--- On Wed, 20/1/10, Fabio Zona wrote:
> recently, several articles have been published on graphical
> tools for testing interaction in regressions with
> dichothomous dependent variable (i.e., logit and probit).
> They say that simply looking at the significance of the
> interaction coefficient is not enough, and that one should
> look at graphs to establish whether an interaction effect is
> significant.
> Is it the same also for poisson and zero-inflated poisson
> models? Or - in these latter models - I can simply look at
> the significance of the interaction to state that the
> interaction effect is significant?
The issue is that in these models the effect of an
explanatory variable on the predicted probability depends on
the values of all other explanatory variables, so the size
of the interaction effect *in this probability metric* also
depends on the values of all other explanatory variables.
So, as long as you want to interpret this effects in terms of
the probability metric, there isn't one effect or interaction
effect, but as many as there are observations (actually the
number of distinct combinations of values on the other
covariates). That is where those graphical comparisons come
in, that is one way of comunicating that many effects.
The obvious alternative solution is to interpret the results
on the odds ratio metric, in which case the effect of one
variable is separate from the other variables (except for
interactions), so there is still one effect and one
interaction effect, so you can safely interpret the
interaction term(*).
Whether you want your effects in terms of the probability
differences or odds ratios is a substantive question which I
discussed briefly in this post: <http://www.stata.com/
statalist/archive/2010-01/msg00276.html>
Pretty much the same argument holds for other non-linear
models like -poisson- or -zip-, except that now the choice
is between effects in terms of count differences or rate
ratios.
Hope this helps,
Maarten
(*) There is another issue with the influence unobserved
heterogeneity can have on interaction terms in non-linear
models, see for instance:
Williams, Richard. 2009. "Using Heterogeneous Choice Models
To Compare Logit and Probit Coefficients Across Groups."
Sociological Methods and Research, 37(4):531-559.
A pre-publication version is available at:
<http://www.nd.edu/~rwilliam/oglm/RW_Hetero_Choice.pdf>
--------------------------
Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
Germany
http://www.maartenbuis.nl
--------------------------
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