Cover: Controlling for Individual Heterogeneity in Longitudinal Models, with Applications to Student Achievement

Controlling for Individual Heterogeneity in Longitudinal Models, with Applications to Student Achievement

Published Sep 4, 2007

by J. R. Lockwood, Daniel F. McCaffrey

Download eBook for Free

FormatFile SizeNotes
PDF file 3.3 MB

Use Adobe Acrobat Reader version 10 or higher for the best experience.

Longitudinal data tracking repeated measurements on individuals are highly valued for research because they offer controls for unmeasured individual heterogeneity that might otherwise bias results. Random effects or mixed models approaches, which treat individual heterogeneity as part of the model error term and use generalized least squares to estimate model parameters, are often criticized because correlation between unobserved individual effects and other model variables can lead to biased and inconsistent parameter estimates. Starting with an examination of the relationship between random effects and fixed effects estimators in the standard unobserved effects model, this article demonstrates through analysis and simulation that the mixed model approach has a “bias compression” property under a general model for individual heterogeneity that can mitigate bias due to uncontrolled differences among individuals. The general model is motivated by the complexities of longitudinal student achievement measures, but the results have broad applicability to longitudinal modeling.

Originally published in: Electronic Journal of Statistics, Vol. 1, No. 1, pp. 223-252.

This report is part of the RAND reprint series. The Reprint was a product of RAND from 1992 to 2011 that represented previously published journal articles, book chapters, and reports with the permission of the publisher. RAND reprints were formally reviewed in accordance with the publisher's editorial policy and compliant with RAND's rigorous quality assurance standards for quality and objectivity. For select current RAND journal articles, see External Publications.

This document and trademark(s) contained herein are protected by law. This representation of RAND intellectual property is provided for noncommercial use only. Unauthorized posting of this publication online is prohibited; linking directly to this product page is encouraged. Permission is required from RAND to reproduce, or reuse in another form, any of its research documents for commercial purposes. For information on reprint and reuse permissions, please visit

RAND is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.