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NAEP Analysis and Scaling → Estimation of NAEP Score Scales → Checks for Violations of Assumptions → Comparisons of Empirical and Theoretical Item Response Functions

NAEP Technical DocumentationComparisons of Empirical and Theoretical Item Response Functions

			Items Showing Good Item Fit Items Showing Poor Item Fit

Theoretical item response functions (IRFs) plot the probability of success on an item against underlying performance on the scales, using the item parameters estimated for the NAEP scales. The empirical proportions that are plotted as empirical IRFs are calculated from the posterior distributions of the θs for the students who received the item. By visually comparing the theoretical and empirical IRFs the fit of the Item Response Theory (IRT) models to the observed data within each scale, measurement specialists can identify items that do not fit the IRT models for a variety of reasons.

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