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re: Re: Re: st: Why does a non-statistically significant covariate in a a regression model become significant in margins?


From   "Ariel Linden, DrPH" <ariel.linden@gmail.com>
To   <statalist@hsphsun2.harvard.edu>
Subject   re: Re: Re: st: Why does a non-statistically significant covariate in a a regression model become significant in margins?
Date   Fri, 14 Dec 2012 16:40:59 -0500

Thank you, once again Joerg! This now tells the complete story and is
extremely insightful!

Ariel





Ariel had a follow-up question which he sent to me offlist.

Here is his question:

On Fri, Dec 14, 2012 at 4:08 PM, Ariel Linden, DrPH <ariel.linden@gmail.com>
wrote:
> Joerg,
>
> As a quick followup (I can post this on the listserve if you prefer to 
> respond publically):
>
> How would I get the predicted values for the binary part of the model 
> via margins? I thought perhaps predict(pr), but that doesn't seem to 
> give the same results as your manual calculation:
>
> . sum p_c p_t
>
>     Variable |       Obs        Mean    Std. Dev.       Min        Max
> -------------+--------------------------------------------------------
>          p_c |     10000    .4449147    .1127882   .1127662   .8525233
>          p_t |     10000      .33073    .1019106   .0709849   .7765486
>
> . margins, at(treat=(0 1)) expression(predict(pr))
>
> Predictive margins                                Number of obs   =
> 10000
> Model VCE    : OIM
>
> Expression   : Pr(y=0), predict(pr)
>
> 1._at        : treat           =           0
>
> 2._at        : treat           =           1
>
> ----------------------------------------------------------------------
> ------
> --
>              |            Delta-method
>              |     Margin   Std. Err.      z    P>|z|     [95% Conf.
> Interval]
> -------------+--------------------------------------------------------
> -------------+------
> --
>          _at |
>           1  |   .5550853   .0076111    72.93   0.000     .5401679
> .5700028
>           2  |     .66927   .0076781    87.17   0.000     .6542211
> .6843188
> ----------------------------------------------------------------------
> ------
> --
>

My response:

In the inflation part of the model, we predict the probability of y=0.
However, with the marginal predictions of counts using both model
components, we weight the nonzero counts with the probability of y>0, which
is simply 1 - p(y=0). Therefore, we can type:

margins, at(treat=(0 1)) expression(1-(predict(pr)))

in order to get the marginal predictions for p(y>0).

Joerg

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