Are you hesitating between PCR and PLS to calibrate your models? The question comes up every semester with my students and in industry workshops. “PCR or PLS: Which chemometric regression method should you choose?” sums up the dilemma very well. I propose a practical guide, drawn from field experiences, to decide calmly, save time, and ensure your predictions.
PCR or PLS: which chemometric regression method to choose?
Both belong to the family of multivariate regression and deal with datasets with a large number of correlated variables, typical of spectroscopy. PCR first builds components on X, then regresses Y. PLS extracts directions directly correlated with Y. As you will have realized: same destination, different routes, and concrete consequences on robustness, explainability, and performance.
Quick definitions to get started
- PCR: we first perform a principal component analysis (PCA) on X, then a linear regression of Y on the PCA scores.
- PLS: we extract latent variables maximizing the covariance between X and Y, then project the response onto these directions. For solid foundations, also see the article “PLS regression.”
What each approach optimizes
PCR first explains the variance of X, even if that means neglecting part of the information relevant to Y. PLS, on the other hand, seeks predictive directions of Y from the start. This methodological choice influences the number of components retained, the handling of multicollinearity, and the stability of the coefficients.
| Criterion | PCR | PLS |
|---|---|---|
| Objective | Maximize the variance of X | Maximize the covariance X–Y |
| Number of components | Sometimes higher | Often more compact |
| Noisy data | May dilute information useful for Y | Better captures predictive directions |
| Interpretability | Easy on the X structure | Good importance metrics (e.g. VIP) |
| Risk of overfitting | Related to the number of components | To monitor via cross-validation |
| Multi-response | Less natural | PLS2 well suited |
Fundamental reminders and key differences
In PCR, the early components translate the dominant structure of X: thickness, baseline variation, global intensities. If these trends do not explain Y, you must increase the number of components, at the risk of introducing noise. In PLS, the factors are shaped to carry the X→Y relationship; you often gain in parsimony and relevance, especially when the response is weak or buried.
Where PCR excels at exploring the structure of predictors, PLS often yields better initial predictions. I keep PCR for pedagogical challenges, exploring the scores and loadings, or when X alone structures the problem. I opt for PLS when every sample counts and the variance explained of Y must rise quickly and cleanly.
Criteria to choose based on your data and goals
- Noise and drift: if your spectra are noisy, PLS naturally filters what speaks to Y. PCR requires more components to catch up with the relationship.
- Number of variables vs samples: with p ≫ n, both methods cope, but PLS remains more frugal in useful factors.
- Explainability constraints: PCR to tell the story of X, PLS to tell the story of Y, with tools like VIP and regression weights.
- Multiple responses: PLS2 is advantageous when modeling several correlated analytes simultaneously.
- Stability in production: PLS often proves more resilient if conditions vary slightly.
Two weak signals I always look at: stability of coefficients across folds of cross-validation and the reproducibility of the selection of the number of components. A winning method does not waver from one draw to another.
Practical modeling and validation protocols
Recommended pipeline
- Cleaning and consistent spectral pretreatments (SNV, Savitzky–Golay derivatives, baseline correction). Standardize what needs to be standardized; do not touch what carries the analytical information.
- Segmentation of datasets: calibration, external test. Keep a true “virgin” dataset to estimate RMSEP.
- Choice of the number of factors via stratified cross-validation. I use the rule of “minimum + 1 standard deviation” on RMSECV to stay conservative.
- Quality controls: residuals, influence, leverage, coherence of the components. Monitor the drift of the coefficients across folds.
Métriques à suivre
- Performance: RMSECV, RMSEP, R², Q². Always compare CV and external test.
- Complexity: number of factors retained, samples-to-factors ratio.
- Robustness: stability of effects, sensitivity to outliers, diagnostics of overfitting.
A habit that has saved me more than once: recalculating predictions after removing 5 to 10% of key samples and checking the impact on the slope and intercept. If the relationship collapses, the model is not ready for the workshop.
Concrete laboratory examples
Moisture by NIR on pharmaceutical powders
Calibration set on 180 samples, spectra 1100–2500 nm, first derivative and SNV. In PCR, 10 components are required to achieve a good Q². In PLS, 6 factors are enough to reach the same precision, with the expected OH bands highlighted by the loadings. Choice: PLS, fewer parameters to maintain and better generalization across pilot batches.
Fermentation and sugar monitoring by Raman
Signal weakly correlated with fluorescence noise. PCR struggles to stabilize the slope beyond 8 components. PLS highlights, in 4 factors, the characteristic vibrations of the targeted sugars, while maintaining a high explained variance of Y on external validation. Immediate decision: PLS.
Quantification of an additive in a polymer by MIR
Clean spectral region, quasi-linear relationship and very high signal-to-noise ratio. PCR, 3 components, delivers a precision equivalent to PLS and offers a didactic interpretation of the X structures. For the formulation team, it’s a valuable pedagogical plus. Verdict: PCR.
Common traps and best practices
- Preprocess blindly: avoid stacking filters without justification. Test them one by one, document the impact.
- Choosing too many factors: the rising RMSECV curve is a clear signal. Stop before entering the unfavorable bias–variance zone.
- Information leakage: normalize calibration and test separately, otherwise your results will be overly optimistic.
- Ignoring outliers: a single influential sample can invert coefficients. Inspect leverage and T².
- Confounding interpretation with causality: high coefficients do not prove a physico-chemical relationship. Cross-check with domain expertise.
Interpreting and communicating your models
With PCR, I first comment on the structure of X via the scores and loadings: dominant spectral segments, plausible physical phenomena, risk zones. With PLS, I expose the importance of the variables via the VIP and the stability of the coefficients. In both cases, I provide uncertainty intervals and predictions on blind samples, because that’s what resonates with quality teams.
On a steering committee, three slides are enough: analytical objectives, cross-validation protocol and external test, then a performance matrix (R², RMSECV, RMSEP) accompanied by the number of factors. Clarity is worth more than a fireworks display of graphs.
Final benchmarks to decide without regret
- Weak relationships, few samples, need for fast reliable prediction: lean toward PLS.
- Interesting X structure to document, clean signal, pedagogical objective: PCR is sovereign.
- Correlated multi-analytes: PLS2 will simplify your life.
- Limited maintenance time and a drive for parsimony: advantage PLS, provided a solid validation protocol.
In summary, both approaches are excellent tools, each with its own personality. I encourage my teams to prototype both, with the same pipeline of spectral pretreatments and cross-validation, then decide on the evidence: external performance, stability of coefficients, readability for the operators. And if curiosity tickles you, revisit the foundations of PCA for PCR, or refine your PLS practice according to your use cases. It’s up to you; your samples probably already have the answer.