caret plsda() in R: PLS Discriminant Analysis
The plsda() function in caret fits a partial least squares discriminant analysis model. It dummy-codes a factor outcome, fits PLS regression on the resulting indicator matrix, and returns a classifier that supports class and probability predictions, ideal for high-dimensional data where predictors outnumber rows.
plsda(x = iris[, 1:4], y = iris$Species, ncomp = 2) # basic fit plsda(x, y, ncomp = 3, probMethod = "softmax") # softmax probs (default) plsda(x, y, ncomp = 3, probMethod = "Bayes") # Bayes-rule probs plsda(x, y, ncomp = 5, prior = c(0.5, 0.3, 0.2)) # custom class priors predict(fit, newdata = x[1:5, ], type = "class") # predicted class predict(fit, newdata = x[1:5, ], type = "prob") # class probabilities splsda(x, y, ncomp = 3, keepX = c(5, 5, 5)) # sparse variant
Need explanation? Read on for examples and pitfalls.
What plsda() does in one sentence
plsda() is caret's wrapper around pls::plsr() for classification. You pass a numeric predictor matrix and a factor outcome, pick ncomp, and the function dummy-codes the response, fits a PLS model, and stores everything predict() needs to score new rows.
Ordinary LDA fails when predictors are collinear or when there are more predictors than rows. PLS-DA solves both by projecting predictors onto latent components that maximize covariance with the dummy-coded response, then classifies in that low-rank space.
plsda() syntax and arguments
The signature centers on three inputs: predictors x, factor outcome y, and the number of components ncomp. Everything else has reasonable defaults.
The full call shape is:
plsda(x, y, ncomp = 2, probMethod = "softmax", prior = NULL, ...)x: a numeric matrix or data frame of predictors, one column per feature. No factor columns allowed; dummy-code them first.y: a factor vector of class labels, same length asnrow(x).ncomp: the number of latent components retained. Defaults to 2; cap atmin(nrow(x), ncol(x)).probMethod: how class probabilities are computed from the dummy-coded predictions."softmax"(default) is the simple normalization;"Bayes"fits per-class normal densities vianaiveBayes().prior: optional named or unnamed numeric vector of class priors. Defaults to empirical frequencies....: extra arguments passed to the underlyingpls::plsr()call, includingmethod = "kernelpls"or"simpls".
plsda() always returns an object that inherits from mvr (the pls package class). Anything that works on a pls regression fit (scores(), loadings(), coef()) also works on a plsda fit, which is useful for inspecting the latent space directly.plsda() examples by use case
1. Fit a basic PLS-DA classifier on iris
The shortest call uses the four numeric iris features to separate the three species. With only 4 predictors, two components capture nearly all the discriminant signal.
The returned object stores the fitted PLS model, the response, and the chosen probMethod. Use scores(fit) to see how species separate in the 2D component space, the standard PLS-DA diagnostic.
2. Predict classes and probabilities
predict.plsda() mirrors the convention of other caret model objects. Use type = "class" for hard predictions and type = "prob" for the softmax probability matrix.
The probability matrix is three-dimensional because predict() can return scores for multiple ncomp values at once. The third dimension labels the component count. Collapse it by indexing predict(...)[, , "2 comps"].
3. Tune ncomp by holding out a test set
The single dial worth turning on PLS-DA is ncomp. Too few components underfit; too many drift into noise. A held-out split gives a quick read on the sweet spot.
Two components are enough on iris. Going from 1 to 2 captures the second discriminant direction; beyond that, accuracy plateaus.
4. Use the Bayes probability method
Softmax probabilities are produced by normalizing the raw dummy-code predictions. The "Bayes" alternative fits a per-class Gaussian on the PLS scores and applies Bayes' rule, which often yields better-calibrated probabilities when class densities are roughly normal in the latent space.
Bayes pushes confident predictions closer to 0 or 1; softmax keeps a thin tail on the wrong classes. For threshold-tuning or ROC analysis, prefer softmax; for hard decision rules, Bayes is fine.
5. Sparse PLS-DA via splsda()
When you have hundreds or thousands of predictors and want feature selection baked in, switch to splsda(). It keeps only keepX variables per component, zeroing out the rest.
