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- All Subjects: Statistics
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- Creators: West, Stephen G.
- Creators: Fotheringham, A. Stewart
- Creators: Zhou, Shuang
- Member of: ASU Electronic Theses and Dissertations
Description
Missing data are common in psychology research and can lead to bias and reduced power if not properly handled. Multiple imputation is a state-of-the-art missing data method recommended by methodologists. Multiple imputation methods can generally be divided into two broad categories: joint model (JM) imputation and fully conditional specification (FCS) imputation. JM draws missing values simultaneously for all incomplete variables using a multivariate distribution (e.g., multivariate normal). FCS, on the other hand, imputes variables one at a time, drawing missing values from a series of univariate distributions. In the single-level context, these two approaches have been shown to be equivalent with multivariate normal data. However, less is known about the similarities and differences of these two approaches with multilevel data, and the methodological literature provides no insight into the situations under which the approaches would produce identical results. This document examined five multilevel multiple imputation approaches (three JM methods and two FCS methods) that have been proposed in the literature. An analytic section shows that only two of the methods (one JM method and one FCS method) used imputation models equivalent to a two-level joint population model that contained random intercepts and different associations across levels. The other three methods employed imputation models that differed from the population model primarily in their ability to preserve distinct level-1 and level-2 covariances. I verified the analytic work with computer simulations, and the simulation results also showed that imputation models that failed to preserve level-specific covariances produced biased estimates. The studies also highlighted conditions that exacerbated the amount of bias produced (e.g., bias was greater for conditions with small cluster sizes). The analytic work and simulations lead to a number of practical recommendations for researchers.
ContributorsMistler, Stephen (Author) / Enders, Craig K. (Thesis advisor) / Aiken, Leona (Committee member) / Levy, Roy (Committee member) / West, Stephen G. (Committee member) / Arizona State University (Publisher)
Created2015
Description
Coarsely grouped counts or frequencies are commonly used in the behavioral sciences. Grouped count and grouped frequency (GCGF) that are used as outcome variables often violate the assumptions of linear regression as well as models designed for categorical outcomes; there is no analytic model that is designed specifically to accommodate GCGF outcomes. The purpose of this dissertation was to compare the statistical performance of four regression models (linear regression, Poisson regression, ordinal logistic regression, and beta regression) that can be used when the outcome is a GCGF variable. A simulation study was used to determine the power, type I error, and confidence interval (CI) coverage rates for these models under different conditions. Mean structure, variance structure, effect size, continuous or binary predictor, and sample size were included in the factorial design. Mean structures reflected either a linear relationship or an exponential relationship between the predictor and the outcome. Variance structures reflected homoscedastic (as in linear regression), heteroscedastic (monotonically increasing) or heteroscedastic (increasing then decreasing) variance. Small to medium, large, and very large effect sizes were examined. Sample sizes were 100, 200, 500, and 1000. Results of the simulation study showed that ordinal logistic regression produced type I error, statistical power, and CI coverage rates that were consistently within acceptable limits. Linear regression produced type I error and statistical power that were within acceptable limits, but CI coverage was too low for several conditions important to the analysis of counts and frequencies. Poisson regression and beta regression displayed inflated type I error, low statistical power, and low CI coverage rates for nearly all conditions. All models produced unbiased estimates of the regression coefficient. Based on the statistical performance of the four models, ordinal logistic regression seems to be the preferred method for analyzing GCGF outcomes. Linear regression also performed well, but CI coverage was too low for conditions with an exponential mean structure and/or heteroscedastic variance. Some aspects of model prediction, such as model fit, were not assessed here; more research is necessary to determine which statistical model best captures the unique properties of GCGF outcomes.
