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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
… types of misfit. Date Created 2014 Contributors Crawford, Aaron (Author) Levy, Roy (Thesis advisor) Green, Samuel … Statement of Responsibility by AAron Crawford Description Source Viewed on May 6, 2015 … Posterior Predictive Model Checking in Bayesian Networks by AAron Crawford A Dissertation Presented in Partial …
Description
Accurate data analysis and interpretation of results may be influenced by many potential factors. The factors of interest in the current work are the chosen analysis model(s), the presence of missing data, and the type(s) of data collected. If analysis models are used which a) do not accurately capture the structure of relationships in the data such as clustered/hierarchical data, b) do not allow or control for missing values present in the data, or c) do not accurately compensate for different data types such as categorical data, then the assumptions associated with the model have not been met and the results of the analysis may be inaccurate. In the presence of clustered
ested data, hierarchical linear modeling or multilevel modeling (MLM; Raudenbush & Bryk, 2002) has the ability to predict outcomes for each level of analysis and across multiple levels (accounting for relationships between levels) providing a significant advantage over single-level analyses. When multilevel data contain missingness, multilevel multiple imputation (MLMI) techniques may be used to model both the missingness and the clustered nature of the data. With categorical multilevel data with missingness, categorical MLMI must be used. Two such routines for MLMI with continuous and categorical data were explored with missing at random (MAR) data: a formal Bayesian imputation and analysis routine in JAGS (R/JAGS) and a common MLM procedure of imputation via Bayesian estimation in BLImP with frequentist analysis of the multilevel model in Mplus (BLImP/Mplus). Manipulated variables included interclass correlations, number of clusters, and the rate of missingness. Results showed that with continuous data, R/JAGS returned more accurate parameter estimates than BLImP/Mplus for almost all parameters of interest across levels of the manipulated variables. Both R/JAGS and BLImP/Mplus encountered convergence issues and returned inaccurate parameter estimates when imputing and analyzing dichotomous data. Follow-up studies showed that JAGS and BLImP returned similar imputed datasets but the choice of analysis software for MLM impacted the recovery of accurate parameter estimates. Implications of these findings and recommendations for further research will be discussed.
ested data, hierarchical linear modeling or multilevel modeling (MLM; Raudenbush & Bryk, 2002) has the ability to predict outcomes for each level of analysis and across multiple levels (accounting for relationships between levels) providing a significant advantage over single-level analyses. When multilevel data contain missingness, multilevel multiple imputation (MLMI) techniques may be used to model both the missingness and the clustered nature of the data. With categorical multilevel data with missingness, categorical MLMI must be used. Two such routines for MLMI with continuous and categorical data were explored with missing at random (MAR) data: a formal Bayesian imputation and analysis routine in JAGS (R/JAGS) and a common MLM procedure of imputation via Bayesian estimation in BLImP with frequentist analysis of the multilevel model in Mplus (BLImP/Mplus). Manipulated variables included interclass correlations, number of clusters, and the rate of missingness. Results showed that with continuous data, R/JAGS returned more accurate parameter estimates than BLImP/Mplus for almost all parameters of interest across levels of the manipulated variables. Both R/JAGS and BLImP/Mplus encountered convergence issues and returned inaccurate parameter estimates when imputing and analyzing dichotomous data. Follow-up studies showed that JAGS and BLImP returned similar imputed datasets but the choice of analysis software for MLM impacted the recovery of accurate parameter estimates. Implications of these findings and recommendations for further research will be discussed.
ContributorsKunze, Katie L (Author) / Levy, Roy (Thesis advisor) / Enders, Craig K. (Committee member) / Thompson, Marilyn S (Committee member) / Arizona State University (Publisher)
Created2016
… for her friendship and faith in me. To Dubravka Svetina, AAron Crawford, and Derek Fay for being the wonderful …
Description
The study examined how ATFIND, Mantel-Haenszel, SIBTEST, and Crossing SIBTEST function when items in the dataset are modelled to differentially advantage a lower ability focal group over a higher ability reference group. The primary purpose of the study was to examine ATFIND's usefulness as a valid subtest selection tool, but it also explored the influence of DIF items, item difficulty, and presence of multiple examinee populations with different ability distributions on both its selection of the assessment test (AT) and partitioning test (PT) lists and on all three differential item functioning (DIF) analysis procedures. The results of SIBTEST were also combined with those of Crossing SIBTEST, as might be done in practice.
