ANOVA-PCA Analysis of Spectra Data
ANOVA-PCA is a combination of both methods developed by Harrington. The data is partitioned into submatrices corresponding to each experimental factor, which are then subjected to PCA separately after adding the residual error back. If the effect of a factor is large compared to the residual error, separation along the 1st PC in the score plot should be evident. With this method, the significance of a factor can be visually determined (ANOVA-PCA is not blind to group membership). ANOVA-PCA with only one factor is the same as standard PCA and gives no additional separation.
aov_pcaSpectra(spectra, fac)
A list of matrices for each factor and their interactions, along with the residual error and mean centered data matrix.
Matthew J. Keinsley and Bryan A. Hanson, DePauw University.
Pinto, Bosc, Nocairi, Barros, and Rutledge. "Using ANOVA-PCA for Discriminant Analysis: ..." Analytica Chimica Acta 629.1-2 (2008): 47-55.
Harrington, Vieira, Espinoza, Nien, Romero, and Yergey. "Analysis of Variance–Principal Component Analysis: ..." Analytica Chimica Acta 544.1-2 (2005): 118-27.
The output of this function is used in
used in aovPCAscores and aovPCAloadings.
Additional documentation at https://bryanhanson.github.io/ChemoSpec/
data(metMUD2)
# Original factor encoding:
levels(metMUD2$groups)
# Split those original levels into 2 new ones (re-code them)
new.grps <- list(geneBb = c("B", "b"), geneCc = c("C", "c"))
mM3 <- splitSpectraGroups(metMUD2, new.grps)
# run aov_pcaSpectra
mats <- aov_pcaSpectra(mM3, fac = c("geneBb", "geneCc"))
apca1 <- aovPCAscores(mM3, mats, plot = 1, main = "aovPCA: B vs b", ellipse = "cls")
apca2 <- aovPCAscores(mM3, mats, plot = 2, main = "aovPCA: C vs c")
apca3 <- aovPCAscores(mM3, mats, plot = 3, main = "aovPCA: Interaction Term")
apca4 <- aovPCAloadings(
spectra = mM3, LM = mats, pca = apca1,
main = "aov_pcaSpectra: Bb Loadings"
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