A Posterior Predictive Model Checking Method Assuming Posterior Normality for Item Response Theory

This study investigated the violation of local independence assumptions within unidimensional item response theory (IRT) models. IRT models assume that for a given value of the latent variable, the value of any observed variable is conditionally independent of all other variables. Violation of this assumption can bias item parameter estimates and latent trait scores. There are two existing classes of procedures to check for local dependence (LD): (a) frequentist model appraisal methods that rely on the expected and observed bivariate item frequencies, and (b) posterior predictive model checking (PPMC) methods, which are a flexible family of Bayesian model checking procedures. The advantages of the PPMC method is that it accounts for parameter estimation uncertainty and does not require asymptotic arguments. Given the current dominance of maximum likelihood approaches for the estimation of IRT models, I propose a posterior predictive model checking method for evaluating LD in IRT models that can be implemented using only byproducts of likelihood-based estimation. This approach, which relies on a posterior normality approximation, was found to be comparable to the fully Bayesian PPMC approach in terms of the sensitivity to local dependence in IRT models