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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 → Items Showing Good Item Fit → Polytomous Item With Data for One Assessment Year

NAEP Technical DocumentationPolytomous Item With Data for One Assessment Year

This figure contains a plot of the empirical and theoretical item response functions (IRFs) for a polytomous item from the 2000 grade 8 national main science assessment. The horizontal axis represents the provisional theta (θ) scale with mean 0 and standard deviation 1, while the vertical axis represents the probability of having a response fall in each category. The solid curves are the theoretical IRFs based on the item parameter estimates and the equation for the generalized partial credit model. The centers of the symbols represent the empirical proportions of students with responses in each category. The sizes of the symbols are proportional to the sum of the posteriors at each point on the θ scale for the students who received the item; this is related to the number of students contributing to the estimation of that empirical proportion.

Triangles represent 2000 grade 8 science assessment data. The curve indicates the estimated IRF using a generalized partial credit model. This item is a three category constructed-response item.

Polytomous item exhibiting good model fit

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP).

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