Matching Items (23)
Filtering by
- All Subjects: Statistics
- Genre: Academic theses
- Creators: Levy, Roy
- Creators: West, Stephen G.
- Creators: Zhou, Shuang
Description
Dimensionality assessment is an important component of evaluating item response data. Existing approaches to evaluating common assumptions of unidimensionality, such as DIMTEST (Nandakumar & Stout, 1993; Stout, 1987; Stout, Froelich, & Gao, 2001), have been shown to work well under large-scale assessment conditions (e.g., large sample sizes and item pools; see e.g., Froelich & Habing, 2007). It remains to be seen how such procedures perform in the context of small-scale assessments characterized by relatively small sample sizes and/or short tests. The fact that some procedures come with minimum allowable values for characteristics of the data, such as the number of items, may even render them unusable for some small-scale assessments. Other measures designed to assess dimensionality do not come with such limitations and, as such, may perform better under conditions that do not lend themselves to evaluation via statistics that rely on asymptotic theory. The current work aimed to evaluate the performance of one such metric, the standardized generalized dimensionality discrepancy measure (SGDDM; Levy & Svetina, 2011; Levy, Xu, Yel, & Svetina, 2012), under both large- and small-scale testing conditions. A Monte Carlo study was conducted to compare the performance of DIMTEST and the SGDDM statistic in terms of evaluating assumptions of unidimensionality in item response data under a variety of conditions, with an emphasis on the examination of these procedures in small-scale assessments. Similar to previous research, increases in either test length or sample size resulted in increased power. The DIMTEST procedure appeared to be a conservative test of the null hypothesis of unidimensionality. The SGDDM statistic exhibited rejection rates near the nominal rate of .05 under unidimensional conditions, though the reliability of these results may have been less than optimal due to high sampling variability resulting from a relatively limited number of replications. Power values were at or near 1.0 for many of the multidimensional conditions. It was only when the sample size was reduced to N = 100 that the two approaches diverged in performance. Results suggested that both procedures may be appropriate for sample sizes as low as N = 250 and tests as short as J = 12 (SGDDM) or J = 19 (DIMTEST). When used as a diagnostic tool, SGDDM may be appropriate with as few as N = 100 cases combined with J = 12 items. The study was somewhat limited in that it did not include any complex factorial designs, nor were the strength of item discrimination parameters or correlation between factors manipulated. It is recommended that further research be conducted with the inclusion of these factors, as well as an increase in the number of replications when using the SGDDM procedure.
ContributorsReichenberg, Ray E (Author) / Levy, Roy (Thesis advisor) / Thompson, Marilyn S. (Thesis advisor) / Green, Samuel B. (Committee member) / Arizona State University (Publisher)
Created2013
Description
This simulation study compared the utility of various discrepancy measures within a posterior predictive model checking (PPMC) framework for detecting different types of data-model misfit in multidimensional Bayesian network (BN) models. The investigated conditions were motivated by an applied research program utilizing an operational complex performance assessment within a digital-simulation educational context grounded in theories of cognition and learning. BN models were manipulated along two factors: latent variable dependency structure and number of latent classes. Distributions of posterior predicted p-values (PPP-values) served as the primary outcome measure and were summarized in graphical presentations, by median values across replications, and by proportions of replications in which the PPP-values were extreme. An effect size measure for PPMC was introduced as a supplemental numerical summary to the PPP-value. Consistent with previous PPMC research, all investigated fit functions tended to perform conservatively, but Standardized Generalized Dimensionality Discrepancy Measure (SGDDM), Yen's Q3, and Hierarchy Consistency Index (HCI) only mildly so. Adequate power to detect at least some types of misfit was demonstrated by SGDDM, Q3, HCI, Item Consistency Index (ICI), and to a lesser extent Deviance, while proportion correct (PC), a chi-square-type item-fit measure, Ranked Probability Score (RPS), and Good's Logarithmic Scale (GLS) were powerless across all investigated factors. Bivariate SGDDM and Q3 were found to provide powerful and detailed feedback for all investigated types of misfit.
ContributorsCrawford, Aaron (Author) / Levy, Roy (Thesis advisor) / Green, Samuel (Committee member) / Thompson, Marilyn (Committee member) / Arizona State University (Publisher)
Created2014
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
Many methodological approaches have been utilized to predict student retention and persistence over the years, yet few have utilized a Bayesian framework. It is believed this is due in part to the absence of an established process for guiding educational researchers reared in a frequentist perspective into the realms of Bayesian analysis and educational data mining. The current study aimed to address this by providing a model-building process for developing a Bayesian network (BN) that leveraged educational data mining, Bayesian analysis, and traditional iterative model-building techniques in order to predict whether community college students will stop out at the completion of each of their first six terms. The study utilized exploratory and confirmatory techniques to reduce an initial pool of more than 50 potential predictor variables to a parsimonious final BN with only four predictor variables. The average in-sample classification accuracy rate for the model was 80% (Cohen's κ = 53%). The model was shown to be generalizable across samples with an average out-of-sample classification accuracy rate of 78% (Cohen's κ = 49%). The classification rates for the BN were also found to be superior to the classification rates produced by an analog frequentist discrete-time survival analysis model.
ContributorsArcuria, Philip (Author) / Levy, Roy (Thesis advisor) / Green, Samuel B (Committee member) / Thompson, Marilyn S (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
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