ContributorsCoxe, Stefany (Author) / Aiken, Leona S. (Thesis advisor) / West, Stephen G. (Thesis advisor) / Mackinnon, David P (Committee member) / Reiser, Mark R. (Committee member) / Arizona State University (Publisher)
Created2012
Description
Researchers are often interested in estimating interactions in multilevel models, but many researchers assume that the same procedures and interpretations for interactions in single-level models apply to multilevel models. However, estimating interactions in multilevel models is much more complex than in single-level models. Because uncentered (RAS) or grand mean centered (CGM) level-1 predictors in two-level models contain two sources of variability (i.e., within-cluster variability and between-cluster variability), interactions involving RAS or CGM level-1 predictors also contain more than one source of variability. In this Master’s thesis, I use simulations to demonstrate that ignoring the four sources of variability in a total level-1 interaction effect can lead to erroneous conclusions. I explain how to parse a total level-1 interaction effect into four specific interaction effects, derive equivalencies between CGM and centering within context (CWC) for this model, and describe how the interpretations of the fixed effects change under CGM and CWC. Finally, I provide an empirical example using diary data collected from working adults with chronic pain.
ContributorsMazza, Gina L (Author) / Enders, Craig K. (Thesis advisor) / Aiken, Leona S. (Thesis advisor) / West, Stephen G. (Committee member) / Arizona State University (Publisher)
Created2015
Description
Understanding how adherence affects outcomes is crucial when developing and assigning interventions. However, interventions are often evaluated by conducting randomized experiments and estimating intent-to-treat effects, which ignore actual treatment received. Dose-response effects can supplement intent-to-treat effects when participants are offered the full dose but many only receive a partial dose due to nonadherence. Using these data, we can estimate the magnitude of the treatment effect at different levels of adherence, which serve as a proxy for different levels of treatment. In this dissertation, I conducted Monte Carlo simulations to evaluate when linear dose-response effects can be accurately and precisely estimated in randomized experiments comparing a no-treatment control condition to a treatment condition with partial adherence. Specifically, I evaluated the performance of confounder adjustment and instrumental variable methods when their assumptions were met (Study 1) and when their assumptions were violated (Study 2). In Study 1, the confounder adjustment and instrumental variable methods provided unbiased estimates of the dose-response effect across sample sizes (200, 500, 2,000) and adherence distributions (uniform, right skewed, left skewed). The adherence distribution affected power for the instrumental variable method. In Study 2, the confounder adjustment method provided unbiased or minimally biased estimates of the dose-response effect under no or weak (but not moderate or strong) unobserved confounding. The instrumental variable method provided extremely biased estimates of the dose-response effect under violations of the exclusion restriction (no direct effect of treatment assignment on the outcome), though less severe violations of the exclusion restriction should be investigated.
ContributorsMazza, Gina L (Author) / Grimm, Kevin J. (Thesis advisor) / West, Stephen G. (Thesis advisor) / Mackinnon, David P (Committee member) / Tein, Jenn-Yun (Committee member) / Arizona State University (Publisher)
Created2018
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
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
Mediation analysis is used to investigate how an independent variable, X, is related to an outcome variable, Y, through a mediator variable, M (MacKinnon, 2008). If X represents a randomized intervention it is difficult to make a cause and effect inference regarding indirect effects without making no unmeasured confounding assumptions using the potential outcomes framework (Holland, 1988; MacKinnon, 2008; Robins & Greenland, 1992; VanderWeele, 2015), using longitudinal data to determine the temporal order of M and Y (MacKinnon, 2008), or both. The goals of this dissertation were to (1) define all indirect and direct effects in a three-wave longitudinal mediation model using the causal mediation formula (Pearl, 2012), (2) analytically compare traditional estimators (ANCOVA, difference score, and residualized change score) to the potential outcomes-defined indirect effects, and (3) use a Monte Carlo simulation to compare the performance of regression and potential outcomes-based methods for estimating longitudinal indirect effects and apply the methods to an empirical dataset. The results of the causal mediation formula revealed the potential outcomes definitions of indirect effects are equivalent to the product of coefficient estimators in a three-wave longitudinal mediation model with linear and additive relations. It was demonstrated with analytical comparisons that the ANCOVA, difference score, and residualized change score models’ estimates of two time-specific indirect effects differ as a function of the respective mediator-outcome relations at each time point. The traditional model that performed the best in terms of the evaluation criteria in the Monte Carlo study was the ANCOVA model and the potential outcomes model that performed the best in terms of the evaluation criteria was sequential G-estimation. Implications and future directions are discussed.
