Re: st: Evaluating the importance of interaction effects in logistic regression

[Thomas Speidel <thomas@tmbx.com>]

Thank you Maarten for the informative reply.

On Wed, 31 Aug 2011 09:48:10 +0200, Maarten Buis wrote:
> You cannot determine the significance without deciding how you want 
> to
> interpret the results. Interpretation and significance are not
> independent, as the first determines the null hypothesis of the
> second. This is the key bit of information you need in order to see
> that I (Maarten) and Norton et al. do not disagree, even though these
> quotes make it seem like we do. I showed in my Stata tip how to
> interpret interaction terms as ratios of odds ratios, in which case
> you can interpret the p-values as the test that this ratio equals 1,
> i.e. there is no difference between black and white females in the
> effect (measured as odds ratios) of collgrad. Norton et al. want to
> interpret effects as marginal effects, i.e. as differences in
> probabilities rather than ratios of odds, and the marginal effect as
> differences (rather than ratios) in marginal effects. As a
> consequence I and Norton et al. want to test different hypotheses, 
> and
> obviously get different results.
>
> > For example:
********************************************************************************
> > sysuse nlsw88, clear gen byte high_occ = occupation < 3 if 
> > occupation
> <
> &g> race==3 logistic high_occ race##collgrad , nolog is it correct to
> say
> > that the intera
> collgrad is not important because its p-value is 0.161?
>
> Such a conclusion is always wrong as a significance test cannot
> determine whether or not a variable is "important". This may sound
> pedantic, but this misunderstanding is probably the root cause of 
> your
> confusion. As soon as you regard tests as testing a specific
> null-hypothesis the distinction between me and Norton et al. becomes
> much easier to understand. As I stated above this tests the 
> hypothesis
> that the ratio of the effect (measured in odds ratios) of collgrad 
> for
> white women and the effect of collgrad for black women equals 1, i.e.
> that these effects are equal. If that is a hypothesis that is of
> interest to you, than this test is fine. If this> is not of interest 
> to
> you, than this test is not fine. What if, for
> > example, we had 3 levels to race:
********************************************************************************
> > sor
> ace race = 3 in 1/300 lo
>
> > occ race##collgrad, nolog and we want to evaluate the overall
> > importance of the interaction between race and collgrad (i.e.
> jointly)?
> > Is it approriate to use the likelihood ratio test to compare the 
> > model
> > without interaction to the model with interaction, and determine the
> > importance of the interactio
> rding based on the results of LR test?
>
> That depends on whether you want to interpret your results in terms 
> of
> odds ratios and your interaction terms as ratios of odds ratios. If
> you want to do that, than what you propose is one way of doing that.
>
> Hope this helps,
> Maarten
>
> --------------------------
> Maarten L. Buis
> Institut fuer Soziologie
> Universitaet Tuebingen
> Wilhelmstrasse 36
> 72074 Tuebingen
> Germany
>
> http://www.maartenbuis.nl [1]
> --------------------------
>
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--
Thomas Speidel


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