ASU Electronic Theses and Dissertations
This collection includes most of the ASU Theses and Dissertations from 2011 to present. ASU Theses and Dissertations are available in downloadable PDF format; however, a small percentage of items are under embargo. Information about the dissertations/theses includes degree information, committee members, an abstract, supporting data or media.
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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
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