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A principal component method to impute missing values for mixed data. (English) Zbl 1414.62206

Summary: 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.

MSC:

62H25 Factor analysis and principal components; correspondence analysis
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[1] Benzécri JP (1973) L’analyse des données. L’analyse des correspondances. Dunod, Tome II · Zbl 0297.62039
[2] Breiman L (2001) Random forests. Mach Learn 45(1):5-32 · Zbl 1007.68152 · doi:10.1023/A:1010933404324
[3] Bro R, Kjeldahl K, Smilde AK, Kiers HAL (2008) Cross-validation of component model: a critical look at current methods. Anal Bioanal Chem 390:1241-1251 · doi:10.1007/s00216-007-1790-1
[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 Raton
[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 http://www.jstatsoft.org/v31/i04/
[6] Escofier B (1979) Traitement simultané de variables quantitatives et qualitatives en analyse factorielle. Les cahiers de l’analyse des données 4(2):137-146
[7] Gifi A (1990) Nonlinear multivariate analysis. Wiley, Chichester · Zbl 0697.62048
[8] Greenacre M, Blasius J (2006) Multiple correspondence analysis and related methods. Chapman and Hall/CRC. · Zbl 1277.62156
[9] 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 · Zbl 1316.62006
[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 http://dl.acm.org/citation.cfm?id=1859890.1859917 · Zbl 1242.62047
[11] Josse J, Husson F (2011) Selecting the number of components in PCA using cross-validation approximations. Comput Statist Data Anal 56(6):1869-1879 · Zbl 1243.62082 · doi:10.1016/j.csda.2011.11.012
[12] Josse J, Husson F (2012) Handling missing values in exploratory multivariate data analysis methods. Journal de la Société Française de Statistique 153(2):1-21 · Zbl 1316.62006
[13] Josse J, Pagès J, Husson F (2009) Gestion des données manquantes en analyse en composantes principales. Journal de la Société Française de Statistique 150:28-51 · Zbl 1311.62091
[14] Josse J, Chavent M, Liquet B, Husson F (2012) Handling missing values with regularized iterative multiple correspondence analysis. J Classif 29:91-116 · Zbl 1360.62306 · doi:10.1007/s00357-012-9097-0
[15] Kiers HAL (1991) Simple structure in component analysis techniques for mixtures of qualitative and quantitative variables. Psychometrika 56:197-212 · Zbl 0850.62461 · doi:10.1007/BF02294458
[16] Kiers HAL (1997) Weighted least squares fitting using ordinary least squares algorithms. Psychometrika 62:251-266 · Zbl 0873.62058 · doi:10.1007/BF02295279
[17] Lafaye de Micheaux P, Drouilhet R, Liquet B (2011) Le logiciel R. Springer, Paris · Zbl 1216.68006 · doi:10.1007/978-2-8178-0115-5
[18] 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
[19] Lebart L, Morineau A, Werwick KM (1984) Multivariate descriptive statistical analysis. Wiley, New York · Zbl 0658.62069
[20] Little RJA, Rubin DB (1987, 2002) Statistical analysis with missing data. Wiley series in probability and statistics, New York
[21] Mazumder R, Hastie T, Tibshirani R (2010) Spectral regularization algorithms for learning large incomplete matrices. J Mach Learn Res 11:2287-2322 · Zbl 1242.68237
[22] Michailidis G, de Leeuw J (1998) The Gifi system of descriptive multivariate analysis. Statist Sci 13(4):307-336 · Zbl 1059.62551 · doi:10.1214/ss/1028905828
[23] Peters A, Hothorn T (2012) ipred: Improved Predictors. URL http://CRAN.R-project.org/package=ipred, 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 http://www.R-project.org/, ISBN 3-900051-07-0
[25] Rubin DB (1976) Inference and missing data. Biometrika 63:581-592 · Zbl 0344.62034 · doi:10.1093/biomet/63.3.581
[26] Schafer JL (1997) Analysis of incomplete multivariate data. Chapman and Hall/CRC, London · Zbl 0997.62510 · doi:10.1201/9781439821862
[27] Stekhoven D, Bühlmann P (2011) Missforest - nonparametric missing value imputation for mixed-type data. Bioinformatics 28:113-118
[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 50:91-119 · Zbl 0585.62104 · doi:10.1007/BF02294151
[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):520-525 · doi:10.1093/bioinformatics/17.6.520
[30] van Buuren S (2007) Multiple imputation of discrete and continuous data by fully conditional specification. Statist Method Med Res 16:219-242 · Zbl 1122.62382 · doi:10.1177/0962280206074463
[31] van Buuren S, Boshuizen H, Knook D (1999) Multiple imputation of missing blood pressure covariates in survival analysis. Statist Med 18:681-694 · doi:10.1002/(SICI)1097-0258(19990330)18:6<681::AID-SIM71>3.0.CO;2-R
[32] van der Heijden P, Escofier B (2003) Multiple correspondence analysis with missing data. In: Analyse des correspondances, Presse universitaire de Rennes, pp 153-170
[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 33:369-397
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