withinVariation {mixOmics} | R Documentation

## Within matrix decomposition for repeated measurements (cross-over design)

### Description

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.

### Usage

    withinVariation(X, design)

### Arguments

`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.

### Details

`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.

### Value

`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).

### Author(s)

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

### References

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.

### See Also

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

### Examples

    ## 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')

[Package mixOmics version 6.6.2 Index]