What does “holding constant” mean in regression analysis?

1 February, 2013 at 17:53 | Posted in Statistics & Econometrics | Leave a comment

As a descriptive exercise, all is well. One can compare the average salary of men and women, holding constant potential confounders. The result is a summary of how salaries differ on the average by gender, conditional on the values of one or more covariates. Why the salaries may on the average differ is not represented explicitly in the regression model …

Berk_Regression_72ppiRGB_150pixelsMoving to causal inference is an enormous step that needs to be thoroughly considered. To begin, one must ponder … whether the causal variable of interest can be usefully conceptualized as an intervention within a response schedule framework [a formal structure in which to consider what the value of the response y would be if an input x were set to some vaue]. Once again consider gender. Imagine a particular faculty member. Now imagine intervening so that the faculty member’s gender could be set to ‘male.’ One would do this while altering nothing else about this person …

Clearly, the fit between the requisite response schedule and the academic  world in which salaries are determined fails for at least two reasons: The idea of setting gender to male or female is an enormous stretch, and even, if gender could be manipulated, it is hard to accept that only gender would be changed. In short, the causal story is in deep trouble even before the matter of holding constant surfaces …

This is not to imply that it never makes sense to apply regression-based adjustments in causal modeling. The critical issue is that the real world must cooperate by providing interventions that could be delivered separately …

As a technical move, it is easy to apply regression-based adjustmens to confounders. Whether it is sensible to do so is an entirely different matter …

The most demanding material [is] the examination of what it means to ‘hold constant’ … The problem [is] the potential incongruence between the mechanics of regression-based adjustments and the natural or social world under study.

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