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- All Subjects: Statistics
- Creators: Reiser, Mark R.
- Creators: Levy, Roy
Description
This dissertation investigates the classification of systemic lupus erythematosus (SLE) in the presence of non-SLE alternatives, while developing novel curve classification methodologies with wide ranging applications. Functional data representations of plasma thermogram measurements and the corresponding derivative curves provide predictors yet to be investigated for SLE identification. Functional nonparametric classifiers form a methodological basis, which is used herein to develop a) the family of ESFuNC segment-wise curve classification algorithms and b) per-pixel ensembles based on logistic regression and fused-LASSO. The proposed methods achieve test set accuracy rates as high as 94.3%, while returning information about regions of the temperature domain that are critical for population discrimination. The undertaken analyses suggest that derivate-based information contributes significantly in improved classification performance relative to recently published studies on SLE plasma thermograms.
ContributorsBuscaglia, Robert, Ph.D (Author) / Kamarianakis, Yiannis (Thesis advisor) / Armbruster, Dieter (Committee member) / Lanchier, Nicholas (Committee member) / McCulloch, Robert (Committee member) / Reiser, Mark R. (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
Investigation of measurement invariance (MI) commonly assumes correct specification of dimensionality across multiple groups. Although research shows that violation of the dimensionality assumption can cause bias in model parameter estimation for single-group analyses, little research on this issue has been conducted for multiple-group analyses. This study explored the effects of mismatch in dimensionality between data and analysis models with multiple-group analyses at the population and sample levels. Datasets were generated using a bifactor model with different factor structures and were analyzed with bifactor and single-factor models to assess misspecification effects on assessments of MI and latent mean differences. As baseline models, the bifactor models fit data well and had minimal bias in latent mean estimation. However, the low convergence rates of fitting bifactor models to data with complex structures and small sample sizes caused concern. On the other hand, effects of fitting the misspecified single-factor models on the assessments of MI and latent means differed by the bifactor structures underlying data. For data following one general factor and one group factor affecting a small set of indicators, the effects of ignoring the group factor in analysis models on the tests of MI and latent mean differences were mild. In contrast, for data following one general factor and several group factors, oversimplifications of analysis models can lead to inaccurate conclusions regarding MI assessment and latent mean estimation.
ContributorsXu, Yuning (Author) / Green, Samuel (Thesis advisor) / Levy, Roy (Committee member) / Thompson, Marilyn (Committee member) / Arizona State University (Publisher)
Created2018
Description
A simulation study was conducted to explore the robustness of general factor mean difference estimation in bifactor ordered-categorical data. In the No Differential Item Functioning (DIF) conditions, the data generation conditions varied were sample size, the number of categories per item, effect size of the general factor mean difference, and the size of specific factor loadings; in data analysis, misspecification conditions were introduced in which the generated bifactor data were fit using a unidimensional model, and/or ordered-categorical data were treated as continuous data. In the DIF conditions, the data generation conditions varied were sample size, the number of categories per item, effect size of latent mean difference for the general factor, the type of item parameters that had DIF, and the magnitude of DIF; the data analysis conditions varied in whether or not setting equality constraints on the noninvariant item parameters.
Results showed that falsely fitting bifactor data using unidimensional models or failing to account for DIF in item parameters resulted in estimation bias in the general factor mean difference, while treating ordinal data as continuous had little influence on the estimation bias as long as there was no severe model misspecification. The extent of estimation bias produced by misspecification of bifactor datasets with unidimensional models was mainly determined by the degree of unidimensionality (i.e., size of specific factor loadings) and the general factor mean difference size. When the DIF was present, the estimation accuracy of the general factor mean difference was completely robust to ignoring noninvariance in specific factor loadings while it was very sensitive to failing to account for DIF in threshold parameters. With respect to ignoring the DIF in general factor loadings, the estimation bias of the general factor mean difference was substantial when the DIF was -0.15, and it can be negligible for smaller sizes of DIF. Despite the impact of model misspecification on estimation accuracy, the power to detect the general factor mean difference was mainly influenced by the sample size and effect size. Serious Type I error rate inflation only occurred when the DIF was present in threshold parameters.
