Likelihood identifiability and parameter estimation with nonignorable missing data

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

View graph of relations


Related Research Unit(s)


Original languageEnglish
Journal / PublicationCanadian Journal of Statistics
Online published27 May 2022
Publication statusOnline published - 27 May 2022


We identify sufficient conditions to resolve the identification problem under nonignorable missingness, especially the identifiability of the observed likelihood when some of the covariate values are missing not at random, or, simultaneously, the response is also missing not at random. It is more difficult to tackle these cases than the nonignorable nonresponse case, and, to the best of our knowledge, the simultaneously missing case has never been discussed before. Under these conditions, we propose some parameter estimation methods. As an illustration, when some of the covariate values are missing not at random, we adopt a semiparametric logistic model with a tilting parameter to model the missingness mechanism and use an imputed estimating equation based on the generalized method of moments to estimate the parameters of interest and the tilting parameter simultaneously. This approach avoids the requirement for other independent surveys or a validation sample to estimate the unknown tilting parameter. The asymptotic properties of our proposed estimators are derived, and the proofs can be modified to show that our methods of estimation, which are based on inverse probability weighting, augmented inverse probability weighting, and estimating equation projection, have the same asymptotic efficiency when the tilting parameter is either known or unknown but estimated by some other method. In simulation studies, we compare our methods with various alternative approaches and find that our methods are more robust and effective.

Research Area(s)

  • Equivalent asymptotic efficiency, exponentially tilting, generalized method of moments, identifiability, nonignorable missingness, ESTIMATING EQUATIONS INFERENCE, GENERALIZED-METHOD, MODELS, REGRESSION, MOMENTS