pcamb_classic {SCOUTer}

pcamb_classic

Description

Principal Component Analysis (PCA) model fitting according to a matrix X using singular value decomposition (svd)

Usage

pcamb_classic(X, ncomp, alpha, prepro)

Arguments

X

Matrix with observations that will used to fit the PCA model.

ncomp

An integer indicating the number of PCs that the model will have.

alpha

A number between 0 and 1 indicating the type I risk assumed to calculate the Upper Control Limits (UCLs) for the Squared Prediction Error (SPE), the Hotelling's T^2_A and the scores. The confidence level of these limits will be (1-alpha)*100.

prepro

A string indicating the preprocessing to be performed on X. Its possible values are: "none", for any preprocessing, "cent", for a mean-centering, or "autosc", for a mean-centering and unitary variance scaling (autoscaling).

Value

list with elements containing information about PCA model:

• m: mean vector.

• s: standard deviation vector.

• P: loading matrix with the loadings of each PC stored as columns.

• Pfull: full loading matrix obtained by the svd,

• lambda: vector with the variance of each PC.

• limspe: Upper Control Limit for the SPE with a confidence level (1-alpha)*100 %.

• limt2: Upper Control Limit for the T^2_A with a confidence level (1-alpha)*100 %.

• limits_t: Upper control Limits for the scores with a confidence level (1-alpha)*100 %.

• prepro: string indicating the type of preprocessing performed on X.

• ncomp: number of PCs of the PCA model, A.

• alpha: value of the type I risk assumed to calculate the Upper Control Limits of the SPE, T^2_A and scores.

• n: dimension of the number of rows in X.

• S: covariance matrix of X.

Examples

X <- as.matrix(X)
pcamodel.ref <- pcamb_classic(X, 3, 0.1, "autosc") # PCA-MB with all observations
pcamodel.ref <- pcamb_classic(X[1:40,], 2, 0.05, "cent") # PCA-MB with first 40 
# observations