R: Compute evaluation criteria for PLS, sPLS, PLS-DA, sPLS-DA,...

perf {mixOmics} | R Documentation

## Compute evaluation criteria for PLS, sPLS, PLS-DA, sPLS-DA, MINT and DIABLO

### Description

Function to evaluate the performance of the fitted PLS, sparse PLS, PLS-DA, sparse PLS-DA, MINT (mint.splsda) and DIABLO (block.splsda) models using various criteria.

### Usage

    ## S3 method for class 'pls'
    perf(object,validation = c("Mfold", "loo"),
               folds = 10, progressBar = TRUE, ...)

    ## S3 method for class 'spls'
    perf(object,validation = c("Mfold", "loo"),
              folds = 10, progressBar = TRUE, ...)

    ## S3 method for class 'plsda'
    perf(object,
              dist = c("all", "max.dist", "centroids.dist", "mahalanobis.dist"),
              validation = c("Mfold", "loo"),
              folds = 10, nrepeat =1, auc = FALSE, progressBar = TRUE, cpus, ...)

    ## S3 method for class 'splsda'
    perf(object,
    dist = c("all", "max.dist", "centroids.dist", "mahalanobis.dist"),
    validation = c("Mfold", "loo"),
    folds = 10, nrepeat =1, auc = FALSE, progressBar = TRUE, cpus, ...)

    ## S3 method for class 'mint.splsda'
    perf(object,
                dist = c("all", "max.dist", "centroids.dist", "mahalanobis.dist"),
                auc = FALSE, progressBar = TRUE, ...)

    ## S3 method for class 'sgccda'
    perf(object,
                dist = c("all", "max.dist", "centroids.dist", "mahalanobis.dist"),
                validation = c("Mfold", "loo"),
                folds = 10, nrepeat =1, cpus, ...)

### Arguments

`object` | object of class inheriting from `"pls"`, `"plsda"`, `"spls"`, `"splsda"` or `"mint.splsda"`. The function will retrieve some key parameters stored in that object.
`dist` | only applies to an object inheriting from `"plsda"`, `"splsda"` or `"mint.splsda"` to evaluate the classification performance of the model. Should be a subset of `"max.dist"`, `"centroids.dist"`, `"mahalanobis.dist"`. Default is `"all"`. See `predict`.
`validation` | character. What kind of (internal) validation to use, matching one of `"Mfold"` or `"loo"` (see below). Default is `"Mfold"`.
`folds` | the folds in the Mfold cross-validation. See Details.
`nrepeat` | Number of times the Cross-Validation process is repeated. This is an important argument to ensure the estimation of the performance to be as accurate as possible.
`auc` | if `TRUE` calculate the Area Under the Curve (AUC) performance of the model.
`progressBar` | by default set to `TRUE` to output the progress bar of the computation.
`cpus` | Number of cpus to use when running the code in parallel.
`...` | not used

### Details

Procedure. The process of evaluating the performance of a fitted model `object` is similar for all PLS-derived methods; a cross-validation approach is used to fit the method of `object` on `folds-1` subsets of the data and then to predict on the subset left out. Different measures of performance are available depending on the model. Parameters such as `logratio`, `multilevel`, `keepX` or `keepY` are retrieved from `object`.

Parameters. If `validation = "Mfold"`, M-fold cross-validation is performed. `folds` specifies the number of folds to generate. The folds also can be supplied as a list of vectors containing the indexes defining each fold as produced by `split`. When using `validation = "Mfold"`, make sure that you repeat the process several times (as the results will be highly dependent on the random splits and the sample size).

If `validation = "loo"`, leave-one-out cross-validation is performed (in that case, there is no need to repeat the process).

Measures of performance. For fitted PLS and sPLS regression models, `perf` estimates the mean squared error of prediction (MSEP), R^2, and Q^2 to assess the predictive perfity of the model using M-fold or leave-one-out cross-validation. Note that only the `classic`, `regression` and `invariant` modes can be applied. For sPLS, the MSEP, R^2, and Q^2 criteria are averaged across all folds. The `Q2.total` combines the Q^2 values for each Y variable and provides an overall assessment of fit. According to Tenenhaus (1998) the rule of thumb to decide whether a component contributes significantly to the prediction is when its Q2.total is still greater than 0.0975. However whe dealing with a large number of variables, especially in X, we have often experienced Q2.total values that do not decrease. The sPLS method also may not reach this cutoff, depending on the type of data and problem. Note that for PLS and sPLS objects, perf is performed on the pre-processed data after log ratio transform and multilevel analysis, when applied.

