withinVariation: Within matrix decomposition for repeated measurements...
In mixOmics: Omics Data Integration Project

Description Usage Arguments Details Value Author(s) References See Also Examples

This function is internally called by pca, pls, spls, plsda and splsda functions for cross-over design data, but can be called independently prior to any kind of multivariate analyses.

1	withinVariation(X, design)

`X`	numeric matrix of predictors. `NA`s are allowed.
`design`	a numeric matrix or data frame. The first column indicates the repeated measures on each individual, i.e. the individuals ID. The 2nd and 3rd columns are to split the variation for a 2 level factor.

withinVariation function decomposes the Within variation in the X data set. The resulting Xw matrix is then input in the multilevel function.

One or two-factor analyses are available.

withinVariation simply returns the Xw within matrix, which can be input in the other multivariate approaches already implemented in mixOmics (i.e. spls or splsda, see multilevel, but also pca or ipca).

Benoit Liquet, Kim-Anh Lê Cao, Benoit Gautier, Ignacio González.

On multilevel analysis:

Liquet, B., Lê Cao, K.-A., Hocini, H. and Thiebaut, R. (2012) A novel approach for biomarker selection and the integration of repeated measures experiments from two platforms. BMC Bioinformatics 13:325.

Westerhuis, J. A., van Velzen, E. J., Hoefsloot, H. C., and Smilde, A. K. (2010). Multivariate paired data analysis: multilevel PLSDA versus OPLSDA. Metabolomics, 6(1), 119-128.

spls, splsda, plotIndiv, plotVar, cim, network.

## Example: one-factor analysis matrix decomposition
#--------------------------------------------------------------
data(vac18)
X <- vac18$genes
# in design we only need to mention the repeated measurements to split the one level variation
design <- data.frame(sample = vac18$sample)

Xw <- withinVariation(X = X, design = design)
# multilevel PCA
res.pca.1level <- pca(Xw, ncomp = 3)

# compare a normal PCA with a multilevel PCA for repeated measurements.
# note: PCA makes the assumptions that all samples are independent, 
# so this analysis is flawed and you should use a multilevel PCA instead
res.pca <- pca(X, ncomp = 3)

# set up colors for plotIndiv
col.stim <- c("darkblue", "purple", "green4","red3")
col.stim <- col.stim[as.numeric(vac18$stimulation)]

# plotIndiv comparing both PCA and PCA multilevel
plotIndiv(res.pca, ind.names = vac18$stimulation, group = col.stim)
title(main = 'PCA ')
plotIndiv(res.pca.1level, ind.names = vac18$stimulation, group = col.stim)
title(main = 'PCA multilevel')