PCA on the effect matrices — lmpPcaEffects • limpca

Performs a PCA on each of the effect matrices from the outputs of lmpEffectMatrices. It has an option to choose the method applied: ASCA, APCA or ASCA-E. Combined effects (i.e. linear combinations of original effect matrices) can also be created and decomposed by PCA.

Usage

lmpPcaEffects(
  resLmpEffectMatrices,
  method = c("ASCA", "APCA", "ASCA-E"),
  combineEffects = NULL,
  verbose = FALSE
)

Arguments

resLmpEffectMatrices: A resLmpEffectMatrices list resulting of lmpEffectMatrices.
method: The method used to compute the PCA. One of c("ASCA","APCA","ASCA-E").
combineEffects: If not NULL, a list of vectors containing the names of the effects to be combined.
verbose: If TRUE, will display a message with the duration of execution.

Value

A list with first,the PCA results from pcaBySvd for each effect matrix. Those results contain :

scores: Scores from the PCA for each principal component.
loadings: Loadings from the PCA for each principal component.
eigval: Eigenvalues of each principal component.
singvar: Singular values of each principal component.
var: Explained variances of each principal component.
cumvar: Cumulated explained variances of each principal component.
original.dataset: Original dataset.

There are also others outputs :

lmpDataList: The initial object: a list of outcomes, design and formula.
effectsNamesUnique: A character vector with the F+1 names of the model terms, each repeated once.
method: The dimension reduction method used: c("ASCA","APCA","ASCA-E").
type3SS: A vector with the type III SS for each model term.
variationPercentages: A vector with the percentage of variance explained by each model term.

Details

The function allows 3 different methods :

ASCA: PCA is applied directly on each pure effect matrix \(\hat{\mathbf{M}}_f, f=1...F\).
ASCA-E: PCA is applied on each pure effect matrix but then the augmented effect matrix is projected in the space of the ASCA components.
APCA: PCA is applied on each augmented effect matrix : \(\hat{\mathbf{M}}_f+\hat{\mathbf{E}}\).

References

Thiel M.,Feraud B. and Govaerts B. (2017) ASCA+ and APCA+: Extensions of ASCA and APCA in the analysis of unbalanced multifactorial designs. Journal of Chemometrics. 31:e2895. https://doi.org/10.1002/cem.2895

Examples

data("UCH")
resLmpModelMatrix <- lmpModelMatrix(UCH)
resLmpEffectMatrices <- lmpEffectMatrices(resLmpModelMatrix)
resLmpPcaEffects <- lmpPcaEffects(resLmpEffectMatrices, method = "ASCA-E")