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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 Two Assessment Years

NAEP Technical DocumentationPolytomous Item With Data for Two Assessment Years

When the same items are presented in two assessment years, the empirical item response functions (IRFs) for the two years can be compared to one another and to the theoretical IRF. Normally, the curves for the two years differ somewhat due to the sampling of students for each year. This figure contains a plot for a polytomous item from the 1998 and 2000 grade 4 national main reading assessments.

In the plot, the horizontal axis represents the provisional theta () 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 the students with responses in each category. The sizes of the symbols are proportional to the sum of the posteriors at each point on the scale for all of those who received the item; this is related to the number of students contributing to the estimation of that empirical proportion.

Red inverted triangles represent 2000 grade 4 reading assessment data; green triangles represent 1998 grade 4 reading assessment data. The curve indicates the estimated IRF assuming a logistic form. This item is a four 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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