[Limdep Nlogit List] new message to post!

[William Greene]

Trent. You can change the distributions of the random utility functions
in a multinomial choice model to a multivariate normal by
fitting a multinomial probit model. To get something that might
be comparable to an MNL, you would force the off diagonal elements of
the covariance matrix to be zero. You can layer a model on top of 
the MNL by using different distributions for random coefficients, usefully 
the choice specific constants, by using a mixed logit model and using the
different distributions such as lognormal, uniform, etc. NLOGIT offers several.
I'm not sure the idea of a "link function" is meaningful in the setting of 
the multinomial choice models because you are not fitting conditional mean functions 
and you are not obtaining the functional form of the probability by connecting
any type of conditional mean function to the distribution of a single
random variable as you are, for example, with a Poisson regression or
a single binary choice. The form of the probability - exp(Vj)/Sum{Exp(Vj)} 
results from an assumption that the random parts of the random utility 
functions have the type 1 extreme value distribution. If you change that 
latter assumption, you lose the form of the probability. The multinomial
probit model, for example, does not really resemble the multinomial
logit model.  Note, finally, it is not clear what would be meant by
"changes the model."  Certainly the coefficients change. But, that must
happen because of scaling of the utility functions, different variances
across utility functions, etc. The individual coefficients in a multinomial
choice model don't have much meaning on their own.  One might examine the
different elasticities, or measures of willingness to pay, or the fitted
probabilities.  But, it will be tricky to characterize succinctly how
these differ from one model to another because they also differ across
observations.
/Bill Greene




----- Original Message -----
From: "Trent Spears" <trentspears at hotmail.com>
To: limdep at limdep.itls.usyd.edu.au
Sent: Wednesday, September 22, 2010 6:13:03 AM GMT -05:00 Colombia
Subject: [Limdep Nlogit List] new message to post!


G'day,

I have been investigating and estimating various conditional logit models for choice behavior (with a variable number of choice set sizes for each individual).  Note that the utility function of this particular discrete choice model depends on attributes of the choice only.

I was wondering if it was possible, and if so how, to change the assumed distribution of the error terms from the type 1 extreme value distribution to something such as the standard normal.  In other words, I want to explore how the use of a probit (or even complementary log-log) link function instead of the logit link changes the models I am estimating.

Despite my best efforts, I have not been able to find a suitable way to solve this problem myself.  I hope you can help!

Cheers

Trent
 		 	   		  
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