Okay to switch DV and IV in logistic regression with only 2 IVs?

[Frank Flieger]

Hi,

I would like to calculate the effect of gender (binary variable) on strenght and and weight (continuous variables). If regressions measure associations, not causality, why can't I just use

logit gender strength weight ?

I just can't imagine a dataset in which this would give a different result than sem (gender -> strenght weight).

Clearly, strenght and weight does not cause gender, but what are my alternative options here? A MANOVA or two separate regressions

reg strenght gender
reg weight gender

and then comparing both coefficients?

Best,
Frank

[George Ford]

The reg makes more sense, as gender is the IV and others the outcome of interest.

eststo e1: reg strength gender
eststo e2: reg weight gender
suest e1 e2

After suest, you can test for equality of the coefficients, which seems unlikely.

[Frank Flieger]

Thanks, I see. But the benefit of the logit regression would be the interpretation: e.g. you can then backtrack that each lbs heavier weight is associated with X% increase in the odds of being male. Or is there another way to reach such an odds-ratio increase/decrease interpretation?

And my question is also theoretical in nature, because I had the discussion about switching IV and DV and there seems to be no simple answer.

[Jeff Wooldridge]

I agree with George. The only thing to be learned are the average difference in weight by gender and the average difference in strength by gender. I don't see that a logit model for gender is useful, unless you want to be able to predict gender based on knowing someone's strength and weight.

[George Ford]

At some risk I'll say that gender is determined by chromosomes, not weight and strength. So using gender as the DV makes no sense with one qualifier (borrowing from Jeff): if you wanted to see whether you can predict gender using regression better than a carnival act that knows only weight and strength, then maybe it makes sense.

[George Ford]

I suppose in the online data mining space, you might want to predict gender by behavior if gender was unknown. (Not unlike trying to predict gender or race using a person's name).

A potentially interesting question, especially in healthcare, is whether gender fluidity could cause statistical problems when using 0/1 gender variables.