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

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  • Kropko, Jonathan
  • Goodrich, Ben
  • Gelman, Andrew
  • Hill, Jennifer

Abstract

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.

Suggested Citation

  • Kropko, Jonathan & Goodrich, Ben & Gelman, Andrew & Hill, Jennifer, 2014. "Multiple Imputation for Continuous and Categorical Data: Comparing Joint Multivariate Normal and Conditional Approaches," Political Analysis, Cambridge University Press, vol. 22(4), pages 497-519.
  • Handle: RePEc:cup:polals:v:22:y:2014:i:04:p:497-519_01
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    Cited by:

    1. Li, Chao & Zhang, Yuhan & Li, Xiang & Hao, Yanwei, 2024. "Artificial intelligence, household financial fragility and energy resources consumption: Impacts of digital disruption from a demand-based perspective," Resources Policy, Elsevier, vol. 88(C).
    2. Burns, Christopher & Prager, Daniel & Ghosh, Sujit & Goodwin, Barry, 2015. "Imputing for Missing Data in the ARMS Household Section: A Multivariate Imputation Approach," 2015 AAEA & WAEA Joint Annual Meeting, July 26-28, San Francisco, California 205291, Agricultural and Applied Economics Association.
    3. Josse, Julie & Husson, François, 2016. "missMDA: A Package for Handling Missing Values in Multivariate Data Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 70(i01).
    4. Jared S. Murray & Jerome P. Reiter, 2016. "Multiple Imputation of Missing Categorical and Continuous Values via Bayesian Mixture Models With Local Dependence," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1466-1479, October.
    5. Faisal Maqbool Zahid & Shahla Faisal & Christian Heumann, 2020. "Variable selection techniques after multiple imputation in high-dimensional data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(3), pages 553-580, September.
    6. Florian M. Hollenbach & Iavor Bojinov & Shahryar Minhas & Nils W. Metternich & Michael D. Ward & Alexander Volfovsky, 2021. "Multiple Imputation Using Gaussian Copulas," Sociological Methods & Research, , vol. 50(3), pages 1259-1283, August.

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