Simulated population data were used to compare relative performances of the modification index and C. Chou and P. M. Bentler's Lagrange multiplier test (a multivariate generalization of a modification index) for four levels of model misspecification. Both indices failed to recover the true model except at the lowest level of misspecification. (SLD)

Three methods of estimating test score distributions that may improve on using the observed frequencies (OBFs) as estimates of a population test score distribution are considered: the kernel method (KM); the polynomial method (PM); and the four-parameter beta binomial method (FPBBM). The assumption each method makes about the smoothness of the…