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Reducing bias due to missing values of the response variable by joint modeling with an auxiliary variable


  • Alfonso Miranda

    () (Department of Quantitative Social Science, Institute of Education, University of London. 20 Bedford Way, London WC1H 0AL, UK.)

  • Sophia Rabe-Hesketh

    () (Graduate School of Education and Graduate Group in Biostatistics, University of California, Berkeley, USA. Institute of Education, University of London, London, UK.)

  • John W. McDonald

    () (Department of Quantitative Social Science, Institute of Education, University of London. 20 Bedford Way, London WC1H 0AL, UK.)


In this paper, we consider the problem of missing values of a continuous response variable that cannot be assumed to be missing at random. The example considered here is an analysis of pupil's subjective engagement at school using longitudinal survey data, where the engagement score from wave 3 of the survey is missing due to a combination of attrition and item non-response. If less engaged students are more likely to drop out and less likely to respond to questions regarding their engagement, then missingness is not ignorable and can lead to inconsistent estimates. We suggest alleviating this problem by modelling the response variable jointly with an auxiliary variable that is correlated with the response variable and not subject to non-response. Such auxiliary variables can be found in administrative data, in our example, the National Pupil Database containing test scores from national achievement tests. We estimate a joint model for engagement and achievement to reduce the bias due to missing values of engagement. A Monte Carlo study is performed to compare our proposed multivariate response approach with alternative approaches such as the Heckman selection model and inverse probability of selection weighting.

Suggested Citation

  • Alfonso Miranda & Sophia Rabe-Hesketh & John W. McDonald, 2012. "Reducing bias due to missing values of the response variable by joint modeling with an auxiliary variable," DoQSS Working Papers 12-05, Department of Quantitative Social Science - UCL Institute of Education, University College London.
  • Handle: RePEc:qss:dqsswp:1205

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    References listed on IDEAS

    1. Lillard, Lee & Smith, James P & Welch, Finis, 1986. "What Do We Really Know about Wages? The Importance of Nonreporting and Census Imputation," Journal of Political Economy, University of Chicago Press, vol. 94(3), pages 489-506, June.
    2. Patrick Puhani & Andrea Weber, 2007. "Does the early bird catch the worm?," Empirical Economics, Springer, vol. 32(2), pages 359-386, May.
    3. Puhani, Patrick A, 2000. " The Heckman Correction for Sample Selection and Its Critique," Journal of Economic Surveys, Wiley Blackwell, vol. 14(1), pages 53-68, February.
    4. Lorraine Dearden & Alfonso Miranda & Sophia Rabeā€Hesketh, 2011. "Measuring School Value Added with Administrative Data: The Problem of Missing Variables," Fiscal Studies, Institute for Fiscal Studies, vol. 32(2), pages 263-278, June.
    5. Little, Roderick J A, 1985. "A Note about Models for Selectivity Bias," Econometrica, Econometric Society, vol. 53(6), pages 1469-1474, November.
    6. Whitney K. Newey, 2009. "Two-step series estimation of sample selection models," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages 217-229, January.
    7. Francis Vella, 1998. "Estimating Models with Sample Selection Bias: A Survey," Journal of Human Resources, University of Wisconsin Press, vol. 33(1), pages 127-169.
    8. Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-390, March.
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    More about this item


    Auxiliary variable; joint model; multivariate regression; not missing at random; sample selection bias; seemingly-unrelated regressions; selection model; SUR;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • I21 - Health, Education, and Welfare - - Education - - - Analysis of Education

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