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st: RE: Conditional Logit


From   "Steve Stillman" <stillman@motu.org.nz>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: Conditional Logit
Date   Sat, 8 Jul 2006 13:30:31 +1200

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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