Multiple Imputation for Continuous and Categorical Data: Comparing Joint and Conditional Approaches

We consider the relative performance of two common approaches to multiple imputation (MI): joint MI, in which the data are modeled as a sample from a joint distribution; and conditional MI, in which each variable is modeled conditionally on all the others. Implementations of joint MI are typically restricted in two ways: first, the joint distribution of the data is assumed to be multivariate normal, and second, in order to use the multivariate normal distribution, categories of discrete variables are assumed to be probabilistically constructed from continuous values. We use simulations to examine the implications of these assumptions. For each approach, we assess (1) the accuracy of the imputed values, and (2) the accuracy of coefficients and fitted values from a model fit to completed datasets. These simulations consider continuous, binary, ordinal, and unordered-categorical variables. One set of simulations ∗Corresponding author: [email protected]. We thank Yu-sung Su, Yajuan Si, Sonia Torodova, Jingchen Liu, and Michael Malecki, and two anonymous reviewers for their comments. An earlier version of this study was presented at the Annual Meeting of the Society for Political Methodology, Chapel Hill, NC, July 20, 2012.