The main purpose of this study is to improve estimation efficiency in obtaining maximum marginal likelihood estimates of contextual effects in the framework of nonlinear multilevel latent variable model by adopting the Metropolis-Hastings Robbins-Monro algorithm (MH-RM). Results indicate that the MH-RM algorithm can produce estimates and standard…

The main purpose of this study is to improve estimation efficiency in obtaining maximum marginal likelihood estimates of contextual effects in the framework of nonlinear multilevel latent variable model by adopting the Metropolis-Hastings Robbins-Monro algorithm (MH-RM; Cai, 2008, 2010a, 2010b). Results indicate that the MH-RM algorithm can…

A simple, rigorous, small-sample statistical technique is described for testing the hypothesis that two sets of measurements differ only because of errors of measurement and because of differing origins and units of measurement. (Author)

A problem that arises when a differential item functioning (DIF) study is done with samples of examinees differing in ability is examined. A test may function differently when the populations from which the items are calibrated are not of equal ability. Since the lower ability examinees get many difficult items incorrect, the spread (standard…