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- All Subjects: Statistics
- Creators: Department of Information Systems
- Creators: West, Stephen G.
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
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
Over the course of six months, we have worked in partnership with Arizona State University and a leading producer of semiconductor chips in the United States market (referred to as the "Company"), lending our skills in finance, statistics, model building, and external insight. We attempt to design models that help predict how much time it takes to implement a cost-saving project. These projects had previously been considered only on the merit of cost savings, but with an added dimension of time, we hope to forecast time according to a number of variables. With such a forecast, we can then apply it to an expense project prioritization model which relates time and cost savings together, compares many different projects simultaneously, and returns a series of present value calculations over different ranges of time. The goal is twofold: assist with an accurate prediction of a project's time to implementation, and provide a basis to compare different projects based on their present values, ultimately helping to reduce the Company's manufacturing costs and improve gross margins. We believe this approach, and the research found toward this goal, is most valuable for the Company. Two coaches from the Company have provided assistance and clarified our questions when necessary throughout our research. In this paper, we begin by defining the problem, setting an objective, and establishing a checklist to monitor our progress. Next, our attention shifts to the data: making observations, trimming the dataset, framing and scoping the variables to be used for the analysis portion of the paper. Before creating a hypothesis, we perform a preliminary statistical analysis of certain individual variables to enrich our variable selection process. After the hypothesis, we run multiple linear regressions with project duration as the dependent variable. After regression analysis and a test for robustness, we shift our focus to an intuitive model based on rules of thumb. We relate these models to an expense project prioritization tool developed using Microsoft Excel software. Our deliverables to the Company come in the form of (1) a rules of thumb intuitive model and (2) an expense project prioritization tool.
ContributorsAl-Assi, Hashim (Co-author) / Chiang, Robert (Co-author) / Liu, Andrew (Co-author) / Ludwick, David (Co-author) / Simonson, Mark (Thesis director) / Hertzel, Michael (Committee member) / Barrett, The Honors College (Contributor) / Department of Information Systems (Contributor) / Department of Finance (Contributor) / Department of Economics (Contributor) / Department of Supply Chain Management (Contributor) / School of Accountancy (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Mechanical and Aerospace Engineering Program (Contributor) / WPC Graduate Programs (Contributor)
Created2015-05
Description
Coherent vortices are ubiquitous structures in natural flows that affect mixing and transport of substances and momentum/energy. Being able to detect these coherent structures is important for pollutant mitigation, ecological conservation and many other aspects. In recent years, mathematical criteria and algorithms have been developed to extract these coherent structures in turbulent flows. In this study, we will apply these tools to extract important coherent structures and analyze their statistical properties as well as their implications on kinematics and dynamics of the flow. Such information will aide representation of small-scale nonlinear processes that large-scale models of natural processes may not be able to resolve.
ContributorsCass, Brentlee Jerry (Author) / Tang, Wenbo (Thesis director) / Kostelich, Eric (Committee member) / Department of Information Systems (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
Exchange traded funds (ETFs) in many ways are similar to more traditional closed-end mutual funds, although thee differ in a crucial way. ETFs rely on a creation and redemption feature to achieve their functionality and this mechanism is designed to minimize the deviations that occur between the ETF’s listed price and the net asset value of the ETF’s underlying assets. However while this does cause ETF deviations to be generally lower than their mutual fund counterparts, as our paper explores this process does not eliminate these deviations completely. This article builds off an earlier paper by Engle and Sarkar (2006) that investigates these properties of premiums (discounts) of ETFs from their fair market value. And looks to see if these premia have changed in the last 10 years. Our paper then diverges from the original and takes a deeper look into the standard deviations of these premia specifically.
Our findings show that over 70% of an ETFs standard deviation of premia can be explained through a linear combination consisting of two variables: a categorical (Domestic[US], Developed, Emerging) and a discrete variable (time-difference from US). This paper also finds that more traditional metrics such as market cap, ETF price volatility, and even 3rd party market indicators such as the economic freedom index and investment freedom index are insignificant predictors of an ETFs standard deviation of premia when combined with the categorical variable. These findings differ somewhat from existing literature which indicate that these factors should have a significant impact on the predictive ability of an ETFs standard deviation of premia.
Our findings show that over 70% of an ETFs standard deviation of premia can be explained through a linear combination consisting of two variables: a categorical (Domestic[US], Developed, Emerging) and a discrete variable (time-difference from US). This paper also finds that more traditional metrics such as market cap, ETF price volatility, and even 3rd party market indicators such as the economic freedom index and investment freedom index are insignificant predictors of an ETFs standard deviation of premia when combined with the categorical variable. These findings differ somewhat from existing literature which indicate that these factors should have a significant impact on the predictive ability of an ETFs standard deviation of premia.
ContributorsZhang, Jingbo (Co-author, Co-author) / Henning, Thomas (Co-author) / Simonson, Mark (Thesis director) / Licon, L. Wendell (Committee member) / Department of Finance (Contributor) / Department of Information Systems (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2019-05
Description
The object of the present study is to examine methods in which the company can optimize their costs on third-party suppliers whom oversee other third-party trade labor. The third parties in scope of this study are suspected to overstaff their workforce, thus overcharging the company. We will introduce a complex spreadsheet model that will propose a proper project staffing level based on key qualitative variables and statistics. Using the model outputs, the Thesis team proposes a headcount solution for the company and problem areas to focus on, going forward. All sources of information come from company proprietary and confidential documents.
ContributorsLoo, Andrew (Co-author) / Brennan, Michael (Co-author) / Sheiner, Alexander (Co-author) / Hertzel, Michael (Thesis director) / Simonson, Mark (Committee member) / Barrett, The Honors College (Contributor) / Department of Information Systems (Contributor) / Department of Finance (Contributor) / Department of Supply Chain Management (Contributor) / WPC Graduate Programs (Contributor) / School of Accountancy (Contributor)
Created2014-05
Description
Our research encompassed the prospect draft in baseball and looked at what type of player teams drafted to maximize value. We wanted to know which position returned the best value to the team that drafted them, and which level is safer to draft players from, college or high school. We decided to look at draft data from 2006-2010 for the first ten rounds of players selected. Because there is only a monetary cap on players drafted in the first ten rounds we restricted our data to these players. Once we set up the parameters we compiled a spreadsheet of these players with both their signing bonuses and their wins above replacement (WAR). This allowed us to see how much a team was spending per win at the major league level. After the data was compiled we made pivot tables and graphs to visually represent our data and better understand the numbers. We found that the worst position that MLB teams could draft would be high school second baseman. They returned the lowest WAR of any player that we looked at. In general though high school players were more costly to sign and had lower WARs than their college counterparts making them, on average, a worse pick value wise. The best position you could pick was college shortstops. They had the trifecta of the best signability of all players, along with one of the highest WARs and lowest signing bonuses. These were three of the main factors that you want with your draft pick and they ranked near the top in all three categories. This research can help give guidelines to Major League teams as they go to select players in the draft. While there are always going to be exceptions to trends, by following the enclosed research teams can minimize risk in the draft.
ContributorsValentine, Robert (Co-author) / Johnson, Ben (Co-author) / Eaton, John (Thesis director) / Goegan, Brian (Committee member) / Department of Finance (Contributor) / Department of Economics (Contributor) / Department of Information Systems (Contributor) / School of Accountancy (Contributor) / Barrett, The Honors College (Contributor)
Created2017-05