Investigating Some Imputation Methods of Multivariate Imputation Chained Equations


This paper investigates three MICE methods: Predictive Mean Matching (PMM), Quantile Regression-based Multiple Imputation (QR-basedMI) and Simple Random Sampling Imputation (SRSI) at imputation numbers 5, 15, 20 and 30 with 5% and 20% missing values, to ascertain the one that produces imputed values that best matches the observed values and compare the model fit based on the AIC and MSE. The results show that; QR-basedMI produced more imputed values that didn’t match the observed, SRSI produced imputed values that match the observed values better as the number of imputations increases while PMM produced imputed values that matched the observed at all number of imputations and missingness considered. The model fit results for 5% missingness showed that QR-basedMI produced the best results in terms of MSE except for M=15, while AIC results showed that PMM produced best result for M= 5, QR-basedMI produced best results for M=15 and for M=20 and 30 SRSI produced the best results. The model fit results for 20% missingness shows that PMM produced the best results at all the number of imputations considered for both AIC and MSE except the AIC at M=15 where SRSI was seen to produce the best results. It is concluded that in comparison, the PMM is most suited when missingness is 20% but for 5% missingness the model fit is best with QR-basedMI.

  1. Graham JW. Missing data analysis: making it work in the real world. Annu Rev Psychol. 2009; 60(1): 549-576.  |   Google Scholar
  2. Hyun K. The prevention and handling of the missing data. Korean J Anesthesiol. 2013; 64(5): 402–406.  |   Google Scholar
  3. Nwakuya MT, Nwabueze JC. Investigating the effects of imputation numbers on variance of estimates. European Journal of Physical and Agricultural Sciences. 2016; 4(2): 31-37.  |   Google Scholar
  4. Rubin DB. Inference and missing data. Biometrika. 1976; 63: 581–592.  |   Google Scholar
  5. Van Buuren S, Boshuizen HC, Knook DL. Multiple imputation of missing blood pressure covariates in survival analysis. Statistics in Medicine. 1999; 18(3): 681–694.  |   Google Scholar
  6. Schafer JL, Olsen MK. Multiple imputation for multivariate missing data problems: A data analyst’s perspective. Multivariate Behavioral Research. 1998; 33: 545–571.  |   Google Scholar
  7. Huque MH, Carlin JB, Simpson JA. A comparison of multiple imputation methods for missing data in longitudinal studies. BMC Med Res Methodol. 2018; 18: 168.  |   Google Scholar
  8. Van-Buuren S, Brand JP, Groothuis-Oudshoorn C, Rubin DB. Fully conditional specification in multivariate imputation. J Stat Comput Simul. 2006; 76(12): 1049–64.  |   Google Scholar
  9. Schafer JL, Graham JW. Missing data: our view of the state of the art. Psychological Methods. 2002; 7: 147–177.  |   Google Scholar
  10. Azur MJ, Stuart EA, Frangakis C, Leaf PJ. Multiple imputation by chained equations: what is it and how does it work?. International Journal of Methods of Psychiatrics Research. 2011; 20(1): 40-49.  |   Google Scholar
  11. Koenker R. Quantile regression. Cambridge University Press. 2005: 5-14.  |   Google Scholar
  12. Rubin DB. Statistical matching using file concatenation with adjusted weights and multiple imputations. Journal of Business & Economic Statistics. 1986; 4: 87–94.  |   Google Scholar
  13. Little RJA. A Test of Missing Completely at Random for Multivariate Data with Missing Values. Journal of the American Statistical Association. 1988; 83: 1198-1202.  |   Google Scholar
  14. Kristian K, Markus F, Mark S, Jost R, Friedrich L. Quantile Regression-Based Multiple Imputation of Missing Values — An Evaluation and Application to Corporal Punishment Data. Methodology. 2021; 17(3): 205–230.  |   Google Scholar
  15. Vink G, Frank, LE, Pannekoek J, Van-Buuren S. Predictive mean matching imputation of semicontinuous variables. Statistica Neerlandica. 2014; 68(1): 61-90.  |   Google Scholar
  16. Yuan CY. Multiple Imputation for Missing Data: Concepts and New Development. SAS Institute Inc., Rockville, MD. 2005 85–130.  |   Google Scholar

How to Cite

Nwakuya, M. T., & Biu, E. O. (2022). Investigating Some Imputation Methods of Multivariate Imputation Chained Equations. European Journal of Mathematics and Statistics, 3(3), 13–20.

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 M. T. Nwakuya
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 E. O. Biu
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