Results showed that falsely fitting bifactor data using unidimensional models or failing to account for DIF in item parameters resulted in estimation bias in the general factor mean difference, while treating ordinal data as continuous had little influence on the estimation bias as long as there was no severe model misspecification. The extent of estimation bias produced by misspecification of bifactor datasets with unidimensional models was mainly determined by the degree of unidimensionality (i.e., size of specific factor loadings) and the general factor mean difference size. When the DIF was present, the estimation accuracy of the general factor mean difference was completely robust to ignoring noninvariance in specific factor loadings while it was very sensitive to failing to account for DIF in threshold parameters. With respect to ignoring the DIF in general factor loadings, the estimation bias of the general factor mean difference was substantial when the DIF was -0.15, and it can be negligible for smaller sizes of DIF. Despite the impact of model misspecification on estimation accuracy, the power to detect the general factor mean difference was mainly influenced by the sample size and effect size. Serious Type I error rate inflation only occurred when the DIF was present in threshold parameters.
ContributorsLiu, Yixing (Author) / Thompson, Marilyn (Thesis advisor) / Levy, Roy (Committee member) / O’Rourke, Holly (Committee member) / Arizona State University (Publisher)
Created2019
Description
The concept of distribution is one of the core ideas of probability theory and inferential statistics, if not the core idea. Many introductory statistics textbooks pay lip service to stochastic/random processes but how do students think about these processes? This study sought to explore what understandings of stochastic process students develop as they work through materials intended to support them in constructing the long-run behavior meaning for distribution.
I collected data in three phases. First, I conducted a set of task-based clinical interviews that allowed me to build initial models for the students’ meanings for randomness and probability. Second, I worked with Bonnie in an exploratory teaching setting through three sets of activities to see what meanings she would develop for randomness and stochastic process. The final phase consisted of me working with Danielle as she worked through the same activities as Bonnie but this time in teaching experiment setting where I used a series of interventions to test out how Danielle was thinking about stochastic processes.
My analysis shows that students can be aware that the word “random” lives in two worlds, thereby having conflicting meanings. Bonnie’s meaning for randomness evolved over the course of the study from an unproductive meaning centered on the emotions of the characters in the context to a meaning that randomness is the lack of a pattern. Bonnie’s lack of pattern meaning for randomness subsequently underpinned her image of stochastic/processes, leading her to engage in pattern-hunting behavior every time she needed to classify a process as stochastic or not. Danielle’s image of a stochastic process was grounded in whether she saw the repetition as being reproducible (process can be repeated, and outcomes are identical to prior time through the process) or replicable (process can be repeated but the outcomes aren’t in the same order as before). Danielle employed a strategy of carrying out several trials of the process, resetting the applet, and then carrying out the process again, making replicability central to her thinking.
I collected data in three phases. First, I conducted a set of task-based clinical interviews that allowed me to build initial models for the students’ meanings for randomness and probability. Second, I worked with Bonnie in an exploratory teaching setting through three sets of activities to see what meanings she would develop for randomness and stochastic process. The final phase consisted of me working with Danielle as she worked through the same activities as Bonnie but this time in teaching experiment setting where I used a series of interventions to test out how Danielle was thinking about stochastic processes.
My analysis shows that students can be aware that the word “random” lives in two worlds, thereby having conflicting meanings. Bonnie’s meaning for randomness evolved over the course of the study from an unproductive meaning centered on the emotions of the characters in the context to a meaning that randomness is the lack of a pattern. Bonnie’s lack of pattern meaning for randomness subsequently underpinned her image of stochastic/processes, leading her to engage in pattern-hunting behavior every time she needed to classify a process as stochastic or not. Danielle’s image of a stochastic process was grounded in whether she saw the repetition as being reproducible (process can be repeated, and outcomes are identical to prior time through the process) or replicable (process can be repeated but the outcomes aren’t in the same order as before). Danielle employed a strategy of carrying out several trials of the process, resetting the applet, and then carrying out the process again, making replicability central to her thinking.
