odis {rchemo}

Orthogonal distances from a PCA or PLS score space

Description

odis calculates the orthogonal distances (OD = "X-residuals") for a PCA or PLS model. OD is the Euclidean distance of a row observation to its projection to the score plan (see e.g. Hubert et al. 2005, Van Branden & Hubert 2005, p. 66; Varmuza & Filzmoser, 2009, p. 79).

A distance cutoff is computed using a moment estimation of the parameters of a Chi-squared distribution for OD^2 (see Nomikos & MacGregor 1995, and Pomerantzev 2008). In the function output, column dstand is a standardized distance defined as OD / cutoff. A value dstand > 1 can be considered as extreme.

The cutoff for detecting extreme OD values is computed using a moment estimation of a Chi-squared distrbution for the squared distance.

Usage

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

Arguments

object

A fitted model, output of a call to a fitting function.

Xtrain

Training X-data that was used to fit the model.

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 distance and a standardized distance calculated for Xtrain.

res

matrix with distance and a standardized distance calculated for X.

cutoff

distance cutoff computed using a moment estimation of the parameters of a Chi-squared distribution for OD^2.

References

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

Nomikos, P., MacGregor, J.F., 1995. Multivariate SPC Charts for Monitoring Batch Processes. null 37, 41-59. https://doi.org/10.1080/00401706.1995.10485888

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

K. Vanden Branden, M. Hubert (2005). Robuts classification in high dimension based on the SIMCA method. Chem. Lab. Int. Syst, 79, 10-21.

K. Varmuza, P. Filzmoser (2009). Introduction to multivariate statistical analysis in chemometrics. CRC Press, Boca Raton.

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)
odis(fm, Xtrain)
odis(fm, Xtrain, nlv = 2)
odis(fm, Xtrain, X = Xtest, nlv = 2)