A principal component method to impute missing values for mixed data

  • Vincent Audigier
  • François HussonEmail author
  • Julie Josse
Regular Article


We propose a new method to impute missing values in mixed data sets. It is based on a principal component method, the factorial analysis for mixed data, which balances the influence of all the variables that are continuous and categorical in the construction of the principal components. Because the imputation uses the principal axes and components, the prediction of the missing values is based on the similarity between individuals and on the relationships between variables. The properties of the method are illustrated via simulations and the quality of the imputation is assessed using real data sets. The method is compared to a recent method (Stekhoven and Buhlmann Bioinformatics 28:113–118, 2011) based on random forest and shows better performance especially for the imputation of categorical variables and situations with highly linear relationships between continuous variables.


Missing values Mixed data Imputation Principal component method Factorial analysis of mixed data 

Mathematics Subject Classification



  1. Benzécri JP (1973) L’analyse des données. L’analyse des correspondances. Dunod, Tome IIGoogle Scholar
  2. Breiman L (2001) Random forests. Mach Learn 45(1):5–32CrossRefzbMATHGoogle Scholar
  3. Bro R, Kjeldahl K, Smilde AK, Kiers HAL (2008) Cross-validation of component model: a critical look at current methods. Anal Bioanal Chem 390:1241–1251CrossRefGoogle Scholar
  4. Cornillon PA, Guyader A, Husson F, Jégou N, Josse J, Kloareg M, Matzner-Løber E, Rouvière L (2012) R for Statistics. Chapman and Hall/CRC, Boca RatonGoogle Scholar
  5. de Leeuw J, Mair P (2009) Gifi methods for optimal scaling in R: The package homals. J Statist Software 31(4):1–20, URL
  6. Escofier B (1979) Traitement simultané de variables quantitatives et qualitatives en analyse factorielle. Les cahiers de l’analyse des données 4(2):137–146Google Scholar
  7. Gifi A (1990) Nonlinear multivariate analysis. Wiley, ChichesterzbMATHGoogle Scholar
  8. Greenacre M, Blasius J (2006) Multiple correspondence analysis and related methods. Chapman and Hall/CRC.Google Scholar
  9. Husson F, Josse J (2012) missMDA: Handling missing values with/in multivariate data analysis (principal component methods). URL, r package version 1.4
  10. Ilin A, Raiko T (2010) Practical approaches to principal component analysis in the presence of missing values. J Mach Learn Res 99:1957–2000, URL
  11. Josse J, Husson F (2011) Selecting the number of components in PCA using cross-validation approximations. Comput Statist Data Anal 56(6):1869–1879CrossRefMathSciNetGoogle Scholar
  12. Josse J, Husson F (2012) Handling missing values in exploratory multivariate data analysis methods. Journal de la Société Française de Statistique 153(2):1–21MathSciNetGoogle Scholar
  13. Josse J, Pagès J, Husson F (2009) Gestion des données manquantes en analyse en composantes principales. Journal de la Société Française de Statistique 150:28–51zbMATHGoogle Scholar
  14. Josse J, Chavent M, Liquet B, Husson F (2012) Handling missing values with regularized iterative multiple correspondence analysis. J Classif 29:91–116CrossRefMathSciNetGoogle Scholar
  15. Kiers HAL (1991) Simple structure in component analysis techniques for mixtures of qualitative and quantitative variables. Psychometrika 56:197–212CrossRefMathSciNetzbMATHGoogle Scholar
  16. Kiers HAL (1997) Weighted least squares fitting using ordinary least squares algorithms. Psychometrika 62:251–266CrossRefMathSciNetzbMATHGoogle Scholar
  17. Lafaye de Micheaux P, Drouilhet R, Liquet B (2011) Le logiciel R. Springer, ParisCrossRefzbMATHGoogle Scholar
  18. Lang DT, Swayne D, Wickham H, Lawrence M (2012) rggobi: Interface between R and GGobi. URL, r package version 2.1.19
  19. Lebart L, Morineau A, Werwick KM (1984) Multivariate descriptive statistical analysis. Wiley, New YorkzbMATHGoogle Scholar
  20. Little RJA, Rubin DB (1987, 2002) Statistical analysis with missing data. Wiley series in probability and statistics, New YorkGoogle Scholar
  21. Mazumder R, Hastie T, Tibshirani R (2010) Spectral regularization algorithms for learning large incomplete matrices. J Mach Learn Res 11:2287–2322MathSciNetzbMATHGoogle Scholar
  22. Michailidis G, de Leeuw J (1998) The Gifi system of descriptive multivariate analysis. Statist Sci 13(4):307–336CrossRefMathSciNetzbMATHGoogle Scholar
  23. Peters A, Hothorn T (2012) ipred: Improved Predictors. URL, R package version 0.9-1
  24. R Development Core Team (2011) R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria, URL, ISBN 3-900051-07-0
  25. Rubin DB (1976) Inference and missing data. Biometrika 63:581–592CrossRefMathSciNetzbMATHGoogle Scholar
  26. Schafer JL (1997) Analysis of incomplete multivariate data. Chapman and Hall/CRC, LondonCrossRefzbMATHGoogle Scholar
  27. Stekhoven D, Bühlmann P (2011) Missforest - nonparametric missing value imputation for mixed-type data. Bioinformatics 28:113–118Google Scholar
  28. Tenenhaus M, Young FW (1985) An analysis and synthesis of multiple correspondence analysis, optimal scaling, dual scaling, homogeneity analysis and other methods for quantifying categorical multivariate data. Psychometrika 50:91–119CrossRefMathSciNetzbMATHGoogle Scholar
  29. Troyanskaya O, Cantor M, Sherlock G, Brown P, Hastie T, Tibshirani R, Botstein D, Altman RB (2001) Missing value estimation methods for DNA microarrays. Bioinformatics 17(62001):520–525CrossRefGoogle Scholar
  30. van Buuren S (2007) Multiple imputation of discrete and continuous data by fully conditional specification. Statist Method Med Res 16:219–242CrossRefzbMATHGoogle Scholar
  31. van Buuren S, Boshuizen H, Knook D (1999) Multiple imputation of missing blood pressure covariates in survival analysis. Statist Med 18:681–694CrossRefGoogle Scholar
  32. van der Heijden P, Escofier B (2003) Multiple correspondence analysis with missing data. In: Analyse des correspondances, Presse universitaire de Rennes, pp 153–170Google Scholar
  33. Vermunt JK, van Ginkel JR, van der Ark LA, Sijtsma K (2008) Multiple imputation of incomplete categorical data using latent class analysis. Sociol Methodol 33:369–397Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Vincent Audigier
    • 1
  • François Husson
    • 1
    Email author
  • Julie Josse
    • 1
  1. 1.Agrocampus OuestRennesFrance

Personalised recommendations