A study of a fit index for explanatory item response theory models

Abstract

Likelihood ratio chi square tests for nested models are typically used to determine model significance. Multiple correlations of item difficulties estimated with the explanatory predictors are often used to provide further information about model quality. However, the regression approach is not statistically justifiable, since the effective sample size becomes the number of items. Applying explanatory item response theory (IRT) models is advantageous when designing and selecting items. A simulation study was conducted to compare an explanatory item response theory fit statistic, Δ2 (Embretson, 1997; 2016), to traditionally used fit indices (nested model likelihoods and limited information multiple correlations) for assessing model quality. Simulation conditions include varying test length, item difficulty and the number of predictors.