With only 4 predictors, sparsity does little here. The same call on a gene-expression matrix with 20,000 probes would shrink the active set to a handful of interpretable variables per component.
plsda() vs splsda() and train(method = "pls")
plsda() is the direct fit; splsda() adds sparsity; train(method = "pls") adds resampling. All three lean on the same underlying PLS engine.
| Function | Use it when | Resampling built in | Feature selection |
|---|---|---|---|
plsda() |
quick fit, you pick ncomp yourself |
No, use train() for that |
No |
splsda() |
wide data, want variable selection per component | No | Yes, via keepX |
train(method = "pls") |
want cross-validated ncomp tuning |
Yes, via trControl |
No |
Pick plsda() for prototyping or when ncomp is known. Pick splsda() for high-dimensional omics-style problems. Pick train(method = "pls") to let caret pick the components by cross-validation. See the caret reference for the full method list, including "simpls" and "oscorespls" algorithm variants.
Common pitfalls
Pitfall 1: passing a non-numeric predictor matrix. plsda() calls as.matrix(x) internally; factor columns get coerced to character then NA. Dummy-code categorical predictors with model.matrix(~ . - 1, data = df) or caret::dummyVars() first.
Pitfall 2: forgetting to scale. PLS-DA is scale-sensitive because component directions maximize covariance. A variable on a larger scale dominates the first component. Either pre-scale with scale() or pass scale = TRUE through ... to the underlying pls::plsr().
Pitfall 3: picking ncomp too high. With ncomp near min(n, p), PLS-DA reproduces the outcome exactly on training data and overfits. Cross-validate or hold out a test set; never pick by training accuracy.
Pitfall 4: misreading the 3D probability array. predict(fit, type = "prob") returns a [n, n_classes, length(ncomp)] array, not a matrix. Always index the third dimension explicitly or pass a single ncomp = k to predict().
plsda object does not store the original predictor matrix. Unlike knn3(), you cannot recover x from the fitted model. Save your training data separately if you plan to inspect scores or refit; otherwise scores(fit) is the only window into the latent space you have.Try it yourself
Try it: Fit a plsda model on iris with ncomp = 3, predict the class and probabilities for the first row of iris, and save the results to ex_class and ex_prob.
Click to reveal solution
Explanation: Passing ncomp = 3 to both plsda() and predict() keeps the call symmetric. The probability matrix has the same softmax shape as the basic example; the third array dimension reflects that only one ncomp was requested.
Related caret functions
These pair naturally with a PLS-DA workflow:
splsda(): sparse PLS-DA with variable selection per componenttrain()withmethod = "pls": resampled, cross-validated PLS-DAdummyVars(): convert factor predictors to a numeric matrixpreProcess(): center, scale, or impute predictors before fittingconfusionMatrix(): per-class precision, recall, and kappa for predictions
FAQ
What is the difference between plsda() and LDA in R?
LDA inverts the within-class covariance matrix and fails when predictors are collinear or outnumber rows. plsda() sidesteps that by projecting onto PLS components that maximize covariance with the dummy-coded outcome. Pick LDA for well-behaved tabular data; pick plsda() for wide or correlated data such as spectra, gene expression, or metabolomics.
How do I choose the number of components for plsda?
Cross-validate it. Wrap plsda() inside train(x, y, method = "pls", tuneLength = 10, trControl = trainControl("cv", number = 10)). caret reports accuracy or kappa for each candidate ncomp and stores the winner in bestTune. A good starting search range is 1 to min(20, ncol(x)); accuracy typically rises, plateaus, then dips as you add noise components.
Does plsda() return class probabilities?
Yes. Call predict(fit, newdata = ..., type = "prob") to get a 3D array shaped [n_rows, n_classes, length(ncomp)]. The default probMethod = "softmax" normalizes the raw dummy-code predictions; "Bayes" fits per-class Gaussians on the PLS scores and applies Bayes' rule for better-calibrated probabilities in roughly normal latent spaces.
Can plsda() handle binary classification?
Yes. Pass a two-level factor as y and PLS-DA reduces to PLS regression on a single indicator column. The latent-score threshold can be tuned via ROC. For binary outcomes you can also call pls::plsr() directly and threshold the predicted indicator yourself.
Is plsda() suitable for very wide data like gene expression?
It is one of the standard tools for that exact use case. PLS-DA handles p much greater than n without numerical issues because it never inverts a covariance matrix. For 10,000+ predictors, switch to splsda() so each component selects only the most informative variables, which makes results interpretable and reduces overfitting on noise features.