ContributorsValente, Matthew J (Author) / Mackinnon, David P (Thesis advisor) / West, Stephen G. (Committee member) / Grimm, Keving (Committee member) / Chassin, Laurie (Committee member) / Arizona State University (Publisher)
Created2018
Description
The comparison of between- versus within-person relations addresses a central issue in psychological research regarding whether group-level relations among variables generalize to individual group members. Between- and within-person effects may differ in magnitude as well as direction, and contextual multilevel models can accommodate this difference. Contextual multilevel models have been explicated mostly for cross-sectional data, but they can also be applied to longitudinal data where level-1 effects represent within-person relations and level-2 effects represent between-person relations. With longitudinal data, estimating the contextual effect allows direct evaluation of whether between-person and within-person effects differ. Furthermore, these models, unlike single-level models, permit individual differences by allowing within-person slopes to vary across individuals. This study examined the statistical performance of the contextual model with a random slope for longitudinal within-person fluctuation data.
A Monte Carlo simulation was used to generate data based on the contextual multilevel model, where sample size, effect size, and intraclass correlation (ICC) of the predictor variable were varied. The effects of simulation factors on parameter bias, parameter variability, and standard error accuracy were assessed. Parameter estimates were in general unbiased. Power to detect the slope variance and contextual effect was over 80% for most conditions, except some of the smaller sample size conditions. Type I error rates for the contextual effect were also high for some of the smaller sample size conditions. Conclusions and future directions are discussed.
A Monte Carlo simulation was used to generate data based on the contextual multilevel model, where sample size, effect size, and intraclass correlation (ICC) of the predictor variable were varied. The effects of simulation factors on parameter bias, parameter variability, and standard error accuracy were assessed. Parameter estimates were in general unbiased. Power to detect the slope variance and contextual effect was over 80% for most conditions, except some of the smaller sample size conditions. Type I error rates for the contextual effect were also high for some of the smaller sample size conditions. Conclusions and future directions are discussed.
ContributorsWurpts, Ingrid Carlson (Author) / Mackinnon, David P (Thesis advisor) / West, Stephen G. (Committee member) / Grimm, Kevin J. (Committee member) / Suk, Hye Won (Committee member) / Arizona State University (Publisher)
Created2016
Description
Time-to-event analysis or equivalently, survival analysis deals with two variables simultaneously: when (time information) an event occurs and whether an event occurrence is observed or not during the observation period (censoring information). In behavioral and social sciences, the event of interest usually does not lead to a terminal state such as death. Other outcomes after the event can be collected and thus, the survival variable can be considered as a predictor as well as an outcome in a study. One example of a case where the survival variable serves as a predictor as well as an outcome is a survival-mediator model. In a single survival-mediator model an independent variable, X predicts a survival variable, M which in turn, predicts a continuous outcome, Y. The survival-mediator model consists of two regression equations: X predicting M (M-regression), and M and X simultaneously predicting Y (Y-regression). To estimate the regression coefficients of the survival-mediator model, Cox regression is used for the M-regression. Ordinary least squares regression is used for the Y-regression using complete case analysis assuming censored data in M are missing completely at random so that the Y-regression is unbiased. In this dissertation research, different measures for the indirect effect were proposed and a simulation study was conducted to compare performance of different indirect effect test methods. Bias-corrected bootstrapping produced high Type I error rates as well as low parameter coverage rates in some conditions. In contrast, the Sobel test produced low Type I error rates as well as high parameter coverage rates in some conditions. The bootstrap of the natural indirect effect produced low Type I error and low statistical power when the censoring proportion was non-zero. Percentile bootstrapping, distribution of the product and the joint-significance test showed best performance. Statistical analysis of the survival-mediator model is discussed. Two indirect effect measures, the ab-product and the natural indirect effect are compared and discussed. Limitations and future directions of the simulation study are discussed. Last, interpretation of the survival-mediator model for a made-up empirical data set is provided to clarify the meaning of the quantities in the survival-mediator model.
ContributorsKim, Han Joe (Author) / Mackinnon, David P. (Thesis advisor) / Tein, Jenn-Yun (Thesis advisor) / West, Stephen G. (Committee member) / Grimm, Kevin J. (Committee member) / Arizona State University (Publisher)
Created2017