• This research was supported by NSF grant DMS04-37167, the James McKeen Cattell Fund, and grants DA01070 and DA00017 from the National Institute on Drug Abuse. We would like to thank Bengt Muthén and Siek-Toon Khoo for providing the School Data and their unpublished manuscript. We also thank two reviewers who provided suggestions that helped to improve the paper.


Data in social and behavioral sciences are often hierarchically organized. Multilevel statistical procedures have been developed to analyze such data while taking into account the dependence of observations. When simultaneously evaluating models at all levels, a significant statistic provides no information on the level at which the model is misspecified. Model misspecification can exist at one or several levels simultaneously. When one level is misspecified, the other levels may be affected even when they are correctly specified. Motivated by these observations, we propose to separate a multilevel covariance structure into multiple single-level covariance structure models and to fit these single-level models as in conventional covariance structure analysis. A procedure for segregating the multilevel model into single-level models is developed. Five test statistics for evaluating a model at each level are provided. Standard error formulas for the separate estimators are also provided, and their efficiency is compared to simultaneous estimators. Empirical and Monte Carlo results demonstrate the advantages of the segregated procedure over the simultaneous procedure. Computer programs that will allow the developed procedure to be used in practice are also presented.