with nonlinear models, not putting in the product term will still allow
the probabilities to vary interactively: the effect of x1 will vary with
the effect of x2. you can see this easily. supose its a binary logit
model and Pr(Y=1) is a function of both. well if you move x1 to a very
large value, then the prob will be near 1. if you then move x2 higher it
won't have much effect. if x1 is near .5 and you increase x2 then it has
the possibility of having a larger effect. (in a linear model where Y can
take on any value, this doesn't happen)
but this is an impovershed notion of interaction, it is entirely assumed
by the functional form and not estiamted as a function of the data, and it
does not allow for much variation at all. you can fix this to some degree
by putting in the product term. that doesn't allow all types of
interactions, but it allows for more than not doing it.
Gary
On Sun, 11 May 2003, Stanislav Markus wrote:
not to beat a dead dog, but here's another
question on interaction
terms:
with multinomial logit, simulated first differences vary given different
values of control variables *without any interaction terms* in the
model. from what i understand, this would not be the case in a linear
model? (there, only intercept, but not fdiffs would change.)
so would it suffice for non-linear-model simulation to vary the value of
control variable w/o including interaction terms?
thanks!
****************************
Stanislav Markus
Ph.D. Candidate
Harvard University
Department of Government
e: smarkus(a)fas.harvard.edu
t: 617.513.5407
-----Original Message-----
From: Kosuke Imai [mailto:kimai@fas.harvard.edu]
Sent: Thursday, May 01, 2003 9:24 AM
To: Stanislav Markus
Cc: gov2001-l(a)fas.harvard.edu
Subject: Re: [gov2001-l] pooled data: dummies vs interaction terms
This is the matter of degree. At one extreme, you can run separete
regression for each region. This assumes that you have nothing to learn
about one region from another. That's probably not the case. At the
other
extreme, you can run the pooled regression using the entire sample. This
means that all countries in each region are "exchangeable" after
controlling for covariates. There is no unobserved heterogeneity. This
is
probably not the case either. In the middle between these two extremes,
there are models like fixed effects, random effects models. You can vary
an intercept from one region to another. Or you can vary some
coefficents
from one region to another.
Kosuke
On Wed, 30 Apr 2003, Stanislav Markus wrote:
I'm reading an article that critiques the
use of pooled
cross-sectional
time series data, and wonder about the validity
of the following
claim:
"Researchers often contemplate the use of 'dummy variables' to capture
country or period effects. However, what the dummies actually capture
are differences in the intercept or 'baseline value' of the dependent
variable. Interaction terms, far more costly in degrees of freedom,
would be required to test country or period differences in slopes."
So what's the verdict on dummies vs interaction terms - if, say, I
want
to control for the Gulf region?
Thanks,
Stan
****************************
Stanislav Markus
Ph.D. Candidate
Harvard University
Department of Government
e: smarkus(a)fas.harvard.edu
t: 617.513.5407
-----Original Message-----
From: gov2001-l-admin(a)fas.harvard.edu
[mailto:gov2001-l-admin@fas.harvard.edu] On Behalf Of Stanislav Markus
Sent: Wednesday, April 30, 2003 10:28 PM
To: gov2001-l(a)fas.harvard.edu
Subject: RE: [gov2001-l] control variables
Since oil is measured as export percentage, I was thinking more about
countries like the U.S.: one could argue it does not export oil
*because* it is rich and does not need to sell its resources.. So, to
estimate effect of oil on democracy, controlling for income may be
important for the U.S., but not for the Gulf states.. (Obviously,
there's also some endogeneity among explanatory variables involved.)
Does this make sense at all?
Stan
****************************
Stanislav Markus
Ph.D. Candidate
Harvard University
Department of Government
e: smarkus(a)fas.harvard.edu
t: 617.513.5407
-----Original Message-----
From: gov2001-l-admin(a)fas.harvard.edu
[mailto:gov2001-l-admin@fas.harvard.edu] On Behalf Of
kimai(a)fas.harvard.edu
Sent: Wednesday, April 30, 2003 10:21 PM
To: gov2001-l(a)fas.harvard.edu
Subject: Re: [gov2001-l] control variables
It seems to me that income seems to be causally affected by oil
whether
they
are oil-dependent or not. For example, countries would be richer if
they
had
oil. The problem is that we don't know how rich Afganistan is if it
had
oil.
This is the fundametal problem of causal inference: You only observe
one
outcome (if they didn't have oil) and not
the other (if they did have
oil).
Kosuke
Quoting Stanislav Markus <smarkus(a)fas.harvard.edu>du>:
My general question is about controlling for a
variable that is
causally
> prior to the key quantity of interest in *some* observations, but
not
in
others - when the two categories of observations
are known ex ante.
Specifically for our article, we are examining the effect of oil on
democracy - and deciding whether to control for income. Income is
probably causally posterior to oil in highly oil-dependent countries
(and hence shouldn't be controlled for), but causally
independent/prior
to oil in others (and hence should be added as a
control) - can we
somehow "weigh" the control variable to account for this? Or, if the
choice is between keeping or dropping it, and we choose the latter,
should we argue that the degree of any induced omitted variable bias
is
less severe than the bias from post-treatment
control variable would
have been had we kept it..?
Grateful,
Stan
p.s. Amelia is still kaput, crashing after 100 iterations with same
error message..
****************************
Stanislav Markus
Ph.D. Candidate
Harvard University
Department of Government
e: smarkus(a)fas.harvard.edu
t: 617.513.5407
-----Original Message-----
From: gov2001-l-admin(a)fas.harvard.edu
[mailto:gov2001-l-admin@fas.harvard.edu] On Behalf Of Kosuke Imai
Sent: Tuesday, April 29, 2003 1:11 PM
To: gov2001-l(a)fas.harvard.edu
Subject: [gov2001-l] office hrs (fwd)
I will have a regular office hour today from 4 to 6pm.
Kosuke
---------- Forwarded message ----------
Date: Tue, 29 Apr 2003 11:58:30 -0400 (EDT)
From: Yevgeniy Kirpichevsky <kirpich(a)fas.harvard.edu>
To: Kosuke Imai <kimai(a)fas.harvard.edu>
Subject: office hrs
Kosuke,
will you be in the office today @4?
-y and p
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