Sparse methods. The sPLS, sPLS-DA and sgccda functions are run on several and different subsets of data (the cross-folds) and will certainly lead to different subset of selected features. Those are summarised in the output `features$stable` (see output Value below) to assess how often the variables are selected across all folds. Note that for PLS-DA and sPLS-DA objects, perf is performed on the original data, i.e. before the pre-processing step of the log ratio transform and multilevel analysis, if any. In addition for these methods, the classification error rate is averaged across all folds.

The mint.sPLS-DA function estimates errors based on Leave-one-group-out cross validation (where each levels of object$study is left out (and predicted) once) and provides study-specific outputs (`study.specific.error`) as well as global outputs (`global.error`).

AUROC. For PLS-DA, sPLS-DA, mint.PLS-DA and mint.sPLS-DA methods: if `auc=TRUE`, Area Under the Curve (AUC) values are calculated from the predicted scores obtained from the `predict` function applied to the internal test sets in the cross-validation process, either for all samples or for study-specific samples (for mint models). Therefore we minimise the risk of overfitting. See `auroc` for more details. Our multivariate supervised methods already use a prediction threshold based on distances (see `predict`) that optimally determine class membership of the samples tested. As such AUC and ROC are not needed to estimate the performance of the model. We provide those outputs as complementary performance measures. See more details in our mixOmics article.

Prediction distances. See details from `?predict`, and also our supplemental material in the mixOmics article.

Repeats of the CV-folds. Repeated cross-validation implies that the whole CV process is repeated a number of times (`nrepeat`) to reduce variability across the different subset partitions. In the case of Leave-One-Out CV (`validation = 'loo'`), each sample is left out once (`folds = N` is set internally) and therefore nrepeat is by default 1.

BER is appropriate in case of an unbalanced number of samples per class as it calculates the average proportion of wrongly classified samples in each class, weighted by the number of samples in each class. BER is less biased towards majority classes during the performance assessment.

More details about the PLS modes in `?pls`.

### Value

For PLS and sPLS models, `perf` produces a list with the following components:

`MSEP` | Mean Square Error Prediction for each Y variable, only applies to object inherited from `"pls"`, and `"spls"`.
`R2` | a matrix of R^2 values of the Y-variables for models with 1, … ,`ncomp` components, only applies to object inherited from `"pls"`, and `"spls"`.
`Q2` | if Y containts one variable, a vector of Q^2 values else a list with a matrix of Q^2 values for each Y-variable. Note that in the specific case of an sPLS model, it is better to have a look at the Q2.total criterion, only applies to object inherited from `"pls"`, and `"spls"`
`Q2.total` | a vector of Q^2-total values for models with 1, … ,`ncomp` components, only applies to object inherited from `"pls"`, and `"spls"`
`features` | a list of features selected across the folds (`$stable.X` and `$stable.Y`) for the `keepX` and `keepY` parameters from the input object.
`error.rate` | For PLS-DA and sPLS-DA models, `perf` produces a matrix of classification error rate estimation. The dimensions correspond to the components in the model and to the prediction method used, respectively. Note that error rates reported in any component include the performance of the model in earlier components for the specified `keepX` parameters (e.g. error rate reported for component 3 for `keepX = 20` already includes the fitted model on components 1 and 2 for `keepX = 20`). For more advanced usage of the `perf` function, see www.mixomics.org/methods/spls-da/ and consider using the `predict` function.
`auc` | Averaged AUC values over the `nrepeat`

For mint.splsda models, `perf` produces the following outputs:

`study.specific.error` | A list that gives BER, overall error rate and error rate per class, for each study
`global.error` | A list that gives BER, overall error rate and error rate per class for all samples
`predict` | A list of length `ncomp` that produces the predicted values of each sample for each class
`class` | A list which gives the predicted class of each sample for each `dist` and each of the `ncomp` components. Directly obtained from the `predict` output.
`auc` | AUC values
`auc.study` | AUC values for each study

For sgccda models, `perf` produces the following outputs:

