Multiply imputing missing values in data sets with mixed measurement scales using a sequence of generalised linear models

Abstract

Multiple imputation is a commonly used approach to deal with missing values. In this approach, an imputer repeatedly imputes the missing values by taking draws from the posterior predictive distribution for the missing values conditional on the observed values, and releases these completed data sets to analysts. With each completed data set the analyst performs the analysis of interest, treating the data as if it were fully observed. These analyses are then combined with standard combining rules, allowing the analyst to make appropriate inferences which take into account the uncertainty present due to the missing data. In order to preserve the statistical properties present in the data, the imputer must use a plausible distribution to generate the imputed values. In data sets containing variables with different measurement scales, e.g. some categorical and some continuous variables, Multivariate Imputation by Chained Equations (MICE) is a commonly used multiple imputation method. However, imputations from such an approach are not necessarily drawn from 1 a proper posterior predictive distribution. We propose a method to multiply impute missing values in such data sets by modelling the joint distribution of the variables in the data through a sequence of generalised linear models, and use data augmentation methods to draw imputations from a proper posterior distribution using Markov Chain Monte Carlo (MCMC). We compare the performance of our method with MICE using simulation studies and on a genuine data set taken from a breast feeding study.

A monotone data augmentation algorithm for multivariate nonnormal data: With applications to controlled imputations for longitudinal trials

“…19 It is unclear under what situations FCS works well, and its performance is mainly evaluated by simulations. The FCS can be slightly less efficient than the MCMC-based method, 16,23,57 and this is also observed in our numerical examples.…”

“…Tang 22 developed MDA algorithms for longitudinal binary and ordinal outcomes based respectively on a sequence of logistic regression and the multivariate probit model, and the latter approach is a type of Gaussian copula model. Lee and Mitra 23 proposed a full data augmentation algorithm for the sequential regression. It allows binary, ordinal, nominal, and continuous outcomes and models the binary and ordinal outcomes by the probit regression.…”

Multiple imputation for discrete data: Evaluation of the joint latent normal model

“…Other papers have compared JM‐MI with FCS‐MI with noncontinuous data in recent years, but most of these papers used different strategies for including categorical variables; for example, Lee and Mitra () used sequential generalized linear models, while (Wu, Jia, & Enders, ) used an ordered version of the latent normal model, which matches our model only for the imputation of binary variables. Other simulation studies made use of our latent normal approach to compare FCS‐MI and JM‐MI in specific settings, e.g.…”

Multiple Imputation: A Review of Practical and Theoretical Findings

“…Examples of this approach include (Lipsitz and Ibrahim, 1996;Ibrahim, Lipsitz and Chen, 1999;Ibrahim et al, 2005;Lee and Mitra, 2016;Xu, Daniels and Winterstein, 2016), among others.…”