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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.

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Paper provided by Department of Quantitative Social Science - UCL Institute of Education, University College London in its series DoQSS Working Papers with number 12-05.

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Date of creation: 29 Jun 2012
Date of revision:
Handle: RePEc:qss:dqsswp:1205
Contact details of provider: Postal: Department of Quantitative Social Science. UCL IOE, 20 Bedford Way London WC1H 0AL
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  1. Patrick Puhani & Andrea Weber, 2007. "Does the early bird catch the worm?," Empirical Economics, Springer, vol. 32(2), pages 359-386, May.
  2. 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.
  3. Lee Lillard & James P. Smith & Finis Welch, 2004. "What Do We Really Know About Wages: The Importance of Nonreporting and Census Imputation," Labor and Demography 0404005, EconWPA.
  4. Whitney Newey, 1999. "Two Step Series Estimation of Sample Selection Models," Working papers 99-04, Massachusetts Institute of Technology (MIT), Department of Economics.
  5. 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.
  6. Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-90, March.
  7. 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, 06.
  8. Little, Roderick J A, 1985. "A Note about Models for Selectivity Bias," Econometrica, Econometric Society, vol. 53(6), pages 1469-74, November.
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