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Multiple Imputation: Application

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Applied Multiple Imputation

Part of the book series: Statistics for Social and Behavioral Sciences ((SSBS))

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Abstract

In this chapter, we discuss the most important and most commonly used multiple imputation tools in R (Table 5.1 gives an overview of the download frequencies of various MI packages in R.) for both multivariate and clustered data sets, including packages mice, norm2, Amelia, mi, pan, as well as function aregImpute( ) from package Hmisc, and show practical applications. We give hands-on step by step tutorials regarding how to carry out MI in practice.

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Notes

  1. 1.

    Table 5.1 gives an overview of the download frequencies of various MI packages in R.

  2. 2.

    Note that classical zero-inflation models allow two sources of zeros. They can stem either from the zero-process or from the count process. A highly similar model class (so-called hurdle models) allows only one source of zeros. These models fit a zero-truncated Poisson or negative binomial model for the count process.

  3. 3.

    From today’s perspective, a more appropriate model would have been the zero-inflated negative binomial model, which allows to estimate a dispersion parameter (Hilbe, 2011). However, this model was not available in standard SEM software like Mplus (Muthén & Muthén, 2017) at that time.

  4. 4.

    To keep computation times of the examples in this book low, we only estimate and report the ‘fixed’ part of the model, i.e., we assume variances and covariances of the latent growth factors to be zero. Hence, η ij = α j for all i, j.

  5. 5.

    File crim4.dat can be found in subdirectory ‘data’ in the supplementary material of the book. To be able to reproduce the examples in the book, we ask readers to set the pathname of the supplementary material as working directory using the setwd( ) function.

  6. 6.

    The output of the md.pairs( ) function is a list of four components named rr, rm, mr, and mm. These components can be accessed using the $ operator. See help( "md.pairs") for details.

  7. 7.

    Reinecke and Weins (2013) have split the zero-inflated count variables into zero vs. non-zero indicators and zero-truncated count variables. They imputed both variables jointly under the multivariate normal model.

  8. 8.

    To reduce simulation error due to small numbers of imputations, we will create m = 100 sets of imputations in all applications throughout this book (see, for example, the recommendations by Graham et al., 2007 or Bodner, 2008). Even with modern computers, this can take a considerable amount of time, especially when imputation models are more complex. To reproduce the examples within a reasonable amount of time, readers could set the number of imputations to 5. Additionally, all sets of imputations are available from the supplementary material of the book.

  9. 9.

    Sometimes the term ‘plausibility’ refers to imputations that lead to valid statistical inferences. In our context, the true parameters are unknown. Here we regard imputations as plausible if they meet our expectations about these values and their distributions, based on what we know about the data set and based on the underlying theory. For the CrimoC data, for example, we can expect boys and students from Hauptschule to receive higher delinquency scores on average.

  10. 10.

    At the time of writing, the most recent version 1.0-9.5 of the norm package was published in February 2013.

  11. 11.

    Panel data however could be imputed in wide format, which would implicitly consider the longitudinal information (for a discussion, see Sect. 5.6.3.1).

  12. 12.

    We once again would like to caution applied researchers to use normal model MI after transformation on highly non-normal data. Transformations and roundings were applied in the past, when more appropriate strategies and models were not yet available.

  13. 13.

    Note that emNorm( ) produces maximum likelihood estimates of the mean vector and covariance matrix of the variables in the model, which can also be directly used as input for further statistical analyses (e.g., structural equation models).

  14. 14.

    https://cran.r-project.org/package=Amelia. Descriptions of the algorithm, and detailed documentation of the software may be found at the project website https://gking.harvard.edu/amelia.

  15. 15.

    https://cran.r-project.org/package=mi.

  16. 16.

    https://cran.r-project.org/web/packages/mi/vignettes/mi_vignette.pdf.

  17. 17.

    https://cran.r-project.org/package=Hmisc.

  18. 18.

    See Sect. 5.2.2 for details about the growth curve ZIP model. Note that the intercept of the zero model has been fixed to zero (cf. Muthén & Muthén, 2017, Example 6.7). See Sects. 5.5.1–5.5.4 for details about the respective imputation methods and models that are used to create the multiple imputations.

  19. 19.

    Shortcomings of some imputation techniques or consequences of misspecifications in simple data sets are discussed in de Jong et al. (2016) or He and Raghunathan (2009).

  20. 20.

    Graham (2009) also recommends to keep the total number of variables in the imputation model below 100.

  21. 21.

    An exception is the statistical package Stata. See the FAQ document ‘How can I account for clustering when creating imputations with mi impute?’, https://www.stata.com/support/faqs/statistics/clustering-and-mi-impute/.

  22. 22.

    Additional R packages like miceadds or countimp provide further two-level imputation functions for the mice framework.

  23. 23.

    In the supplementary material of the book, we provide R code to extract the imputed data sets from the mids object and to write the data to disk for further analysis in Mplus.

  24. 24.

    An introduction to the lavaan syntax may be found at Yves Rosseel’s website http://lavaan.ugent.be/.

  25. 25.

    Another option would be to use functions from package semTools, which we introduce in Sect. 5.7.7.5.

  26. 26.

    https://cran.r-project.org/package=glmmTMB.

  27. 27.

    More precisely, we average the Fisher-Z-transformed correlations and then, in a second step, bring the mean of these transformed correlations back to the original scale (see, for example, Schafer, 1997, for details on how to pool correlation coefficients). Functions cor2fisher( ) and fisher2cor( ) , which we use for the transformation and back-transformation are available from the supplementary material of the book.

  28. 28.

    For further details, see the help files of functions abind( ) and apply( ) .

  29. 29.

    https://github.com/glmmTMB/glmmTMB/blob/master/glmmTMB/R/family.R

  30. 30.

    https://cran.r-project.org/package=miceadds.

  31. 31.

    For further information, see option mimic="Mplus" in lavaan (https://cran.r-project.org/web/packages/lavaan/lavaan.pdf).

  32. 32.

    The transformation of imputed data lists that were created by other packages to an object of class mids is described in Sect. 5.7.

  33. 33.

    Instead of a simple MCAR mechanism, applied researchers could also simulate more complex and more realistic MAR or MNAR mechanisms that are believed to be present in the empirical data.

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Authors and Affiliations

  1. Department of Education Studies and Psychology, University of Siegen, Siegen, Germany

    Kristian Kleinke

  2. Faculty of Sociology, University of Bielefeld, Bielefeld, Germany

    Jost Reinecke

  3. University of Hamburg, Institute of Psychology, Hamburg, Germany

    Daniel Salfrán & Martin Spiess

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  1. Kristian Kleinke
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  2. Jost Reinecke
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  4. Martin Spiess
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Kleinke, K., Reinecke, J., Salfrán, D., Spiess, M. (2020). Multiple Imputation: Application. In: Applied Multiple Imputation. Statistics for Social and Behavioral Sciences. Springer, Cham. https://doi.org/10.1007/978-3-030-38164-6_5

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