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Copula selection models for non-Gaussian responses that are missing not at random

Gomes, M., Radice, R., Camarena Brenes, J. & Marra, G. (2019). Copula selection models for non-Gaussian responses that are missing not at random. Statistics in Medicine, 38(3), pp. 480-496. doi: 10.1002/sim.7988


Missing not at random (MNAR) data poses key challenges for statistical inference because the model of interest is typically not identifiable without imposing further (e.g., distributional) assumptions. Sample selection models have been routinely used for handling MNAR by jointly modelling the outcome and selection variables assuming that these follow a bivariate normal distribution. Recent studies have advocated parametric selection model approaches, for example estimated by multiple imputation and maximum likelihood, that are more robust to departures from the normality assumption. However, the proposed methods have been mostly restricted to a specific joint distribution (e.g., bivariate t-distribution). This paper discusses a flexible copula-based selection approach (which accommodates a wide range of non-Gaussian outcome distributions and offers great flexibility in the choice of functional form specifications for both the outcome and selection equations) and proposes a flexible imputation procedure that generates plausible imputed values from the copula selection model. A simulation study characterises the relative performance of the copula model compared with the most commonly used selection models for estimating average treatment effects with MNAR data. We illustrate the methods in the REFLUX study, which evaluates the causal effect of laparoscopic surgery compared to usual medical management on long-term quality of life in patients with reflux disease. We provide software code for implementing the proposed copula framework using the R package GJRM.

Publication Type: Article
Additional Information: This is the peer reviewed version of the following article: Gomes M, Radice R, Camarena Brenes J, Marra G. Copula selection models for nonGaussian outcomes that are missing not at random. Statistics in Medicine. 2019;38:480–496., which has been published in final form at This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.
Publisher Keywords: copula, joint model, missing not at random, multiple imputation, non-Gaussian outcome, selection model, simultaneous equation model
Subjects: H Social Sciences > HA Statistics
Departments: Bayes Business School > Actuarial Science & Insurance
SWORD Depositor:
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