Nonignorable Missing Data, Single Index Propensity Score and Profile Synthetic Distribution Function

Abstract

In missing data problems, missing not at random is difficult to handle since the response probability or propensity score is confounded with the outcome data model in the likelihood. Existing works often assume the propensity score is known up to a finite dimensional parameter. We relax this assumption and consider an unspecified single index model for the propensity score. A pseudo-likelihood based on the complete data is constructed by profiling out a synthetic distribution function that involves the unknown propensity score. The pseudo-likelihood gives asymptotically normal estimates. Simulations show the method compares favorably with existing methods.

Keywords:

• Missing not at random
• Nonignorable missing
• Pseudo-conditional likelihood
• Single index model
• Synthetic distribution

Supplementary Materials

The proofs of the asymptotic properties are given in the Supplementary Materials.

Acknowledgments

The authors would like to thank an associate editor and two anonymous referees for comments and suggestions, that have led to a much improved article.

Additional information

Funding

Chen’s work was supported by the National Natural Science Foundation of China (NSFC) (11871402, 11931014) and the Fundamental Research Funds for the Central Universities (JBK1806002).