`error.rate` | Prediction error rate for each block of `object$X` and each `dist`
`error.rate.per.class` | Prediction error rate for each block of `object$X`, each `dist` and each class
`predict` | Predicted values of each sample for each class, each block and each component
`class` | Predicted class of each sample for each block, each `dist`, each component and each nrepeat
`features` | a list of features selected across the folds (`$stable.X` and `$stable.Y`) for the `keepX` and `keepY` parameters from the input object.
`AveragedPredict.class` | if more than one block, returns the average predicted class over the blocks (averaged of the `Predict` output and prediction using the `max.dist` distance)
`AveragedPredict.error.rate` | if more than one block, returns the average predicted error rate over the blocks (using the `AveragedPredict.class` output)
`WeightedPredict.class` | if more than one block, returns the weighted predicted class over the blocks (weighted average of the `Predict` output and prediction using the `max.dist` distance)
`WeightedPredict.error.rate` | if more than one block, returns the weighted average predicted error rate over the blocks (using the `WeightedPredict.class` output)
`MajorityVote` | if more than one block, returns the majority class over the blocks. NA for a sample means that there is no consensus on the predicted class for this particular sample over the blocks.
`MajorityVote.error.rate` | if more than one block, returns the error rate of the `MajorityVote` output
`WeightedVote` | if more than one block, returns the weighted majority class over the blocks. NA for a sample means that there is no consensus on the predicted class for this particular sample over the blocks.
`WeightedVote.error.rate` | if more than one block, returns the error rate of the `WeightedVote` output
`weights` | Returns the weights of each block used for the weighted predictions, for each nrepeat and each fold
`choice.ncomp` | For supervised models; returns the optimal number of components for the model for each prediction distance using one-sided t-tests that test for a significant difference in the mean error rate (gain in prediction) when components are added to the model. See more details in Rohart et al 2017 Suppl. For more than one block, an optimal ncomp is returned for each prediction framework.

### Author(s)

Ignacio González, Amrit Singh, Kim-Anh Lê Cao, Benoit Gautier, Florian Rohart.

### References

DIABLO:

Singh A., Gautier B., Shannon C., Vacher M., Rohart F., Tebbutt S. and Lê Cao K.A. (2016). DIABLO - multi omics integration for biomarker discovery.

mixOmics article:

Rohart F, Gautier B, Singh A, Lê Cao K-A. mixOmics: an R package for 'omics feature selection and multiple data integration. PLoS Comput Biol 13(11): e1005752

MINT:

Rohart F, Eslami A, Matigian, N, Bougeard S, Lê Cao K-A (2017). MINT: A multivariate integrative approach to identify a reproducible biomarker signature across multiple experiments and platforms. BMC Bioinformatics 18:128.

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

Chavent, Marie and Patouille, Brigitte (2003). Calcul des coefficients de regression et du PRESS en regression PLS1. Modulad n, 30 1-11. (this is the formula we use to calculate the Q2 in perf.pls and perf.spls)

Mevik, B.-H., Cederkvist, H. R. (2004). Mean Squared Error of Prediction (MSEP) Estimates for Principal Component Regression (PCR) and Partial Least Squares Regression (PLSR). Journal of Chemometrics 18(9), 422-429.

sparse PLS regression mode:

Lê Cao, K. A., Rossouw D., Robert-Granie, C. and Besse, P. (2008). A sparse PLS for variable selection when integrating Omics data. Statistical Applications in Genetics and Molecular Biology 7, article 35.

One-sided t-tests (suppl material):

Rohart F, Mason EA, Matigian N, Mosbergen R, Korn O, Chen T, Butcher S, Patel J, Atkinson K, Khosrotehrani K, Fisk NM, Lê Cao K-A&, Wells CA& (2016). A Molecular Classification of Human Mesenchymal Stromal Cells. PeerJ 4:e1845.

### See Also

`predict`, `nipals`, `plot.perf`, `auroc` and www.mixOmics.org for more details.

### Examples

    ## Not run:
    ## validation for objects of class 'pls' (regression)
    # ----------------------------------------
    data(liver.toxicity)
    X <- liver.toxicity$gene
    Y <- liver.toxicity$clinic

    # try tune the number of component to choose
    # ---------------------
    # first learn the full model
    liver.pls <- pls(X, Y, ncomp = 10)

    # with 5-fold cross validation: we use the same parameters as in model above
    # but we perform cross validation to compute the MSEP, Q2 and R2 criteria
    # ---------------------------
    liver.val <- perf(liver.pls, validation = "Mfold", folds = 5)

