explained_variance {mixOmics} | R Documentation

## Calculates the proportion of explained variance of multivariate components

### Description

`explained_variance` calculates the proportion of variance explained by a set of *orthogonal* variates / components and divides by the total variance in `data` using the definition of 'redundancy'. This applies to any component-based approaches where components are orthogonal. It is worth noting that any missing values are set to zero (which is the column mean for the centered input data) prior to calculation of total variance in the data. Therefore, this function would underestimate the total variance in presence of abundant missing values. One can use `impute.nipals` function to impute the missing values to avoid such behaviour.

### Usage

    explained_variance(data, variates, ncomp)

### Arguments

`data` | numeric matrix of predictors
`variates` | variates as obtained from a `pls` object for instance
`ncomp` | number of components. Should be lower than the number of columns of `variates`

### Details

Variance explained by component t_h in X for dimension h:

Rd(X, t_h) = \frac{1}{p} ∑_{j = 1}^p \mbox{cor}^2(X^j, t_h)

where X^j is the variable centered and scaled, p is the total number of variables.

### Value

`explained_variance` returns a named numeric vector containing the proportion of explained variance for each variate after setting all missing values in the data to zero (see details).

### Author(s)

Florian Rohart, Kim-Anh Lê Cao, Al J Abadi

### References

Tenenhaus, M., La Régression PLS théorie et pratique (1998). Technip, Paris, chap2.

### See Also

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

### Examples

    data(liver.toxicity)
    X <- liver.toxicity$gene
    Y <- liver.toxicity$clinic

    toxicity.spls <- spls(X, Y, ncomp = 2, keepX = c(50, 50), keepY = c(10, 10))

    ex = explained_variance(toxicity.spls$X, toxicity.spls$variates$X, ncomp =2)

    # ex should be the same as
    toxicity.spls$prop_expl_var$X

[Package mixOmics version 6.16.3 Index]