Evaluation of Residual-Based Fit Statistics for Item Response Theory Models in the Presence of Non-Responses

Abstract

Residual-based fit statistics, which compare observed item statistics (e.g., proportions) with model-implied probabilities, are widely used to evaluate model fit, item fit, and local dependence in item response theory (IRT) models. Despite the prevalence of item non-responses in empirical studies, their impact on these statistics has not been systematically examined. Existing software (package) often applies heuristic treatments (e.g., listwise or pairwise deletion), which can distort fit statistics because missing data further inflate discrepancies between observed and expected proportions. This study evaluates the appropriateness of such treatments through extensive simulation. Results show that deletion methods degrade the accuracy of fit testing: fit indices are inflated under both null and power conditions, with the bias worsening as missingness increases. In addition, the impact of missing data exceeds that of model misspecification. Practical recommendations and alternative methods are discussed to guide applied researchers.