NAEP Analysis and Scaling → Estimation of NAEP Score Scales → Item Scaling Models → The Two-Parameter Logistic Model → Exemplar Theoretical Item Response Function (IRF) for the Two-Parameter Logistic Item Response Theory (IRT) Model Exemplar Theoretical Item Response Function (IRF) for the Two-Parameter Logistic Item Response Theory (IRT) ModelThis 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. In this case the scale has a mean of zero and a standard deviation of one.
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 25 June 2008 (MH) |