Re: st: xtlogit, margins

["JVerkuilen (Gmail)" <jvverkuilen@gmail.com>]

On Thu, Nov 8, 2012 at 7:36 AM, Maarten Buis <maartenlbuis@gmail.com> wrote:

> To me an effect is just a comparison of groups (*). Such a comparison
> can be done be computing a difference or a ratio. You can say group A
> earns on average x euros/dollars/yen/pounds/... more than group B
> (effect as a difference) or you can say group A earns on average y%
> more than group B (effect as a ratio). I don't understand why one
> statement would be more coherent than the other.

Mathematically they are 100% equivalent. Unfortunately our brains
aren't mathematical and tend to process things we see greatly. The
odds ratio is a good example of this. Half the range of variation is
between 0 and 1 and the other half is between 1 and Infinity and odds
combine multiplicatively, not additively. Raw probability is even
worse because there concatenation rule is both additive and
multiplicative. There has been a lot of research on whether ratios are
accurately perceived and the general answer is no, but log ratios are.
Um, a summary of the rather large literature:

     Hardin, C. & Birnbaum, MH. (1990). The malleability of "ratio"
judgments of occupational prestige. American Journal of Psychology,
103(1), 1-20.

I'm willing to believe that we can train ourselves to work with ratios
but they are simply not natural for the brains we have so my guess is
that we're never great at it.

It's actually quite similar to the reason that -hangroot- works the
way it does. You square root because frequency changes too fast to be
able to perceive accurately. You also hang from the expected curve
rather than go up to it so that the deviations are more apparent. Thus
-hangroot- is more psychophysically coherent than a histogram, in
general.



> This misconception is the source of many errors. The safest thing is
> to interpret odds ratios as odds ratios and risk ratios as risk ratios
> and not try to see one as an approximation of the other. The
> approximation only applies under special circumstances, and too often
> people just conveniently forget that. If you want relative risk you
> should estimate a model that return relative risks (-poisson-).

Yes I forgot the caveat. ;) It only works when you're talking about
rare events. RR isn't so fantastic either given that the effect of the
margins restricts it quite substantially.
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