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st: asmprobit without alternative-specific variables


From   J Gonzalez <jgonzalez.1981@yahoo.com>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   st: asmprobit without alternative-specific variables
Date   Fri, 7 Oct 2011 16:27:50 +0100 (BST)

Hi

I am studying multinomial models following chapter 15 of Cameron & Trivedi (2005), and working on examples of those models using Stata 11.2, fully updated. I have reached section 15.8. Multinomial Probit, which is one of the models that does not assume independent errors among alternatives, and hence solves the problem of indepence of irrelevant alternatives.

Then I started to look for commands in Stata to estimate such model, and I found asmprobit (Alternative-specific multinomial probit regression). In the help file (h asmprobit) it is clarified that "the model allows you to relax the independence of irrelevant alternatives (IIA) property that is characteristic of the multinomial logistic model".

So, I start reading the Stata Manual to learn a little bit more of the estimation procedure and the use of the, and I found that "If there are no alternative-specific variables in your model, the variance–covariance matrix parameters are not identifiable. For such a model to converge, you would therefore need to use correlation(independent) and stddev(homoskedastic) . A better alternative is to use mprobit, which is geared specifically toward models with only case-specific variables". Hence, with this command is not possible to estimate a multinomial probit using only case specific variables (which, looking backwards, it is clear from the command name!), and I would have to rely on mprobit command. However, "MPROBIT command is the normal error counterpart to the MLOGIT command in the same way that the PROBIT command is the normal counterpart to the LOGIT command" (NYU, 2009). Therefore, the model fitted by mprobit command does not relax the
 independence of irrelevant alternatives assumption.

Now, my questions:

Is there any command in Stata to estimate a multinomial probit, relaxing the IIA assumption, but using only case variables (of the individual making the decision), and not alternative-specific variables???

Actually, now I am wondering if it is really possible to do something like that, ..., initially I thought it was possible (and actually the model definition is similar to that of the multinomial logit, which may indeed be fitted using only case-specific variables), however, I have been looking around and everytime the model is used, it is fitted using alternative-specific variables.

Thanks in advance for any suggestion or comment on this.

Jesús González



References:

Cameron, A. C. and P. K. Trivedi (2005). Microeconometrics. Methods and Applications. New York, Cambridge University Press.

NYU (2009). Handouts of the course Methods IV: Advanced Quantitative Analysis, at New York University, available in https://files.nyu.edu/mrg217/public/unordered_multiresponse.pdf, accessed 07-october-2010.

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