Covariate Measurement Error Adjustment for Multilevel Models With Application to Educational Data

• Published in: Journal of educational and behavioral statistics Vol. 36; no. 3; pp. 283 - 306
• Main Authors: Battauz, Michela, Bellio, Ruggero, Gori, Enrico
• Format: Journal Article
• Language: English
• Published: Los Angeles, CA SAGE Publications 01.06.2011; American Educational Research Association
• Subjects: Academic achievement; Algorithms; Computation; Education; Error of Measurement; Error rates; Estimation bias; Estimation methods; Foreign Countries; Human error; Italy; Item Response Theory; Matrices; Maximum likelihood estimation; Maximum Likelihood Statistics; Measurement errors; Modeling; Multilevel models; Parameter estimation; Parametric models; School Effectiveness; Statistical variance; Italy; random effects; measurement error; multilevel model; Rasch model; structural model; value-added model
• ISSN: 1076-9986; 1935-1054
• DOI: 10.3102/1076998610366262

This article proposes a multilevel model for the assessment of school effectiveness where the intake achievement is a predictor and the response variable is the achievement in the subsequent periods. The achievement is a latent variable that can be estimated on the basis of an item response theory model and hence subject to measurement error. Ignoring covariate measurement error leads to biased parameter estimates. To address this problem, a likelihood-based measurement error adjustment for multilevel models is proposed. In particular, the method deals with a covariate measured with error that has a random coefficient. An application to educational data from the Italian region of Lombardy illustrates the method.