estim_ncpPCA: Estimate the number of dimensions for the Principal Component...

In missMDA: Handling Missing Values with Multivariate Data Analysis

Estimate the number of dimensions for the Principal Component Analysis by cross-validation

Description

Estimate the number of dimensions for the Principal Component Analysis by cross-validation

Usage

estim_ncpPCA(X, ncp.min = 0, ncp.max = 5, method = c("Regularized","EM"), 
       scale = TRUE, method.cv = c("gcv","loo","Kfold"), nbsim = 100, 
	   pNA = 0.05, ind.sup=NULL, quanti.sup=NULL, quali.sup=NULL,
	   threshold=1e-4, verbose = TRUE)

Arguments

X	a data.frame with continuous variables; with missing entries or not
ncp.min	integer corresponding to the minimum number of components to test
ncp.max	integer corresponding to the maximum number of components to test
method	"Regularized" by default or "EM"
scale	boolean. TRUE implies a same weight for each variable
method.cv	string with the values "gcv" for generalised cross-validation, "loo" for leave-one-out or "Kfold" cross-validation
nbsim	number of simulations, useful only if method.cv="Kfold"
pNA	percentage of missing values added in the data set, useful only if method.cv="Kfold"
ind.sup	a vector indicating the indexes of the supplementary individuals
quanti.sup	a vector indicating the indexes of the quantitative supplementary variables
quali.sup	a vector indicating the indexes of the categorical supplementary variables
threshold	the threshold for assessing convergence
verbose	boolean. TRUE means that a progressbar is writtent

Details

For leave-one-out (loo) cross-validation, each cell of the data matrix is alternatively removed and predicted with a PCA model using ncp.min to ncp.max dimensions. The number of components which leads to the smallest mean square error of prediction (MSEP) is retained. For the Kfold cross-validation, pNA percentage of missing values is inserted and predicted with a PCA model using ncp.min to ncp.max dimensions. This process is repeated nbsim times. The number of components which leads to the smallest MSEP is retained.
For both cross-validation methods, missing entries are predicted using the imputePCA function, it means using the regularized iterative PCA algorithm (method="Regularized") or the iterative PCA algorithm (method="EM"). The regularized version is more appropriate when there are already many missing values in the dataset to avoid overfitting issues.
Cross-validation (especially method.cv="loo") is time-consuming. The generalised cross-validation criterion (method.cv="gcv") can be seen as an approximation of the loo cross-validation criterion which provides a straightforward way to estimate the number of dimensions without resorting to a computationally intensive method.

This argument scale has to be chosen in agreement with the PCA that will be performed. If one wants to perform a normed PCA (where the variables are centered and scaled, i.e. divided by their standard deviation), then the argument scale has to be set to the value TRUE.

Value

ncp	the number of components retained for the PCA
criterion	the criterion (the MSEP) calculated for each number of components

Author(s)

Francois Husson [e-mail] and Julie Josse [e-mail]

References

Bro, R., Kjeldahl, K. Smilde, A. K. and Kiers, H. A. L. (2008) Cross-validation of component models: A critical look at current methods. Analytical and Bioanalytical Chemistry, 5, 1241-1251.

Josse, J. and Husson, F. (2011). Selecting the number of components in PCA using cross-validation approximations. Computational Statistics and Data Analysis. 56 (6), pp. 1869-1879.

See Also

imputePCA

Examples

## Not run: 
data(orange)
nb <- estim_ncpPCA(orange,ncp.min=0,ncp.max=4) 

## End(Not run)

missMDA documentation built on Nov. 17, 2023, 5:07 p.m.