Robustness of the School-Level IRT Model

The robustness of the school-level item response theoretic (IRT) model to violations of distributional assumptions was studied in a computer simulation. Estimated precision of "expected a posteriori" (EAP) estimates of the mean school ability from BILOG 3 was compared with actual precision, varying school size, intraclass correlation, school ability, number of forms comprising the test, and item parameters. Under conditions where the school-level precision might be possibly acceptable for real school comparisons, the EAP estimates of school ability were robust over a wide range of violations and conditions, with the estimated precision being either consistent with the actual precision or somewhat conservative. Some lack of robustness was found, however, under conditions where the precision was inherently poor and the test would presumably not be used for serious school comparisons.