Accounting for Regressor-Error Dependencies in Educational Data: A Bayesian Mixture Approach

27 Pages Posted: 16 Jul 2014

See all articles by Peter Ebbes

Peter Ebbes

HEC Paris - Marketing

Ulf Bockenholt

Northwestern University

Michel Wedel

University of Maryland - Robert H. Smith School of Business

Hyoryung Nam

Erasmus University Rotterdam (EUR)

Date Written: July 15, 2014

Abstract

Because frequently random assignment is not feasible in educational studies, our understanding of causal effects of student characteristics on academic performance has made little progress over the years. Omitted variables inducing correlations between regressors and error terms in multilevel data are a major hurdle. If the independence assumption of regressors and error components is not met, standard multilevel regression models yield biased and inconsistent results. This paper focusses on within-level regressor-error dependencies, caused by omitted variables, which are difficult to diagnose and remedy when additional data in the form of instrumental variables are not available. Specifically, we develop a multilevel mixture model that can account for correlations between regressor and error terms. The proposed approach allows for different specifications such as choice- or self-selection models. We present a flexible Bayesian estimation method that can be adapted easily to researchers' specific needs. Investigating the relationship between IQ and educational performance, we find empirical support for self-selection effects that distort substantially the observed relation between these measures.

Keywords: endogeneity, mixture model, fixed-effects estimator, random-effects estimator, omitted variables, regressor-error dependencies

Suggested Citation

Ebbes, Peter and Bockenholt, Ulf and Wedel, Michel and Nam, Hyoryung, Accounting for Regressor-Error Dependencies in Educational Data: A Bayesian Mixture Approach (July 15, 2014). Robert H. Smith School Research Paper No. RHS 2466533. Available at SSRN: https://ssrn.com/abstract=2466533 or http://dx.doi.org/10.2139/ssrn.2466533

Peter Ebbes (Contact Author)

HEC Paris - Marketing ( email )

Paris
France

Ulf Bockenholt

Northwestern University ( email )

2001 Sheridan Road
Evanston, IL 60208
United States

Michel Wedel

University of Maryland - Robert H. Smith School of Business ( email )

College Park, MD 20742-1815
United States

HOME PAGE: http://www.rhsmith.umd.edu/directory/michel-wedel

Hyoryung Nam

Erasmus University Rotterdam (EUR) ( email )

Burgemeester Oudlaan 50
3000 DR Rotterdam, Zuid-Holland 3062PA
Netherlands

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