ContributorsHatfield, Neil (Author) / Thompson, Patrick (Thesis advisor) / Carlson, Marilyn (Committee member) / Middleton, James (Committee member) / Lehrer, Richard (Committee member) / Reiser, Mark R. (Committee member) / Arizona State University (Publisher)
Created2019
Description
Several studies on cheerleading as a sport can be found in the literature; however, there is no research done on the value added to the experience at a university, to an athletic department or at a particular sport. It has been the feeling that collegiate and professional cheerleaders are not given the appropriate recognition nor credit for the amount of work they do. This contribution is sometimes in question as it depends on the school and the sports teams. The benefits are believed to vary based on the university or professional teams. This research investigated how collegiate cheerleaders and dancers add value to the university sport experience. We interviewed key personnel at the university and conference level and polled spectators at sporting events such as basketball and football. We found that the university administration and athletic personnel see the ASU Spirit Squad as value added but spectators had a totally different perspective. The university acknowledges the added value of the Spirit Squad and its necessity. Spectators attend ASU sporting events to support the university and for the entertainment. They enjoy watching the ASU Spirit Squad perform but would continue to attend ASU sporting events even if cheerleaders and dancers were not there.
ContributorsThomas, Jessica Ann (Author) / Wilson, Jeffrey (Thesis director) / Garner, Deana (Committee member) / Department of Supply Chain Management (Contributor) / Department of Marketing (Contributor) / School of Community Resources and Development (Contributor) / Barrett, The Honors College (Contributor)
Created2017-05
Description
Quadratic growth curves of 2nd degree polynomial are widely used in longitudinal studies. For a 2nd degree polynomial, the vertex represents the location of the curve in the XY plane. For a quadratic growth curve, we propose an approximate confidence region as well as the confidence interval for x and y-coordinates of the vertex using two methods, the gradient method and the delta method. Under some models, an indirect test on the location of the curve can be based on the intercept and slope parameters, but in other models, a direct test on the vertex is required. We present a quadratic-form statistic for a test of the null hypothesis that there is no shift in the location of the vertex in a linear mixed model. The statistic has an asymptotic chi-squared distribution. For 2nd degree polynomials of two independent samples, we present an approximate confidence region for the difference of vertices of two quadratic growth curves using the modified gradient method and delta method. Another chi-square test statistic is derived for a direct test on the vertex and is compared to an F test statistic for the indirect test. Power functions are derived for both the indirect F test and the direct chi-square test. We calculate the theoretical power and present a simulation study to investigate the power of the tests. We also present a simulation study to assess the influence of sample size, measurement occasions and nature of the random effects. The test statistics will be applied to the Tell Efficacy longitudinal study, in which sound identification scores and language protocol scores for children are modeled as quadratic growth curves for two independent groups, TELL and control curriculum. The interpretation of shift in the location of the vertices is also presented.
ContributorsYu, Wanchunzi (Author) / Reiser, Mark R. (Thesis advisor) / Barber, Jarrett (Committee member) / Kao, Ming-Hung (Committee member) / St Louis, Robert D (Committee member) / Wilson, Jeffrey (Committee member) / Arizona State University (Publisher)
Created2015
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
A simulation study was conducted to explore the influence of partial loading invariance and partial intercept invariance on the latent mean comparison of the second-order factor within a higher-order confirmatory factor analysis (CFA) model. Noninvariant loadings or intercepts were generated to be at one of the two levels or both levels for a second-order CFA model. The numbers and directions of differences in noninvariant loadings or intercepts were also manipulated, along with total sample size and effect size of the second-order factor mean difference. Data were analyzed using correct and incorrect specifications of noninvariant loadings and intercepts. Results summarized across the 5,000 replications in each condition included Type I error rates and powers for the chi-square difference test and the Wald test of the second-order factor mean difference, estimation bias and efficiency for this latent mean difference, and means of the standardized root mean square residual (SRMR) and the root mean square error of approximation (RMSEA).
