Top

Advances in Data Analysis and Classification

Published in:

01-03-2016 | Regular Article

A principal component method to impute missing values for mixed data

Authors: Vincent Audigier, François Husson, Julie Josse

Published in: Advances in Data Analysis and Classification | Issue 1/2016

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

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.

previous article Editorial for issue 1/2016

next article Extreme logistic regression

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Benzécri JP (1973) L’analyse des données. L’analyse des correspondances. Dunod, Tome II

Breiman L (2001) Random forests. Mach Learn 45(1):5–32CrossRefMATH

Bro R, Kjeldahl K, Smilde AK, Kiers HAL (2008) Cross-validation of component model: a critical look at current methods. Anal Bioanal Chem 390:1241–1251CrossRef

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 Raton

de Leeuw J, Mair P (2009) Gifi methods for optimal scaling in R: The package homals. J Statist Software 31(4):1–20, URL http://www.jstatsoft.org/v31/i04/

Escofier B (1979) Traitement simultané de variables quantitatives et qualitatives en analyse factorielle. Les cahiers de l’analyse des données 4(2):137–146

Gifi A (1990) Nonlinear multivariate analysis. Wiley, ChichesterMATH

Greenacre M, Blasius J (2006) Multiple correspondence analysis and related methods. Chapman and Hall/CRC.

Husson F, Josse J (2012) missMDA: Handling missing values with/in multivariate data analysis (principal component methods). URL http://www.agrocampus-ouest.fr/math/husson, r package version 1.4

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 http://dl.acm.org/citation.cfm?id=1859890.1859917

Josse J, Husson F (2011) Selecting the number of components in PCA using cross-validation approximations. Comput Statist Data Anal 56(6):1869–1879CrossRefMathSciNet

Josse J, Husson F (2012) Handling missing values in exploratory multivariate data analysis methods. Journal de la Société Française de Statistique 153(2):1–21MathSciNet

Josse J, Pagès J, Husson F (2009) Gestion des données manquantes en analyse en composantes principales. Journal de la Société Française de Statistique 150:28–51MATH

Josse J, Chavent M, Liquet B, Husson F (2012) Handling missing values with regularized iterative multiple correspondence analysis. J Classif 29:91–116CrossRefMathSciNet

Kiers HAL (1991) Simple structure in component analysis techniques for mixtures of qualitative and quantitative variables. Psychometrika 56:197–212CrossRefMathSciNetMATH

Kiers HAL (1997) Weighted least squares fitting using ordinary least squares algorithms. Psychometrika 62:251–266CrossRefMathSciNetMATH

Lafaye de Micheaux P, Drouilhet R, Liquet B (2011) Le logiciel R. Springer, ParisCrossRefMATH

Lang DT, Swayne D, Wickham H, Lawrence M (2012) rggobi: Interface between R and GGobi. URL http://CRAN.R-project.org/package=rggobi, r package version 2.1.19

Lebart L, Morineau A, Werwick KM (1984) Multivariate descriptive statistical analysis. Wiley, New YorkMATH

Little RJA, Rubin DB (1987, 2002) Statistical analysis with missing data. Wiley series in probability and statistics, New York

Mazumder R, Hastie T, Tibshirani R (2010) Spectral regularization algorithms for learning large incomplete matrices. J Mach Learn Res 11:2287–2322MathSciNetMATH

Michailidis G, de Leeuw J (1998) The Gifi system of descriptive multivariate analysis. Statist Sci 13(4):307–336CrossRefMathSciNetMATH

Peters A, Hothorn T (2012) ipred: Improved Predictors. URL http://CRAN.R-project.org/package=ipred, R package version 0.9-1

R Development Core Team (2011) R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria, URL http://www.R-project.org/, ISBN 3-900051-07-0

Rubin DB (1976) Inference and missing data. Biometrika 63:581–592CrossRefMathSciNetMATH

Schafer JL (1997) Analysis of incomplete multivariate data. Chapman and Hall/CRC, LondonCrossRefMATH

Stekhoven D, Bühlmann P (2011) Missforest - nonparametric missing value imputation for mixed-type data. Bioinformatics 28:113–118

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 50:91–119CrossRefMathSciNetMATH

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):520–525CrossRef

van Buuren S (2007) Multiple imputation of discrete and continuous data by fully conditional specification. Statist Method Med Res 16:219–242CrossRefMATH

van Buuren S, Boshuizen H, Knook D (1999) Multiple imputation of missing blood pressure covariates in survival analysis. Statist Med 18:681–694CrossRef

van der Heijden P, Escofier B (2003) Multiple correspondence analysis with missing data. In: Analyse des correspondances, Presse universitaire de Rennes, pp 153–170

Vermunt JK, van Ginkel JR, van der Ark LA, Sijtsma K (2008) Multiple imputation of incomplete categorical data using latent class analysis. Sociol Methodol 33:369–397

Title: A principal component method to impute missing values for mixed data
Authors: Vincent Audigier
François Husson
Julie Josse
Publication date: 01-03-2016
Publisher: Springer Berlin Heidelberg
Published in: Advances in Data Analysis and Classification / Issue 1/2016
Print ISSN: 1862-5347
Electronic ISSN: 1862-5355
DOI: https://doi.org/10.1007/s11634-014-0195-1

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Other articles of this Issue 1/2016

Supervised clustering of variables

A multilevel finite mixture item response model to cluster examinees and schools

Extreme logistic regression

Editorial for issue 1/2016

A comparison of reliability coefficients for psychometric tests that consist of two parts

The -means algorithm for 3D shapes with an application to apparel design

Premium Partner