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Re: st: Interaction effects with poisson models

From   Maarten buis <[email protected]>
To   [email protected]
Subject   Re: st: Interaction effects with poisson models
Date   Wed, 20 Jan 2010 02:32:47 -0800 (PST)

--- 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: <

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 

Hope this helps,

(*) 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:

Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen


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