NAEP Technical DocumentationExemplar Theoretical Item Response Function (IRF) for the Two-Parameter Logistic Item Response Theory (IRT) Model

This figure contains a plot of the theoretical item response function (IRF) for a dichotomous item. The item is a constructed-response item that is scored correct or incorrect. In the plot, the horizontal axis represents the theta () scale, while the vertical axis represents the probability of a correct response. The solid curve is the theoretical IRF based on the item parameter estimates and the equation for the two-parameter logistic IRT model.

Example Plot

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2000 and 2001 Assessment.

For items of this type, students are unlikely to guess the correct answer, so students low on the scale are expected to have a little chance to respond correctly. Students high on the scale are more likely to respond correctly to this item.

The b-parameter indicates the place on the scale where students are equally likely to get the item right or wrong (probability of a correct answer is 0.50). For this item b = 1.0. Items with b-parameter values greater than 1.0 are more difficult than this item; items with b-parameter values less than 1.0 are less difficult than this item.

The a-parameter indicates the maximum slope (steepness) of the curve. This happens at the point on this curve that corresponds to the b-parameter value 1.0. The a-parameter value for this item is 1.2. Items with a-parameter values greater than 1.2 are more discriminating than this item; items with a-parameter values less than 1.2 are less discriminating. When an item is more discriminating the curve is steeper, allowing a more exact prediction on the basis of their responses to this item of whether students are above or below 1.0 on the scale.

Last updated 12 August 2008 (RF)

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