Advertisement

Comparison of Nested Models for Multiply Imputed Data

  • Yoonsun JangEmail author
  • Zhenqiu (Laura) Lu
  • Allan Cohen
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 89)

Abstract

The multiple imputation (MI) is one of the most popular and efficient methods to deal with missing data. For MI, the estimated parameters from imputed data sets are combined based on the Rubin’s rule; however, there are no general suggestions on how to combine the log-likelihood functions. The log-likelihood is a key component for model fit statistics. This study compares different ways to combine likelihood functions when MI is used for hierarchically nested models. Specifically, three ways for pooling likelihoods and four weights for combined log-likelihood value suggested by Kientoff are compared. Simulation studies are conducted to investigate the performance of these methods under six conditions, such as different sample sizes, different missing rates, and different numbers of parameters. We imputed missing data using the multiple imputation by chained equations for MI.

References

  1. Allison PD (2002) Missing data. Sage, Los AngeleszbMATHGoogle Scholar
  2. Asparouhov T, Muthen B (2010) Chi-square statistics with multiple imputation. Technical Report. https://www.statmodel.com/download/MI7.pdf
  3. Azur MJ, Stuart EA, Frangakis C, Leaf PJ (2011) Multiple imputation by chained equations: what is it and how does it work? Int J Methods Psychiatr Res 20(1):40–49CrossRefGoogle Scholar
  4. Bradley JV (1978) Robustness? Br J Math Stat Psychol 31:144–152CrossRefGoogle Scholar
  5. Busemeyer JR, Wang YM (2000) Model comparison and model selections based on generalization criterion methodology. J Math Psychol 44:171–189CrossRefzbMATHGoogle Scholar
  6. Davey A (2005) Issues in evaluating model fit with missing data. Struct Equ Modeling 12(4): 578–597CrossRefMathSciNetGoogle Scholar
  7. Enders CK (2010) Applied missing data analysis. The Guilford Press, New YorkGoogle Scholar
  8. Enders CK(2011) Analyzing longitudinal data with missing values. Rehabil Psychol 56(4): 264–288CrossRefGoogle Scholar
  9. Goldstein H (2011) Multilevel statistical models. Wiley, LondonzbMATHGoogle Scholar
  10. Hox JJ (2002) Multilevel analysis techniques and applications. Erlbaum, MahwahzbMATHGoogle Scholar
  11. Kientoff CJ (2011) Development of weighted model fit indexes for structural equation models using multiple imputation. Doctoral dissertation. http://lib.dr.iastate.edu/etd/
  12. LaHuis DM, Ferguson MW (2009) The accuracy of significant tests for slope variance components in multilevel random coefficient models. Organ Res Methods 12(3):418–435CrossRefGoogle Scholar
  13. Lee T, Chi L (2012) Alternative multiple imputation inference for mean and covariance structure modeling. J Educ Behav Stat 37(6):675–702CrossRefGoogle Scholar
  14. Li KH, Raghunathan TE, Rubin DB (1991) Large-sample significance levels from multiply imputed data using moment-based statistics and an F reference distribution. J Am Stat Assoc 86(416):1065–1073MathSciNetGoogle Scholar
  15. Little RJA, Rubin DB (2002) Statistical analysis with missing data. Wiley-Interscience, New YorkCrossRefzbMATHGoogle Scholar
  16. Meng XL, Rubin DB (1992) Performing likelihood ratio tests with multiply-imputed data sets. Biometrika 79(1):103–111CrossRefzbMATHMathSciNetGoogle Scholar
  17. R Development Core Team (2008) R: a language and environment for statistical computing. R-Foundation for Statistical Computing. ISBN 3-900051-07-0. http://www.R-project.org
  18. Singer JD, Willett JB (2003) Applied longitudinal data analysis: modeling change and event occurrence. Oxford University Press, New YorkCrossRefGoogle Scholar
  19. Snijders TAB, Bosker RJ (2012) Multilevel analysis: an introduction to basic and advanced multilevel modeling. Sage, Los AngelesGoogle Scholar
  20. van Buuren S (2011) Multiple imputation of multilevel data. In: Hox JJ, Roberts JK (eds) The handbook of advanced multilevel analysis. Routledge, Milton park, pp 173–196Google Scholar
  21. van Buuren S, Groothuis-Oudshoorn K (2011) Mice: multivariate imputation by chained equations in R. J Stat Softw 45(3):1–67Google Scholar
  22. Wayman JC (2003) Multiple imputation for missing data: what is it and how can I use it? Paper presented at the 2003 annual meeting of the American Educational Research Association, ChicagoGoogle Scholar
  23. Yuan YC (2000) Multiple imputation for missing data: concepts and new development. SUGI Proceedings http://support.sas.com/rnd/app/stat/papers/multipleimputation.pdf

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Yoonsun Jang
    • 1
    Email author
  • Zhenqiu (Laura) Lu
    • 2
  • Allan Cohen
    • 3
  1. 1.The University of Georgia, 126H Aderhold HallThe University of GeorgiaAthensUSA
  2. 2.The University of Georgia, 325V Aderhold HallThe University of GeorgiaAthensUSA
  3. 3.The University of Georgia, 125 Aderhold HallThe University of GeorgiaAthensUSA

Personalised recommendations