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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
Although the issue of factorial invariance has received increasing attention in the literature, the focus is typically on differences in factor structure across groups that are directly observed, such as those denoted by sex or ethnicity. While establishing factorial invariance across observed groups is a requisite step in making meaningful cross-group comparisons, failure to attend to possible sources of latent class heterogeneity in the form of class-based differences in factor structure has the potential to compromise conclusions with respect to observed groups and may result in misguided attempts at instrument development and theory refinement. The present studies examined the sensitivity of two widely used confirmatory factor analytic model fit indices, the chi-square test of model fit and RMSEA, to latent class differences in factor structure. Two primary questions were addressed. The first of these concerned the impact of latent class differences in factor loadings with respect to model fit in a single sample reflecting a mixture of classes. The second question concerned the impact of latent class differences in configural structure on tests of factorial invariance across observed groups. The results suggest that both indices are highly insensitive to class-based differences in factor loadings. Across sample size conditions, models with medium (0.2) sized loading differences were rejected by the chi-square test of model fit at rates just slightly higher than the nominal .05 rate of rejection that would be expected under a true null hypothesis. While rates of rejection increased somewhat when the magnitude of loading difference increased, even the largest sample size with equal class representation and the most extreme violations of loading invariance only had rejection rates of approximately 60%. RMSEA was also insensitive to class-based differences in factor loadings, with mean values across conditions suggesting a degree of fit that would generally be regarded as exceptionally good in practice. In contrast, both indices were sensitive to class-based differences in configural structure in the context of a multiple group analysis in which each observed group was a mixture of classes. However, preliminary evidence suggests that this sensitivity may contingent on the form of the cross-group model misspecification.
ContributorsBlackwell, Kimberly Carol (Author) / Millsap, Roger E (Thesis advisor) / Aiken, Leona S. (Committee member) / Enders, Craig K. (Committee member) / Mackinnon, David P (Committee member) / Arizona State University (Publisher)
Created2011
Description
Designing studies that use latent growth modeling to investigate change over time calls for optimal approaches for conducting power analysis for a priori determination of required sample size. This investigation (1) studied the impacts of variations in specified parameters, design features, and model misspecification in simulation-based power analyses and (2) compared power estimates across three common power analysis techniques: the Monte Carlo method; the Satorra-Saris method; and the method developed by MacCallum, Browne, and Cai (MBC). Choice of sample size, effect size, and slope variance parameters markedly influenced power estimates; however, level-1 error variance and number of repeated measures (3 vs. 6) when study length was held constant had little impact on resulting power. Under some conditions, having a moderate versus small effect size or using a sample size of 800 versus 200 increased power by approximately .40, and a slope variance of 10 versus 20 increased power by up to .24. Decreasing error variance from 100 to 50, however, increased power by no more than .09 and increasing measurement occasions from 3 to 6 increased power by no more than .04. Misspecification in level-1 error structure had little influence on power, whereas misspecifying the form of the growth model as linear rather than quadratic dramatically reduced power for detecting differences in slopes. Additionally, power estimates based on the Monte Carlo and Satorra-Saris techniques never differed by more than .03, even with small sample sizes, whereas power estimates for the MBC technique appeared quite discrepant from the other two techniques. Results suggest the choice between using the Satorra-Saris or Monte Carlo technique in a priori power analyses for slope differences in latent growth models is a matter of preference, although features such as missing data can only be considered within the Monte Carlo approach. Further, researchers conducting power analyses for slope differences in latent growth models should pay greatest attention to estimating slope difference, slope variance, and sample size. Arguments are also made for examining model-implied covariance matrices based on estimated parameters and graphic depictions of slope variance to help ensure parameter estimates are reasonable in a priori power analysis.
ContributorsVan Vleet, Bethany Lucía (Author) / Thompson, Marilyn S. (Thesis advisor) / Green, Samuel B. (Committee member) / Enders, Craig K. (Committee member) / Arizona State University (Publisher)
Created2011
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
The NFL is one of largest and most influential industries in the world. In America there are few companies that have a stronger hold on the American culture and create such a phenomena from year to year. In this project aimed to develop a strategy that helps an NFL team be as successful as possible by defining which positions are most important to a team's success. Data from fifteen years of NFL games was collected and information on every player in the league was analyzed. First there needed to be a benchmark which describes a team as being average and then every player in the NFL must be compared to that average. Based on properties of linear regression using ordinary least squares this project aims to define such a model that shows each position's importance. Finally, once such a model had been established then the focus turned to the NFL draft in which the goal was to find a strategy of where each position needs to be drafted so that it is most likely to give the best payoff based on the results of the regression in part one.