When the model was correctly specified, no obvious estimation bias was observed; when the model was misspecified by constraining noninvariant loadings or intercepts to be equal, the latent mean difference was overestimated if the direction of the difference in loadings or intercepts of was consistent with the direction of the latent mean difference, and vice versa. Increasing the number of noninvariant loadings or intercepts resulted in larger estimation bias if these noninvariant loadings or intercepts were constrained to be equal. Power to detect the latent mean difference was influenced by estimation bias and the estimated variance of the difference in the second-order factor mean, in addition to sample size and effect size. Constraining more parameters to be equal between groups—even when unequal in the population—led to a decrease in the variance of the estimated latent mean difference, which increased power somewhat. Finally, RMSEA was very sensitive for detecting misspecification due to improper equality constraints in all conditions in the current scenario, including the nonzero latent mean difference, but SRMR did not increase as expected when noninvariant parameters were constrained.
When the model was correctly specified, no obvious estimation bias was observed; when the model was misspecified by constraining noninvariant loadings or intercepts to be equal, the latent mean difference was overestimated if the direction of the difference in loadings or intercepts of was consistent with the direction of the latent mean difference, and vice versa. Increasing the number of noninvariant loadings or intercepts resulted in larger estimation bias if these noninvariant loadings or intercepts were constrained to be equal. Power to detect the latent mean difference was influenced by estimation bias and the estimated variance of the difference in the second-order factor mean, in addition to sample size and effect size. Constraining more parameters to be equal between groups—even when unequal in the population—led to a decrease in the variance of the estimated latent mean difference, which increased power somewhat. Finally, RMSEA was very sensitive for detecting misspecification due to improper equality constraints in all conditions in the current scenario, including the nonzero latent mean difference, but SRMR did not increase as expected when noninvariant parameters were constrained.
ContributorsLiu, Yixing (Author) / Thompson, Marilyn (Thesis advisor) / Green, Samuel (Committee member) / Levy, Roy (Committee member) / Arizona State University (Publisher)
Created2016
Description
Although models for describing longitudinal data have become increasingly sophisticated, the criticism of even foundational growth curve models remains challenging. The challenge arises from the need to disentangle data-model misfit at multiple and interrelated levels of analysis. Using posterior predictive model checking (PPMC)—a popular Bayesian framework for model criticism—the performance of several discrepancy functions was investigated in a Monte Carlo simulation study. The discrepancy functions of interest included two types of conditional concordance correlation (CCC) functions, two types of R2 functions, two types of standardized generalized dimensionality discrepancy (SGDDM) functions, the likelihood ratio (LR), and the likelihood ratio difference test (LRT). Key outcomes included effect sizes of the design factors on the realized values of discrepancy functions, distributions of posterior predictive p-values (PPP-values), and the proportion of extreme PPP-values.
In terms of the realized values, the behavior of the CCC and R2 functions were generally consistent with prior research. However, as diagnostics, these functions were extremely conservative even when some aspect of the data was unaccounted for. In contrast, the conditional SGDDM (SGDDMC), LR, and LRT were generally sensitive to the underspecifications investigated in this work on all outcomes considered. Although the proportions of extreme PPP-values for these functions tended to increase in null situations for non-normal data, this behavior may have reflected the true misfit that resulted from the specification of normal prior distributions. Importantly, the LR and the SGDDMC to a greater extent exhibited some potential for untangling the sources of data-model misfit. Owing to connections of growth curve models to the more fundamental frameworks of multilevel modeling, structural equation models with a mean structure, and Bayesian hierarchical models, the results of the current work may have broader implications that warrant further research.
In terms of the realized values, the behavior of the CCC and R2 functions were generally consistent with prior research. However, as diagnostics, these functions were extremely conservative even when some aspect of the data was unaccounted for. In contrast, the conditional SGDDM (SGDDMC), LR, and LRT were generally sensitive to the underspecifications investigated in this work on all outcomes considered. Although the proportions of extreme PPP-values for these functions tended to increase in null situations for non-normal data, this behavior may have reflected the true misfit that resulted from the specification of normal prior distributions. Importantly, the LR and the SGDDMC to a greater extent exhibited some potential for untangling the sources of data-model misfit. Owing to connections of growth curve models to the more fundamental frameworks of multilevel modeling, structural equation models with a mean structure, and Bayesian hierarchical models, the results of the current work may have broader implications that warrant further research.
ContributorsFay, Derek (Author) / Levy, Roy (Thesis advisor) / Thompson, Marilyn (Committee member) / Enders, Craig (Committee member) / Arizona State University (Publisher)
Created2015