I recently received a review back for a paper in which I referred to some previous studies as 'correlational' where they used multiple regression to analyze some population data and make biological conclusions (specifically a linear mixed effects regression). One reviewer made a very big deal about this, suggesting that I "completely mischaracterized" this work (I suspect he/she was an author) which was "far from correlational", "much more sophisticated", and provided "much stronger evidence than mere correlational methods". I suspect the reviewer was referring to the fact that multiple regression models control for other included variables. From my (current) point of view, they are all correlational, just of differing complexity and assumptions between independent and dependent relations. Our study was trying to give a more mechanistic account of the data, therefore I wanted to make a distinction between statistical and mechanistic relationships. So I used the term correlational in a very broad sense.
So my question: Is it inappropriate to describe linear regression models as 'correlational', and would you yourself do so? If not, why not?
I am familiar with the mathematical relationships between regression coefficients and the 'partial correlation coefficients' e.g. discussed here, and here. My question, rather, is about terminology and whether you folks find it too loose (in some sense) to refer to regression methodology as correlational, or if a more broad term like 'statistical' would be more appropriate in this case.
Much thanks.
Best Answer
Correlation can be two things. Correlation is a mathematical construct on one hand, which is de facto Pearson correlation. Correlation is also a counterpart to causal on the other, meaning conditional dependence between an "exposure" and "outcome" that may be mediated by 100s of unmeasured factors. Calling work (i.e. the analyses/results of a study) "correlational" doesn't immediately suggest to me whether you mean they summarized several bivariate associations using partial correlations or whether the study was conducted from observational data.
I am strongly inclined to believe that you and the reviewer hold opposing ideas of what "correlational" means in this context. This is giving generous credit to the idea that other aspects of this communication did not denigrate anyone's research/findings.
As far as regression analyses are concerned, you can use regression models to analyze "quasiexperimental" data (or observational data) in which adjustment for confounding variables is used to infer what a hypothetically controlled (blocked/randomized) experiment would yield as a result. This leads to the distinction between correlation and causation. Only randomized controlled trials are worthy of discussing results in a causal context. Other results are not "correlational" but you may refer to findings as "associations".
The word correlation is confusing. In literature presented to a statistical audience, I am careful to avoid correlation altogether except in the context of Pearson's correlation. I would favor "empirical" or "epidemiological" or something of that ilk to refer to findings from observational studies.