scordis {rchemo}

Score distances (SD) in a PCA or PLS score space

Description

scordis calculates the score distances (SD) for a PCA or PLS model. SD is the Mahalanobis distance of the projection of a row observation on the score plan to the center of the score space.

A distance cutoff is computed using a moment estimation of the parameters of a Chi-squared distrbution for SD^2 (see e.g. Pomerantzev 2008). In the function output, column dstand is a standardized distance defined as SD / cutoff. A value dstand > 1 can be considered as extreme.

The Winisi "GH" is also provided (usually considered as extreme if GH > 3).

Usage

scordis(
    object, X = NULL, 
    nlv = NULL,
    rob = TRUE, alpha = .01
    )

Arguments

object

A fitted model, output of a call to a fitting function (for example from pcasvd, plskern,...).

X

New X-data.

nlv

Number of components (PCs or LVs) to consider.

rob

Logical. If TRUE, the moment estimation of the distance cutoff is robustified. This can be recommended after robust PCA or PLS on small data sets containing extreme values.

alpha

Risk-I level for defining the cutoff detecting extreme values.

Value

res.train

matrix with distances, standardized distances and Winisi "GH", for the training set.

res

matrix with distances, standardized distances and Winisi "GH", for new X-data if any.

cutoff

cutoff value

References

M. Hubert, P. J. Rousseeuw, K. Vanden Branden (2005). ROBPCA: a new approach to robust principal components analysis. Technometrics, 47, 64-79.

Pomerantsev, A.L., 2008. Acceptance areas for multivariate classification derived by projection methods. Journal of Chemometrics 22, 601-609. https://doi.org/10.1002/cem.1147

Examples

n <- 6 ; p <- 4
Xtrain <- matrix(rnorm(n * p), ncol = p)
ytrain <- rnorm(n)
Xtest <- Xtrain[1:3, , drop = FALSE] 

nlv <- 3
fm <- pcasvd(Xtrain, nlv = nlv)
scordis(fm)
scordis(fm, nlv = 2)
scordis(fm, Xtest, nlv = 2)