Assessing Dimensionality of the Ideal Point Item Response Theory Model Using Posterior Predictive Model Checking

Although the use of ideal point item response theory (IRT) models for organizational research has increased over the last decade, the assessment of construct dimensionality of ideal point scales has been overlooked in previous research. In this study, we developed and evaluated dimensionality assessment methods for an ideal point IRT model under the Bayesian framework. We applied the posterior predictive model checking (PPMC) approach to the most widely used ideal point IRT model, the generalized graded unfolding model (GGUM). We conducted a Monte Carlo simulation to compare the performance of item pair discrepancy statistics and to evaluate the Type I error and power rates of the methods. The simulation results indicated that the Bayesian dimensionality detection method controlled Type I errors reasonably well across the conditions. In addition, the proposed method showed better performance than existing methods, yielding acceptable power when 20% of the items were generated from the secondary dimension. Organizational implications and limitations of the study are further discussed.

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. Bayesian posterior predictive model checking (PPMC) methods are increasingly being used to investigate multidimensionality in IRT models. The current work proposes a PPMC method for evaluating local dependence in IRT models that are estimated using full-information maximum likelihood. The proposed approach, which was termed as “PPMC assuming posterior normality” (PPMC-N), provides a straightforward method to account for parameter uncertainty in model fit assessment. A simulation study demonstrated the comparability of the PPMC-N and the Bayesian PPMC approach in the detection of local dependence in dichotomous IRT models.