| Abstract: | The precision of the group-level IRT model applied to school ability estimation is described, assuming use of Bayesian estimation with precision represented by the standard deviation of the posterior distribution. Similarities and differences between the school-level model and the familiar individual-level IRT model are considered. School size and between-school variability, two factors not relevant at the student level, are dominant determinants of school-level precision. Under the multiple-matrix sampling design required for the school-level IRT, the number of items associated with a scale does not influence the precision at the school level. Also, the effects of school ability and item quality on school-level precision are often relatively weak. It was found that the use of Bayesian estimation could result in a systematic distortion of the true ranking of schools based on ability because of an estimation bias which is a function of school size. |