    # Q2 total should decrease until it reaches a threshold
    liver.val$Q2.total

    # ncomp = 2 is enough
    plot(liver.val$Q2.total, type = 'l', col = 'red', ylim = c(-0.5, 0.5),
    xlab = 'PLS components', ylab = 'Q2 total')
    abline(h = 0.0975, col = 'darkgreen')
    legend('topright', col = c('red', 'darkgreen'),
    legend = c('Q2 total', 'threshold 0.0975'), lty = 1)
    title('Liver toxicity PLS 5-fold, Q2 total values')

    #have a look at the other criteria
    # ----------------------
    # R2
    liver.val$R2
    matplot(t(liver.val$R2), type = 'l', xlab = 'PLS components', ylab = 'R2 for each variable')
    title('Liver toxicity PLS 5-fold, R2 values')

    # MSEP
    liver.val$MSEP
    matplot(t(liver.val$MSEP), type = 'l', xlab = 'PLS components', ylab = 'MSEP for each variable')
    title('Liver toxicity PLS 5-fold, MSEP values')

    ## validation for objects of class 'spls' (regression)
    # ----------------------------------------
    ncomp = 7
    # first, learn the model on the whole data set
    model.spls = spls(X, Y, ncomp = ncomp, mode = 'regression',
    keepX = c(rep(10, ncomp)), keepY = c(rep(4,ncomp)))

    # with leave-one-out cross validation
    ##set.seed(45)
    model.spls.val <- perf(model.spls, validation = "Mfold", folds = 5 )#validation = "loo")

    #Q2 total
    model.spls.val$Q2.total

    # R2:we can see how the performance degrades when ncomp increases
    model.spls.val$R2
    plot(model.spls.val, criterion="R2", type = 'l')
    plot(model.spls.val, criterion="Q2", type = 'l')

    ## validation for objects of class 'splsda' (classification)
    # ----------------------------------------
    data(srbct)
    X <- srbct$gene
    Y <- srbct$class

    ncomp = 2

    srbct.splsda <- splsda(X, Y, ncomp = ncomp, keepX = rep(10, ncomp))

    # with Mfold
    # ---------
    set.seed(45)
    error <- perf(srbct.splsda, validation = "Mfold", folds = 8,
    dist = "all", auc = TRUE)
    error
    error$auc

    plot(error)

    # parallel code
    set.seed(45)
    error <- perf(srbct.splsda, validation = "Mfold", folds = 8,
    dist = "all", auc = TRUE, cpus =2)

    \dontrun{
    # with 5 components and nrepeat =5, to get a $choice.ncomp
    ncomp = 5
    srbct.splsda <- splsda(X, Y, ncomp = ncomp, keepX = rep(10, ncomp))

    set.seed(45)
    error <- perf(srbct.splsda, validation = "Mfold", folds = 8,
    dist = "all", nrepeat =5)
    error

    plot(error)

    # parallel code
    set.seed(45)
    error <- perf(srbct.splsda, validation = "Mfold", folds = 8,
    dist = "all", auc = TRUE, cpus =2)

    }

    ## validation for objects of class 'mint.splsda' (classification)
    # ----------------------------------------

    data(stemcells)
    res = mint.splsda(X = stemcells$gene, Y = stemcells$celltype, ncomp = 3, keepX = c(10, 5, 15),
    study = stemcells$study)

    out = perf(res, auc = TRUE)
    out

    out$auc
    out$auc.study

    ## validation for objects of class 'sgccda' (classification)
    # ----------------------------------------

    data(nutrimouse)
    Y = nutrimouse$diet
    data = list(gene = nutrimouse$gene, lipid = nutrimouse$lipid)
    design = matrix(c(0,1,1,1,0,1,1,1,0), ncol = 3, nrow = 3, byrow = TRUE)

    nutrimouse.sgccda <- block.splsda(X=data,
    Y = Y,
    design = design,
    keepX = list(gene=c(10,10), lipid=c(15,15)),
    ncomp = 2,
    scheme = "horst")

    perf = perf(nutrimouse.sgccda)
    perf

    \dontrun{
    #with 5 components and nrepeat=5 to get $choice.ncomp
    nutrimouse.sgccda <- block.splsda(X=data,
    Y = Y,
    design = design,
    keepX = list(gene=c(10,10), lipid=c(15,15)),
    ncomp = 5,
    scheme = "horst")

    perf = perf(nutrimouse.sgccda, folds = 5, nrepeat = 5)
    perf

    perf$choice.ncomp
    }

    ## End(Not run)

[Package mixOmics version 6.3.2 Index]