Re: st: Logit Model- Controlling for Differences Across Groups (Countries)

[David Hoaglin <dchoaglin@gmail.com>]

Dear Michael,

Thank you for the additional explanation.

The limitation would arise with any regression-like model.  It's
inherent in the data.  At the level of the country, you have only 5
data points.  A facile answer is that, if you want to study the
effects of macro variables (which take the same value for all
individuals in a country), you need more countries.  That may not be a
realistic option, but using a different approach in the modeling will
not circumvent that limitation in the data.  I can understand your
frustration, in view of the likely importance of the various macro
variables, but I do not see a solution other than using one (or
perhaps more) of the macro variables instead of the country dummies
(ordinarily, you would drop all the country dummies).

On another point entirely, do you expect individuals' responses to be
more similar within countries than between countries?  If so, you may
want to consider a hierarchical model (in this instance, a generalized
linear mixed model).  That approach would handle variance among
countries by a random effect (one parameter, the variance of the
random-effect distribution, instead of 4 fixed effects for the
countries), and you might be able to include a macro variable (or
two).  Still, with only 5 countries, the estimate of the variance of
the random-effects distribution will be rather imprecise.

I have no reason to believe that the country dummies are essential to
the model.  From your description, the macro variables seem more
important.  You have enough macro variables, however, that it may not
be easy to associate differences among countries with a particular
macro variable.

Regards,

David

On Mon, Apr 2, 2012 at 4:10 PM, Michael Weinberg
<michaelhazeweinberg@gmail.com> wrote:
> Dear Dr. Hoaglin,
>
> Thank you so much for responding to my Statalist question. I thought
> I'd contact you directly to clear up some confusion I still have-- of
> course if you don't have time, I will certainly understand.
>
> My model is meant to explain factors that influence  'Preference for
> Self-Employment' (a binary variable) among the 2000 respondents in the
> 5 countries. In addition to the individual variables (such as age,
> gender, wealth, risk willingness, etc), I wanted to include several
> macro factors, such as GDP per capita, inflation variability, taxes on
> business profits, property rights, and several more. I believe that
> such factors are theoretically important in explaining my dependent
> variable, so I am eager to include them in the model.
>
> As I understood from your advice, I can include this information only
> by removing some or all country dummies, and then I'm still limited to
> only four macro variable. I am unfortunately not an expert with
> binary-response regressions, but this seems like a major limitation to
> these models. Do you recommend any other way (perhaps another model
> entirely?) which I can employ to capture the explanatory power of
> these macro variables without forsaking the country dummies (which
> seem, from your comments, to be rather essential to the model)?
>
> Best,
>
> Michael

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