pls {mixOmics} | R Documentation

## Partial Least Squares (PLS) Regression

### Description

Function to perform Partial Least Squares (PLS) regression.

### Usage

    pls(
      X,
      Y,
      ncomp = 2,
      scale = TRUE,
      mode = c("regression", "canonical", "invariant", "classic"),
      tol = 1e-06,
      max.iter = 100,
      near.zero.var = FALSE,
      logratio = "none",
      multilevel = NULL,
      all.outputs = TRUE
    )

### Arguments

`X` | numeric matrix of predictors with the rows as individual observations. missing values (`NA`s) are allowed.
`Y` | numeric matrix of response(s) with the rows as individual observations matching `X`. missing values (`NA`s) are allowed.
`ncomp` | Positive Integer. The number of components to include in the model. Default to 2.
`scale` | Logical. If scale = TRUE, each block is standardized to zero means and unit variances (default: TRUE)
`mode` | Character string indicating the type of PLS algorithm to use. One of `"regression"`, `"canonical"`, `"invariant"` or `"classic"`. See Details.
`tol` | Positive numeric used as convergence criteria/tolerance during the iterative process. Default to `1e-06`.
`max.iter` | Integer, the maximum number of iterations. Default to 100.
`near.zero.var` | Logical, see the internal `nearZeroVar` function (should be set to TRUE in particular for data with many zero values). Setting this argument to FALSE (when appropriate) will speed up the computations. Default value is FALSE.
`logratio` | Character, one of ('none','CLR') specifies the log ratio transformation to deal with compositional values that may arise from specific normalisation in sequencing data. Default to 'none'. See `?logratio.transfo` for details.
`multilevel` | Numeric, design matrix for repeated measurement analysis, where multilevel decomposition is required. For a one factor decomposition, the repeated measures on each individual, i.e. the individuals ID is input as the first column. For a 2 level factor decomposition then 2nd AND 3rd columns indicate those factors. See examplesin `?spls`.
`all.outputs` | Logical. Computation can be faster when some specific (and non-essential) outputs are not calculated. Default = `TRUE`.

### Details

`pls` function fit PLS models with 1, … ,`ncomp` components. Multi-response models are fully supported. The `X` and `Y` datasets can contain missing values.

The type of algorithm to use is specified with the `mode` argument. Four PLS algorithms are available: PLS regression `("regression")`, PLS canonical analysis `("canonical")`, redundancy analysis `("invariant")` and the classical PLS algorithm `("classic")` (see References). Different modes relate on how the Y matrix is deflated across the iterations of the algorithms - i.e. the different components.

- Regression mode: the Y matrix is deflated with respect to the information extracted/modelled from the local regression on X. Here the goal is to predict Y from X (Y and X play an asymmetric role). Consequently the latent variables computed to predict Y from X are different from those computed to predict X from Y.

- Canonical mode: the Y matrix is deflated to the information extracted/modelled from the local regression on Y. Here X and Y play a symmetric role and the goal is similar to a Canonical Correlation type of analysis.

- Invariant mode: the Y matrix is not deflated

- Classic mode: is similar to a regression mode. It gives identical results for the variates and loadings associated to the X data set, but differences for the loadings vectors associated to the Y data set (different normalisations are used). Classic mode is the PLS2 model as defined by Tenenhaus (1998), Chap 9.

Note that in all cases the results are the same on the first component as deflation only starts after component 1.

### Value

`pls` returns an object of class `"pls"`, a list that contains the following components:

`X` | the centered and standardized original predictor matrix.
`Y` | the centered and standardized original response vector or matrix.
`ncomp` | the number of components included in the model.
`mode` | the algorithm used to fit the model.
`variates` | list containing the variates.
`loadings` | list containing the estimated loadings for the X and Y variates. The loading weights multiplied with their associated deflated (residual) matrix gives the variate.
`loadings.stars` | list containing the estimated weighted loadings for the X and Y variates. The loading weights are projected so that when multiplied with their associated original matrix we obtain the variate.
`names` | list containing the names to be used for individuals and variables.
`tol` | the tolerance used in the iterative algorithm, used for subsequent S3 methods
`iter` | Number of iterations of the algorithm for each component
`max.iter` | the maximum number of iterations, used for subsequent S3 methods
`nzv` | list containing the zero- or near-zero predictors information.
`scale` | whether scaling was applied per predictor.
`logratio` | whether log ratio transformation for relative proportion data was applied, and if so, which type of transformation.
`prop_expl_var` | The proportion of the variance explained by each variate / component divided by the total variance in the `data` (after removing the possible missing values) using the definition of 'redundancy'. Note that contrary to `PCA`, this amount may not decrease in the following components as the aim of the method is not to maximise the variance, but the covariance between data sets (including the dummy matrix representation of the outcome variable in case of the supervised approaches).
`input.X` | numeric matrix of predictors in X that was input, before any scaling / logratio / multilevel transformation.
`mat.c` | matrix of coefficients from the regression of X / residual matrices X on the X-variates, to be used internally by `predict`.
`defl.matrix` | residual matrices X for each dimension.

### missing values

The estimation of the missing values can be performed using the `impute.nipals` function. Otherwise, missing values are handled by element-wise deletion in the `pls` function without having to delete the rows with missing data.

### multilevel

Multilevel (s)PLS enables the integration of data measured on two different data sets on the same individuals. This approach differs from multilevel sPLS-DA as the aim is to select subsets of variables from both data sets that are highly positively or negatively correlated across samples. The approach is unsupervised, i.e. no prior knowledge about the sample groups is included.

### logratio and multilevel

logratio transform and multilevel analysis are performed sequentially as internal pre-processing step, through `logratio.transfo` and `withinVariation` respectively.

### Author(s)

Sébastien Déjean, Ignacio González, Florian Rohart, Kim-Anh Lê Cao, Al J Abadi

### References

Tenenhaus, M. (1998). La regression PLS: theorie et pratique. Paris: Editions Technic.

Wold H. (1966). Estimation of principal components and related models by iterative least squares. In: Krishnaiah, P. R. (editors), Multivariate Analysis. Academic Press, N.Y., 391-420.

Abdi H (2010). Partial least squares regression and projection on latent structure regression (PLS Regression). Wiley Interdisciplinary Reviews: Computational Statistics, 2(1), 97-106.

### See Also

`spls`, `summary`, `plotIndiv`, `plotVar`, `predict`, `perf` and http://www.mixOmics.org for more details.

### Examples

    data(linnerud)
    X <- linnerud$exercise
    Y <- linnerud$physiological
    linn.pls <- pls(X, Y, mode = "classic")

    ## Not run:
    data(liver.toxicity)
    X <- liver.toxicity$gene
    Y <- liver.toxicity$clinic
    toxicity.pls <- pls(X, Y, ncomp = 3)

    ## End(Not run)

[Package mixOmics version 6.14.1 Index]