ATFIND was found to be a less-than-effective matching subtest selection tool with DIF items that are modelled unidimensionally. If an item was modelled with uniform DIF or if it had a referent difficulty parameter in the Medium range, it was found to be selected slightly more often for the AT List than the PT List. These trends were seen to increase as sample size increased. All three DIF analyses, and the combined SIBTEST and Crossing SIBTEST, generally were found to perform less well as DIF contaminated the matching subtest, as well as when DIF was modelled less severely or when the focal group ability was skewed. While the combined SIBTEST and Crossing SIBTEST was found to have the highest power among the DIF analyses, it also was found to have Type I error rates that were sometimes extremely high.
ATFIND was found to be a less-than-effective matching subtest selection tool with DIF items that are modelled unidimensionally. If an item was modelled with uniform DIF or if it had a referent difficulty parameter in the Medium range, it was found to be selected slightly more often for the AT List than the PT List. These trends were seen to increase as sample size increased. All three DIF analyses, and the combined SIBTEST and Crossing SIBTEST, generally were found to perform less well as DIF contaminated the matching subtest, as well as when DIF was modelled less severely or when the focal group ability was skewed. While the combined SIBTEST and Crossing SIBTEST was found to have the highest power among the DIF analyses, it also was found to have Type I error rates that were sometimes extremely high.
ContributorsScott, Lietta Marie (Author) / Levy, Roy (Thesis advisor) / Green, Samuel B (Thesis advisor) / Gorin, Joanna S (Committee member) / Williams, Leila E (Committee member) / Arizona State University (Publisher)
Created2014
… from the other students in the program, especially from AAron Crawford, Derek Fay, and Dubravka Svetina. Your …
Description
The purpose of this study was to investigate the effect of complex structure on dimensionality assessment in compensatory and noncompensatory multidimensional item response models (MIRT) of assessment data using dimensionality assessment procedures based on conditional covariances (i.e., DETECT) and a factor analytical approach (i.e., NOHARM). The DETECT-based methods typically outperformed the NOHARM-based methods in both two- (2D) and three-dimensional (3D) compensatory MIRT conditions. The DETECT-based methods yielded high proportion correct, especially when correlations were .60 or smaller, data exhibited 30% or less complexity, and larger sample size. As the complexity increased and the sample size decreased, the performance typically diminished. As the complexity increased, it also became more difficult to label the resulting sets of items from DETECT in terms of the dimensions. DETECT was consistent in classification of simple items, but less consistent in classification of complex items. Out of the three NOHARM-based methods, χ2G/D and ALR generally outperformed RMSR. χ2G/D was more accurate when N = 500 and complexity levels were 30% or lower. As the number of items increased, ALR performance improved at correlation of .60 and 30% or less complexity. When the data followed a noncompensatory MIRT model, the NOHARM-based methods, specifically χ2G/D and ALR, were the most accurate of all five methods. The marginal proportions for labeling sets of items as dimension-like were typically low, suggesting that the methods generally failed to label two (three) sets of items as dimension-like in 2D (3D) noncompensatory situations. The DETECT-based methods were more consistent in classifying simple items across complexity levels, sample sizes, and correlations. However, as complexity and correlation levels increased the classification rates for all methods decreased. In most conditions, the DETECT-based methods classified complex items equally or more consistent than the NOHARM-based methods. In particular, as complexity, the number of items, and the true dimensionality increased, the DETECT-based methods were notably more consistent than any NOHARM-based method. Despite DETECT's consistency, when data follow a noncompensatory MIRT model, the NOHARM-based method should be preferred over the DETECT-based methods to assess dimensionality due to poor performance of DETECT in identifying the true dimensionality.
ContributorsSvetina, Dubravka (Author) / Levy, Roy (Thesis advisor) / Gorin, Joanna S. (Committee member) / Millsap, Roger (Committee member) / Arizona State University (Publisher)
Created2011
… the passion of dimensionality assessment, I say thank you. AAron V. Crawford and Katie Poole for being open to listen …