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Uncertainty intervals for regression parameters with non-ignorable missingness in the outcome

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  • Minna Genbäck
  • Elena Stanghellini
  • Xavier Luna

Abstract

When estimating regression models with missing outcomes, scientists usually have to rely either on a missing at random assumption (missing mechanism is independent from the outcome given the observed variables) or on exclusion restrictions (some of the covariates affecting the missingness mechanism do not affect the outcome). Both these hypotheses are controversial in applications since they are typically not testable from the data. The alternative, which we pursue here, is to derive identification sets (instead of point identification) for the parameters of interest when allowing for a missing not at random mechanism. The non-ignorability of this mechanism is quantified with a parameter. When the latter can be bounded with a priori information, a bounded identification set follows. Our approach allows the outcome to be continuous and unbounded and relax distributional assumptions. Estimation of the identification sets can be performed via ordinary least squares and sampling variability can be incorporated yielding uncertainty intervals achieving a coverage of at least ( $$1-\alpha )$$ 1 - α ) probability. Our work is motivated by a study on predictors of body mass index (BMI) change in middle age men allowing us to identify possible predictors of BMI change even when assuming little on the missing mechanism. Copyright The Author(s) 2015

Suggested Citation

  • Minna Genbäck & Elena Stanghellini & Xavier Luna, 2015. "Uncertainty intervals for regression parameters with non-ignorable missingness in the outcome," Statistical Papers, Springer, vol. 56(3), pages 829-847, August.
    • Handle: RePEc:spr:stpapr:v:56:y:2015:i:3:p:829-847
    DOI: 10.1007/s00362-014-0610-x
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    References listed on IDEAS

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    Cited by:

    1. Fayyaz Bahari & Safar Parsi & Mojtaba Ganjali, 2021. "Empirical likelihood inference in general linear model with missing values in response and covariates by MNAR mechanism," Statistical Papers, Springer, vol. 62(2), pages 591-622, April.
    2. Minna Genbäck & Nawi Ng & Elena Stanghellini & Xavier de Luna, 2018. "Predictors of decline in self-reported health: addressing non-ignorable dropout in longitudinal studies of aging," European Journal of Ageing, Springer, vol. 15(2), pages 211-220, June.
    3. Gorbach, Tetiana & de Luna, Xavier, 2018. "Inference for partial correlation when data are missing not at random," Statistics & Probability Letters, Elsevier, vol. 141(C), pages 82-89.
    4. Marco Doretti & Martina Raggi & Elena Stanghellini, 2022. "Exact parametric causal mediation analysis for a binary outcome with a binary mediator," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(1), pages 87-108, March.
    5. Anita Lindmark, 2022. "Sensitivity analysis for unobserved confounding in causal mediation analysis allowing for effect modification, censoring and truncation," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(4), pages 785-814, October.
    6. Fayyaz Bahari & Safar Parsi & Mojtaba Ganjali, 2021. "Goodness of fit test for general linear model with nonignorable missing on response variable," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(1), pages 163-196, March.
    7. Emmanuel O. Ogundimu, 2022. "Regularization and variable selection in Heckman selection model," Statistical Papers, Springer, vol. 63(2), pages 421-439, April.

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