Regression: Is it problematic to include a predictor when the outcome variable is based on it?

Question

My question is based on the following discussion we often see when people try to model citation counts for research articles.

The outcome variable is citation counts for an article and some typical predictors are the number of authors and the status of the journal in which the article is published usually quantified using the journal impact factor (JIF).

Not surprisingly, the JIF always turns out to be the best predictor, but the question is whether it is problematic to have it in there to begin with?

The JIF is essentially the average citation score of a set of articles in a journal. In principle, the citation score for article i contributes to the JIF, so y and x are already correlated to begin with. The question is whether this a problem when modelling?

An alternative is to treat this as a multi-level problem, but I am not sure it solves the issue and certainly brings challenges as we can easily end up modelling 10-15,000 different journals.

Answer 1

It may be useful to draw a distinction between the statistical fitting of the regression (which can be done with any two sets of numbers) and the causal inferences being drawn from such an analysis. Causal inference requires more than just a fitted regression; you might find these related answers interesting: Under what conditions does correlation imply causation? and Does simple linear regression imply causation?

Circularity is a problem when causal claims are being made based on a regression. This would be easy to fix in your example by recalculating each journal's impact factor after excluding the article under consideration. Practically speaking, though, the influence of any one article on the JIF is probably negligible, and so the regression is unlikely to change much - which is perhaps why people haven't bothered with this step.