Comparing person infit mean squares for the Andrich model and MSD.

Cumulative distribution functions of the person infit mean squares (blue curves) are compared to cumulative distribution functions of chi square divided by degrees of freedom (red curves), for the Andrich model (left) and MSD (right). The red and blue curves should be identical under the assumption that the only source of variance is random error. MSD satisfies this assumption better than the Andrich model as the number of rating categories increases.