments are conducted. This method is then used to quantify the robustness of simulated hydroclimatic impacts associated with bioenergy crops to alternative physics parameterizations. Results are evaluated against those obtained from three alternative Bayesian spatio-temporal specifications.
grass) offers unique opportunities to mitigate climate change through avoided fossil fuel use and associated greenhouse gas reduction. Although conversion of existing agriculturally intensive lands (e.g., maize and soy) to perennial bioenergy cropping systems has been shown to reduce near-surface temperatures, unintended consequences on natural water resources via depletion of soil moisture may offset these benefits. In the effort of the cross-fertilization across the disciplines of physics-based modeling and spatio-temporal statistics, three topics are investigated in this dissertation aiming to provide a novel quantification and robust justifications of the hydroclimate impacts associated with bioenergy crop expansion. Topic 1 quantifies the hydroclimatic impacts associated with perennial bioenergy crop expansion over the contiguous United States using the Weather Research and Forecasting Model (WRF) dynamically coupled to a land surface model (LSM). A suite of continuous (2000–09) medium-range resolution (20-km grid spacing) ensemble-based simulations is conducted. Hovmöller and Taylor diagrams are utilized to evaluate simulated temperature and precipitation. In addition, Mann-Kendall modified trend tests and Sieve-bootstrap trend tests are performed to evaluate the statistical significance of trends in soil moisture differences. Finally, this research reveals potential hot spots of suitable deployment and regions to avoid. Topic 2 presents spatio-temporal Bayesian models which quantify the robustness of control simulation bias, as well as biofuel impacts, using three spatio-temporal correlation structures. A hierarchical model with spatially varying intercepts and slopes display satisfactory performance in capturing spatio-temporal associations. Simulated temperature impacts due to perennial bioenergy crop expansion are robust to physics parameterization schemes. Topic 3 further focuses on the accuracy and efficiency of spatial-temporal statistical modeling for large datasets. An ensemble of spatio-temporal eigenvector filtering algorithms (hereafter: STEF) is proposed to account for the spatio-temporal autocorrelation structure of the data while taking into account spatial confounding. Monte Carlo experiments are conducted. This method is then used to quantify the robustness of simulated hydroclimatic impacts associated with bioenergy crops to alternative physics parameterizations. Results are evaluated against those obtained from three alternative Bayesian spatio-temporal specifications.
ContributorsWang, Meng, Ph.D (Author) / Kamarianakis, Yiannis (Thesis advisor) / Georgescu, Matei (Thesis advisor) / Fotheringham, A. Stewart (Committee member) / Moustaoui, Mohamed (Committee member) / Reiser, Mark R. (Committee member) / Arizona State University (Publisher)
Created2018
Description
Threshold regression is used to model regime switching dynamics where the effects of the explanatory variables in predicting the response variable depend on whether a certain threshold has been crossed. When regime-switching dynamics are present, new estimation problems arise related to estimating the value of the threshold. Conventional methods utilize an iterative search procedure, seeking to minimize the sum of squares criterion. However, when unnecessary variables are included in the model or certain variables drop out of the model depending on the regime, this method may have high variability. This paper proposes Lasso-type methods as an alternative to ordinary least squares. By incorporating an L_{1} penalty term, Lasso methods perform variable selection, thus potentially reducing some of the variance in estimating the threshold parameter. This paper discusses the results of a study in which two different underlying model structures were simulated. The first is a regression model with correlated predictors, whereas the second is a self-exciting threshold autoregressive model. Finally the proposed Lasso-type methods are compared to conventional methods in an application to urban traffic data.
ContributorsVan Schaijik, Maria (Author) / Kamarianakis, Yiannis (Committee member) / Reiser, Mark R. (Committee member) / Stufken, John (Committee member) / Arizona State University (Publisher)
Created2015
Description
This study concerns optimal designs for experiments where responses consist of both binary and continuous variables. Many experiments in engineering, medical studies, and other fields have such mixed responses. Although in recent decades several statistical methods have been developed for jointly modeling both types of response variables, an effective way to design such experiments remains unclear. To address this void, some useful results are developed to guide the selection of optimal experimental designs in such studies. The results are mainly built upon a powerful tool called the complete class approach and a nonlinear optimization algorithm. The complete class approach was originally developed for a univariate response, but it is extended to the case of bivariate responses of mixed variable types. Consequently, the number of candidate designs are significantly reduced. An optimization algorithm is then applied to efficiently search the small class of candidate designs for the D- and A-optimal designs. Furthermore, the optimality of the obtained designs is verified by the general equivalence theorem. In the first part of the study, the focus is on a simple, first-order model. The study is expanded to a model with a quadratic polynomial predictor. The obtained designs can help to render a precise statistical inference in practice or serve as a benchmark for evaluating the quality of other designs.
ContributorsKim, Soohyun (Author) / Kao, Ming-Hung (Thesis advisor) / Dueck, Amylou (Committee member) / Pan, Rong (Committee member) / Reiser, Mark R. (Committee member) / Stufken, John (Committee member) / Arizona State University (Publisher)
Created2017
Description
The Pearson and likelihood ratio statistics are commonly used to test goodness-of-fit for models applied to data from a multinomial distribution. When data are from a table formed by cross-classification of a large number of variables, the common statistics may have low power and inaccurate Type I error level due to sparseness in the cells of the table. The GFfit statistic can be used to examine model fit in subtables. It is proposed to assess model fit by using a new version of GFfit statistic based on orthogonal components of Pearson chi-square as a diagnostic to examine the fit on two-way subtables. However, due to variables with a large number of categories and small sample size, even the GFfit statistic may have low power and inaccurate Type I error level due to sparseness in the two-way subtable. In this dissertation, the theoretical power and empirical power of the GFfit statistic are studied. A method based on subsets of orthogonal components for the GFfit statistic on the subtables is developed to improve the performance of the GFfit statistic. Simulation results for power and type I error rate for several different cases along with comparisons to other diagnostics are presented.
ContributorsZhu, Junfei (Author) / Reiser, Mark R. (Thesis advisor) / Stufken, John (Committee member) / Zheng, Yi (Committee member) / St Louis, Robert (Committee member) / Kao, Ming-Hung (Committee member) / Arizona State University (Publisher)
Created2017
Description
This article proposes a new information-based subdata selection (IBOSS) algorithm, Squared Scaled Distance Algorithm (SSDA). It is based on the invariance of the determinant of the information matrix under orthogonal transformations, especially rotations. Extensive simulation results show that the new IBOSS algorithm retains nice asymptotic properties of IBOSS and gives a larger determinant of the subdata information matrix. It has the same order of time complexity as the D-optimal IBOSS algorithm. However, it exploits the advantages of vectorized calculation avoiding for loops and is approximately 6 times as fast as the D-optimal IBOSS algorithm in R. The robustness of SSDA is studied from three aspects: nonorthogonality, including interaction terms and variable misspecification. A new accurate variable selection algorithm is proposed to help the implementation of IBOSS algorithms when a large number of variables are present with sparse important variables among them. Aggregating random subsample results, this variable selection algorithm is much more accurate than the LASSO method using full data. Since the time complexity is associated with the number of variables only, it is also very computationally efficient if the number of variables is fixed as n increases and not massively large. More importantly, using subsamples it solves the problem that full data cannot be stored in the memory when a data set is too large.
ContributorsZheng, Yi (Author) / Stufken, John (Thesis advisor) / Reiser, Mark R. (Committee member) / McCulloch, Robert (Committee member) / Arizona State University (Publisher)
Created2017