Posterior predictive model checking for multidimensionality in item response theory and Bayesian networks

摘要: Title of dissertation: POSTERIOR PREDICTIVE MODEL CHECKING FOR MULTIDIMENSIONALITY IN ITEM RESPONSE THEORY AND BAYESIAN NETWORKS Roy Levy, Doctor Philosophy, 2006 Dissertation directed by: Professor Robert J. Mislevy Department Measurement, Statistics & Evaluation If data exhibit a dimensional structure more complex than what is assumed, key conditional independence assumptions the hypothesized model do not hold. The current work pursues posterior predictive checking, flexible family Bayesian checking procedures, as tool for criticizing models in light inadequately modeled structure. Factors to influence dimensionality and assessment are couched covariance theory conveyed via geometric representations multidimensionality. These factors their effects motivate simulation study that investigates context item response dichotomous observables. A unidimensional fit follow compensatory or conjunctive multidimensional assess utility conducting checking. Discrepancy measures formulated at level individual items pairs items. second draws from results first techniques networks with inhibitory effects. Key findings include support manipulated regard on superiority certain discrepancy assessment. application these both familiar those have yet become standard practice speaks generality procedures its potentially broad applicability.