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

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, this is a challenging problem. A method is proposed 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 data augmentation methods are used to draw imputations from a proper posterior distribution using Markov Chain Monte Carlo (MCMC). The performance of the proposed method is illustrated using simulation studies and on a data set taken from a breast feeding study.