Linear multiple-regression models are often built differently according to discipline. In epidemiology, a linear multiple-regression may be fit to test associations using hypotheses about model parameters. The modeling strategy will often aim to reduce the number of variables to only include variables that need to be controlled for, i.e. - confounding variables and potential effect modifiers. Similarly, for prediction in epidemiology, model parsimony and concern about collinearity and multi-collinearity will reduce the number of variables in a model. Generally, these practices limit collinearity and multi-collinearity. In econometrics linear multiple-regression models, many variables are often used to build a model, where collinearity and multi-collinearity can sometimes be ignored.

It seems that the difference in modeling philosophy allows for the different uses of multiple regression analysis according to each discipline. But as statistics is heavily utilized in both epidemiology and econometrics, shouldn't the statistical method used by both fields require the same assumptions during the model building process?

  • $\begingroup$ Why would you presume econometricians wouldn’t be as concerned with collinearity? In general, I don’t think the discipline of econometrics views it as a simple hand-waving exercise in the face of a less parsimonious model. $\endgroup$ Commented Feb 24, 2021 at 22:20
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    $\begingroup$ @Alexis Edited for clarity. $\endgroup$ Commented Feb 25, 2021 at 14:16
  • $\begingroup$ @ThomasBilach Maybe you are right, I suppose I don't have enough of a background in econometrics. I think AdamO's answer hints at this, but comparing the two disciplines is difficult because of what variables are accepted as worthy of inclusion. An epidemiologist may look at two variables in an econometrics model and be concerned about their use, but they generally wouldn't have a background knowledge of the literature to make that call. Same would go vice versa for someone who studies econometrics. $\endgroup$ Commented Feb 25, 2021 at 14:23

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The "model building" process is a misnomer. A well conducted analysis pre-specifies the variables, and their encoding, to be included in the final model based on the scientific expertise of the discipline and based on statistical power of the sample. We can't tell from statistical output alone whether a variable is a "confounder" or a "collider", it merely boils down to the agreement among experts and commitment to the initial analysis specifications.

Model building doesn't mean we stack variables like bricks until we have a bridge from data to publication. "Collinearity" and "parsimony" are abstract concepts that don't factor in to analysis except as a diagnostic. Of course we use extensive diagnostics to look at plots and understand the contributions of the various variables. When "collinearity" specifically refers to extreme collinearity, meaning the results don't converge or they are unstable, some advanced methods or other remediation is needed; I think all accepted methods are viable whether you are an economist or epidemiologist. Similarly, even if an adjustment variable has a perfectly non-significant association with the outcome, you can't remove it on the basis of its non-significant result since you are deviating from your initial proposed analysis.

Economics and epidemiology has a wide breadth of literature, meaning there are bad examples, specifically examples where the technical discussion wanders too far into the weeds to represent a meaningful presentation. This is further complicated since good articles typically have an extremely compact summary statement on the model choice. All this makes it hard to have a true head-to-head comparison between the disciplines.

  • $\begingroup$ I think this is a very helpful description, thank you. One thing though, is that while I believe parsimony is an abstract concept, I believe collinearity is a concrete concept. At what level too much collinearity becomes a problem may be abstract, but it seems that collinearity is a mathematical/statistical phenomenon that can be shown no? I could be wrong. $\endgroup$ Commented Feb 25, 2021 at 14:20
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    $\begingroup$ I once consulted with a senior biostatistician about colinearity in the context of models with a priori specified nonlinearities (including interactions, and a single spline-like function). He made the case that colinearity can be interpreted as inherently part of the structure relating variables: it is not just a simplistic measure of "badness" of a model. :) $\endgroup$
    – Alexis
    Commented Feb 25, 2021 at 15:31
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    $\begingroup$ @Alexis Great point, I agree with that assessment! There's nothing wrong with adjusting for a highly correlated and predictive confounder: adjusting is the right thing to do. The only statistical consideration is increasing sample size to precisely measure the adjusted effect. Dropping the confounder because it's collinear is wrong for all the reasons. $\endgroup$
    – AdamO
    Commented Feb 25, 2021 at 19:53

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