Hi Yvonne. I found this confusing as well the first time through. As strange as it seems, the FE-logit model and the McFadden's choice model have the identical parameterisation, although they are fundamentally different models.
In the case of the McFadden model, the data is (typically) set up as a panel of individuals*potential choices and as you correctly state, only one choice can have a positive outcome (e.g. be chosen).
In the FE-logit model, the data is (typically) set up as a panel of individuals*time and the distribution of positive outcomes is unrestricted.
One other subtle difference is that covariates in the FE-logit model refer to characteristics of the individual since the choice set is just the same decision made repeatedly over time. While in the McFadden model, covariates refer to the characteristics of the possible choices (and can also include characteristics of the individual interacted w/ the choices).
Basically, the same conditional likelihood function solves both these models as long as the data is setup in the appropriate manner.
Cheers,
Steve
PS I am unsure if this model can be extended to handle the situation where people choose from a choice set over multiple time periods - e.g. a fixed effects McFadden model.
-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu]On Behalf Of Yvonne
Capstick
Sent: Friday, July 07, 2006 3:36 PM
To: statalist@hsphsun2.harvard.edu
Subject: st: Conditional Logit
Hi,
I'm using the Stata clogit command and have read
http://www.stata.com/support/faqs/stat/clogit.html and the manual at
http://www.stata-press.com/manuals/stata8/clogit.pdf. I am confused by one
fundamental thing.
As I understand it, the conditional logit model is used for mutually
exclusive choices. You can only have one Yes answer within each group. The
canonical model is McFadden's (1974) transport choice model (which is
mentioned in the manual) where you can choose either bus or train or car.
This is consistent with the fact that the likelihood function is p(i) =
exp(beta*Xi)/Sum(exp(beta*Xi): with more than one Yes answer, the
probabilities won't sum to 1.
However, Stata does allow you to have multiple positive observations within
a group, as in the first example in the manual. How can this be, since the
probabilities should be summing to 1? My initial reading is that what the
Stata manual example is doing isn't the McFadden multiple choice model, but
a fixed effects logit model, and perhaps the clogit command accommodates
both models. However, the Stata manual also says both models are
computationally equivalent, which I am confused by since the McFadden model
doesn't allow for multiple positive observations.
Any advice appreciated.
Yvonne
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