[Limdep Nlogit List] Re: Nested HEV via RP/SP?

[Fred Feinberg]

I found this note by David Hensher (below) from some time back, and it almost solved a problem a co-author and I are having.  We wish to estimate a scale ratio, but with each of the two branches in the nested logit as an HEV model.  That is, the standard deviation structure would look something like this:

    Option 1, RP:  Theta_1 = 1
    Option 2, RP:  Theta_2
    ...
    Option k, RP:  Theta_k

    Option 1, SP:  Sigma*1
    Option 2, SP:  Sigma*Theta_2
    ...
    Option k, SP:  Sigma*Theta_k

That is, in each branch, we have an HEV with standard deviations of Theta_1 = 1, Theta_2, ..., Theta_k, but that the scale ratio between the branches is Sigma.  The model would estimate
{Theta_2, ..., Theta_k} and Sigma.  We have been doing this iteratively, which is slow and cumbersome, and also fails to calculate the Hessian for the Sigma variable we are iterating across. I suspect there is a better way.  In short, can we do Nested HEV?  Many thanks,

Fred

=====

Prof. Fred Feinberg
Ross School of Business
University of Michigan
feinf at umich.edu


David wrote:

> RP\SP is very straightforward if you use nested logit set up with 2 branches, one for RP and one for SP. You can set IV or scale of one branch to 1 and allow other to be free and you get the differences in variance or scale. You can simply treat RP and SP as separate observations that are pooled.
>
> But note that we find that the differences in sacle are often between alts across SP and RP and not between SP and RP (since scale is simply picking up differences in the unobserved effects content). We discuss all of this plus how to do it in Nlogit in our new book
>
> David Hensher, John Rose and Bill Greene (2005) Applied Choice Analysis : a primer, Cambridge uni press, Cambridge.
>
> David