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A Comparison of Joint Model and Fully Conditional Specification Imputation for Multilevel Missing Data

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  • Stephen A. Mistler

    (SAS Institute)

  • Craig K. Enders

    (University of California, Los Angeles)

Abstract

Multiple imputation methods can generally be divided into two broad frameworks: joint model (JM) imputation and fully conditional specification (FCS) imputation. JM draws missing values simultaneously for all incomplete variables using a multivariate distribution, whereas FCS imputes variables one at a time from a series of univariate conditional distributions. In single-level multivariate normal data, these two approaches have been shown to be equivalent, but less is known about their similarities and differences with multilevel data. This study examined four multilevel multiple imputation approaches: JM approaches proposed by Schafer and Yucel and Asparouhov and Muthén and FCS methods described by van Buuren and Carpenter and Kenward. Analytic work and computer simulations showed that Asparouhov and Muthén and Carpenter and Kenward methods are most flexible, as they produce imputations that preserve distinct within- and between-cluster covariance structures. As such, these approaches are applicable to random intercept models that posit level-specific relations among variables (e.g., contextual effects analyses, multilevel structural equation models). In contrast, methods from Schafer and Yucel and van Buuren are more restrictive and impose implicit equality constraints on functions of the within- and between-cluster covariance matrices. The analytic work and simulations underscore the conclusion that researchers should not expect to obtain the same results from alternative imputation routines. Rather, it is important to choose an imputation method that partitions variation in a manner that is consistent with the analysis model of interest. A real data analysis example illustrates the various approaches.

Suggested Citation

  • Stephen A. Mistler & Craig K. Enders, 2017. "A Comparison of Joint Model and Fully Conditional Specification Imputation for Multilevel Missing Data," Journal of Educational and Behavioral Statistics, , vol. 42(4), pages 432-466, August.
  • Handle: RePEc:sae:jedbes:v:42:y:2017:i:4:p:432-466
    DOI: 10.3102/1076998617690869
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    References listed on IDEAS

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    1. Joseph L. Schafer, 2003. "Multiple Imputation in Multivariate Problems When the Imputation and Analysis Models Differ," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 57(1), pages 19-35, February.
    2. Carpenter, James R. & Goldstein, Harvey & Kenward, Michael G., 2011. "REALCOM-IMPUTE Software for Multilevel Multiple Imputation with Mixed Response Types," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 45(i05).
    3. Yongyun Shin & Stephen W. Raudenbush, 2010. "A Latent Cluster-Mean Approach to the Contextual Effects Model With Missing Data," Journal of Educational and Behavioral Statistics, , vol. 35(1), pages 26-53, February.
    4. Yongyun Shin & Stephen W. Raudenbush, 2007. "Just-Identified Versus Overidentified Two-Level Hierarchical Linear Models with Missing Data," Biometrics, The International Biometric Society, vol. 63(4), pages 1262-1268, December.
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