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

  • Jonathan Kropko (a1), Ben Goodrich (a2), Andrew Gelman (a3) and Jennifer Hill (a4)


We consider the relative performance of two common approaches to multiple imputation (MI): joint multivariate normal (MVN) MI, in which the data are modeled as a sample from a joint MVN distribution; and conditional MI, in which each variable is modeled conditionally on all the others. In order to use the multivariate normal distribution, implementations of joint MVN MI typically assume that categories of discrete variables are 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 data sets. These simulations consider continuous, binary, ordinal, and unordered-categorical variables. One set of simulations uses multivariate normal data, and one set uses data from the 2008 American National Election Studies. We implement a less restrictive approach than is typical when evaluating methods using simulations in the missing data literature: in each case, missing values are generated by carefully following the conditions necessary for missingness to be “missing at random” (MAR). We find that in these situations conditional MI is more accurate than joint MVN MI whenever the data include categorical variables.


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Authors' note: An earlier version of this study was presented at the Annual Meeting of the Society for Political Methodology, Chapel Hill, NC, July 20, 2012. Replication code and data are available on the Political Analysis Dataverse, and the full citation to the replication material is included in the references. We thank Yu-sung Su, Yajuan Si, Sonia Torodova, Jingchen Liu, Michael Malecki, and two anonymous reviewers for their comments.



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