ContributorsBalzer, Kevin Ryan (Author) / Goegan, Brian (Thesis director) / Dassanayake, Maduranga (Committee member) / Barrett, The Honors College (Contributor) / Economics Program in CLAS (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2015-05
Description
The concentration factor edge detection method was developed to compute the locations and values of jump discontinuities in a piecewise-analytic function from its first few Fourier series coecients. The method approximates the singular support of a piecewise smooth function using an altered Fourier conjugate partial sum. The accuracy and characteristic features of the resulting jump function approximation depends on these lters, known as concentration factors. Recent research showed that that these concentration factors could be designed using aexible iterative framework, improving upon the overall accuracy and robustness of the method, especially in the case where some Fourier data are untrustworthy or altogether missing. Hypothesis testing methods were used to determine how well the original concentration factor method could locate edges using noisy Fourier data. This thesis combines the iterative design aspect of concentration factor design and hypothesis testing by presenting a new algorithm that incorporates multiple concentration factors into one statistical test, which proves more ective at determining jump discontinuities than the previous HT methods. This thesis also examines how the quantity and location of Fourier data act the accuracy of HT methods. Numerical examples are provided.
ContributorsLubold, Shane Michael (Author) / Gelb, Anne (Thesis director) / Cochran, Doug (Committee member) / Viswanathan, Aditya (Committee member) / Economics Program in CLAS (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
This paper examines the Syrian Civil War using seven different civil war settlement theories in order to assess the likelihood of a negotiated settlement ending the conflict. The costs of war, balance of power, domestic political institutions, ethnic identity, divisibility of stakes, veto player, and credible commitment theories were used in a multi-perspective analysis of the Syrian Civil War and the possibility of a peace settlement. It was found that all of the theories except for costs of war and balance of power predict that a negotiated settlement is unlikely to resolve the conflict. Although the Syrian government and the Syrian National Coalition are currently engaged in diplomatic negotiations through the Geneva II conference, both sides are unwilling to compromise on the underlying grievances driving the conflict. This paper ultimately highlights some of the problems inhibiting a negotiated settlement in the Syrian Civil War. These obstacles include: rival ethno-religious identities of combatants, lack of democratic institutions in Syria, indivisibility of stakes in which combatants are fighting for, number of veto player combatant groups active in Syria, and the lack of a credible third party to monitor and enforce a peace settlement.
ContributorsRidout, Scott Jeffries (Author) / Grossman, Gary (Thesis director) / Siroky, David (Committee member) / Barrett, The Honors College (Contributor) / Economics Program in CLAS (Contributor) / School of Politics and Global Studies (Contributor)
Created2014-05
Description
Beginning with the publication of Moneyball by Michael Lewis in 2003, the use of sabermetrics \u2014 the application of statistical analysis to baseball records - has exploded in major league front offices. Executives Billy Beane, Paul DePoedesta, and Theo Epstein are notable figures that have been successful in incorporating sabermetrics to their team's philosophy, resulting in playoff appearances and championship success. The competitive market of baseball, once dominated by the collusion of owners, now promotes innovative thought to analytically develop competitive advantages. The tiered economic payrolls of Major League Baseball (MLB) has created an environment in which large-market teams are capable of "buying" championships through the acquisition of the best available talent in free agency, and small-market teams are pushed to "build" championships through the drafting and systematic farming of high-school and college level players. The use of sabermetrics promotes both models of success \u2014 buying and building \u2014 by unbiasedly determining a player's productivity. The objective of this paper is to develop a regression-based predictive model that can be used by Majors League Baseball teams to forecast the MLB career average offensive performance of college baseball players from specific conferences. The development of this model required multiple tasks: I. Data was obtained from The Baseball Cube, a baseball records database providing both College and MLB data. II. Modifications to the data were applied to adjust for year-to-year formatting, a missing variable for seasons played, the presence of missing values, and to correct league identifiers. III. Evaluation of multiple offensive productivity models capable of handling the obtained dataset and regression forecasting technique. IV. SAS software was used to create the regression models and analyze the residuals for any irregularities or normality violations. The results of this paper find that there is a relationship between Division 1 collegiate baseball conferences and average career offensive productivity in Major Leagues Baseball, with the SEC having the most accurate reflection of performance.
ContributorsBadger, Mathew Bernard (Author) / Goegan, Brian (Thesis director) / Eaton, John (Committee member) / Department of Economics (Contributor) / Department of Marketing (Contributor) / Barrett, The Honors College (Contributor)
Created2017-05
Description
We seek a comprehensive measurement for the economic prosperity of persons with disabilities. We survey the current literature and identify the major economic indicators used to describe the socioeconomic standing of persons with disabilities. We then develop a methodology for constructing a statistically valid composite index of these indicators, and build this index using data from the 2014 American Community Survey. Finally, we provide context for further use and development of the index and describe an example application of the index in practice.
ContributorsTheisen, Ryan (Co-author) / Helms, Tyler (Co-author) / Lewis, Paul (Thesis director) / Reiser, Mark (Committee member) / Economics Program in CLAS (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / School of Politics and Global Studies (Contributor) / Barrett, The Honors College (Contributor)
Created2017-05
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