Preserving the art of multivariate thinking: PCA and the wisdom of experience

The grand tradition of science as practiced by figures like Darwin (1859) or Alexander von Humboldt (1871), where all observations, thoughts, and conclusions were meticulously recorded, has largely faded. Today's scientific landscape is becoming increasingly specialized, with fewer opportunities to explore knowledge in a holistic, interconnected way. Adding to this challenge, many long-standing academic positions once held by senior professors are often being remodeled or phased out. Even when successors are appointed, much of the predecessor's tacit knowledge often remains undocumented, putting a vast intellectual legacy at risk of vanishing. This makes it all more important that experienced scholars take the time to document and share their accumulated knowledge.

Editorials like “Notes on the Use of Principal Component Analysis in Agronomic Research” by Matthew (2025) offer a valuable remedy, creating space to pass on insights gained over a lifetime that cannot easily be captured in typical research papers. Even if certain methodologies may no longer be at the cutting edge, the context, experience, and wisdom embedded in such reflections can guide new generations of scientists.

In this editorial, the author reflects on four decades of experience using principal component analysis (PCA) in agronomic research, highlighting its strengths as a tool for data exploration and pattern detection, particularly in multivariate datasets where traditional univariate approaches may overlook significant interactions among traits.

Given the wealth of practical insights, he begins the editorial by drawing on his own teaching experience, including an applied student-custom biometric dataset to illustrate how PCA captures both correlated and independent traits. Further, the author challenges the widely held belief that data must always be standardized before conducting PCA, as he shows that even PCA with the correlation matrix on unstandardized data yields the same loading coefficients as standardized data.

The editorial also introduces an innovative approach developed by the author himself after years of use of PCAs. He thereby uses cross-correlation of the original principal component (PC) scores to assess how the inclusion of new variables or exclusion of a variable redistributes information across components. Where a set of PC scores is cross-correlated with themselves, this is depicted as diagonal line of correlation values of 1.0 in a background of zero correlations. In the example shown, it is seen that the addition of a new variable to a five-variable PCA resulted in the original PC3 being split into two PCs at PC3 and PC4, with original PCs 4 and 5 being demoted to PCs 5 and 6.

In the next section, the author questions the common rule of discarding PCs with eigenvalues below 1, demonstrating through concrete examples that such components can still harbor biologically relevant signals. This oversight is frequently rooted in the tendency to overlook or underreport nonsignificant results, despite their potential to carry valuable scientific insight and contextual relevance (Dushoff et al., 2019). Accordingly, the author suggests selecting principal components for biplots based on their biological relevance rather than solely on the amount of variance they explain.

In addition, he highlights a misconception in PCA application of adding linear functions of existing variables as new traits. While such additions may slightly alter loading coefficients, they contribute no new information to the data matrix and simply result in empty components.

Likewise, the editorial raises concerns about the use of varimax rotation, noting that while it may make principal components appear easier to interpret by amplifying larger loadings and suppressing smaller ones, it comes at the cost of redistributing information across components, which may disrupt meaningful pattern detection and obscure biologically relevant signals. In his analysis, rotated PCs exhibit weaker correlations with their original counterparts and unexpected overlaps with other components, ultimately complicating rather than enhancing biological interpretation, as seen in Zhou et al. (2023), where previously observed experimental treatment effects detected in analysis of variance (ANOVA) of PC scores disappeared following varimax rotation.

In the end, the author offers additional application insights, including an uncommon advice for using PCA explicitly for dimensionality reduction, not just trait association, which can effectively overcome the limitations of traditional repeat measured ANOVA when dealing with multilayered data. However, he goes even a step further by highlighting the strength of PCAs not only in dimensionality reduction but also in its capacity for dimensionality retention. Particularly in agronomy, where datasets may contain multiple overlapping trait associations, PCA allows researchers to preserve and distinguish these independent signals.

In sum, this editorial is not just an insightful guide for agronomists seeking to apply PCA to complex datasets to enhance their multivariate analyses, it reminds us that while statistical tools evolve, the deep understanding of their application in context is something only experience can teach. By sharing his insights, Cory Matthew provides both a theoretical background and practical guidance, ensuring that future scientists can stand on solid ground, not only in technique, but in judgment.

Margarita Hartlieb: Conceptualization; writing—original draft.

The author declares no conflicts of interest.