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Semi-parametric regression when some (expensive) covariates are missing by design

Author

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  • Göran Kauermann

    (Ludwig-Maximilians-Universität München)

  • Mehboob Ali

    (Ludwig-Maximilians-Universität München)

Abstract

The paper deals with the scenario where some covariates are observed by design for a subset of the observations only. In the example treated in the paper this occurs with a two phase sampling scheme where in the first phase a relatively large sample is drawn to record a response variable Y and a set of (cheap) covariates x. In a second phase a smaller sample is drawn from the first phase sample where additional (usually expensive) covariates z are also recorded. The second phase can be drawn with unequal probability sampling, where the sampling weights depend on the observed Y and x. The overall intention is to fit a regression model of Y on both, x and z. Due to the design of the data collection we are faced with missing values for z for a majority of observations. We propose an approximate estimation approach using semi-parametric mean and variance regression of Y on x only and augment this fit with a full regression model of Y on x and z. The idea extends the approach of Little (1992) towards non-normal data and non-linear models. The proposed estimation is numerically rather simple and performs convincingly well in simulation studies compared to alternatives such as complete-case and multiple imputation analysis.

Suggested Citation

  • Göran Kauermann & Mehboob Ali, 2021. "Semi-parametric regression when some (expensive) covariates are missing by design," Statistical Papers, Springer, vol. 62(4), pages 1675-1696, August.
    • Handle: RePEc:spr:stpapr:v:62:y:2021:i:4:d:10.1007_s00362-019-01152-5
    DOI: 10.1007/s00362-019-01152-5
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    References listed on IDEAS

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    1. van Buuren, Stef & Groothuis-Oudshoorn, Karin, 2011. "mice: Multivariate Imputation by Chained Equations in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 45(i03).
    2. Horton, Nicholas J. & Kleinman, Ken P., 2007. "Much Ado About Nothing: A Comparison of Missing Data Methods and Software to Fit Incomplete Data Regression Models," The American Statistician, American Statistical Association, vol. 61, pages 79-90, February.
    3. Liang H. & Wang S. & Robins J.M. & Carroll R.J., 2004. "Estimation in Partially Linear Models With Missing Covariates," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 357-367, January.
    4. Qi-Hua Wang, 2009. "Statistical estimation in partial linear models with covariate data missing at random," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(1), pages 47-84, March.
    5. Liang, Hua, 2008. "Generalized partially linear models with missing covariates," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 880-895, May.
    6. J. F. Lawless & J. D. Kalbfleisch & C. J. Wild, 1999. "Semiparametric methods for response‐selective and missing data problems in regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 413-438, April.
    7. Guoyou Qin & Zhongyi Zhu & Wing Fung, 2012. "Robust estimation of the generalised partial linear model with missing covariates," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(2), pages 517-530.
    8. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, November.
    9. M. P. Wand, 2003. "Smoothing and mixed models," Computational Statistics, Springer, vol. 18(2), pages 223-249, July.
    10. Joseph G. Ibrahim & Ming-Hui Chen & Stuart R. Lipsitz & Amy H. Herring, 2005. "Missing-Data Methods for Generalized Linear Models: A Comparative Review," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 332-346, March.
    11. Bernd Fitzenberger & Benjamin Fuchs, 2017. "The Residency Discount for Rents in Germany and the Tenancy Law Reform Act 2001: Evidence from Quantile Regressions," German Economic Review, Verein für Socialpolitik, vol. 18(2), pages 212-236, May.
    12. Guangyu Zhang & Roderick Little, 2009. "Extensions of the Penalized Spline of Propensity Prediction Method of Imputation," Biometrics, The International Biometric Society, vol. 65(3), pages 911-918, September.
    13. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, November.
    14. Helge Toutenburg & Thomas Nittner, 2002. "Linear Regression Models with Incomplete Categorical Covariates," Computational Statistics, Springer, vol. 17(2), pages 215-232, July.
    15. Takumi Saegusa, 2015. "Variance Estimation under Two-Phase Sampling," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(4), pages 1078-1091, December.
    16. Inyoung Kim & Noah D. Cohen & Raymond J. Carroll, 2003. "Semiparametric Regression Splines in Matched Case-Control Studies," Biometrics, The International Biometric Society, vol. 59(4), pages 1158-1169, December.
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