Visualizing different levels of compensation in multidimensional item response theory models


This graphic shows the probability of providing a correct response to an item in a multidimensional item response theory (MIRT) model. The colors represent the probability of a correct response, and the contours represent chunk of 10% probability (i.e., the space between the leftmost and second contours represents ability pairs with a 10-20% probability of answering correctly). In this example, I use a 2-dimensional model to illustrate how the probabilities change depending on the parameterization of the model. In the compensatory model, one dimension is able to compensate for the other, whereas in the noncompensatory model, an individual needs high ability on both dimensions to have a high probability of success. The partially compensatory model is parameterized with an interaction term that allows one dimension to partially compensate for the other.

Educational Measurement: Issues and Practice