Graphical and numerical diagnostic tools to assess multiple imputation models by posterior predictive checking

TL;DR

This paper introduces a posterior predictive checking method using graphical and numerical tools to diagnose the adequacy of multiple imputation models, ensuring they are suitable for the data and analysis.

Contribution

It proposes a new diagnostic approach based on posterior predictive checking to assess the compatibility of imputation models with the observed data.

Findings

The diagnostic method effectively detects model misspecification.

Simulation studies confirm the validity of the approach.

Application demonstrates practical utility in various missing data scenarios.

Abstract

Missing data are often dealt with multiple imputation. A crucial part of the multiple imputation process is selecting sensible models to generate plausible values for incomplete data. A method based on posterior predictive checking is proposed to diagnose imputation models based on posterior predictive checking. To assess the congeniality of imputation models, the proposed diagnostic method compares the observed data with their replicates generated under corresponding posterior predictive distributions. If the imputation model is congenial with the substantive model, the observed data are expected to be located in the centre of corresponding predictive posterior distributions. Simulation and application are designed to investigate the proposed diagnostic method for parametric and semi-parametric imputation approaches, continuous and discrete incomplete variables, univariate and multivariate missingness patterns. The results show the validity of the proposed diagnostic method.