Can you build mixed effects multinomial logit and probit models with discrete choice data?

Question

For a discrete choice experiment with a partial profile balanced design with overlap, can one build a
a) fixed effects multinomial logit model,
b)mixed effects multinomial logit model,
c) fixed effects multinomial probit model,  and
d)mixed effects multinomial probit model?

There are three alternatives per question, 16 attributes, and only three attributes are presented in each question. A total of 18 questions.  We are interested in modelling individual ID as the random/cluster variable, attributes (A1-A16) as fixed effects, and patient demographic as fixed effects.

Answer 1

With only three attributes per choice set and 18 choice sets available to estimate part worth utilities for 16 attributes you have a pretty sparse data set.  Add that the model would seem to combine a polytomous logit portion for patient demographics and a conditional logit for the product attributes and the data supporting your model is more sparse still.

That concern aside, I see no reason you couldn't estimate the four models you list, assuming you have the proper software.    The fixed effects MNL model in particular is readily available but it may be harder to find the others.

Comments

Thanks Keith.  Sorry I should have been more clear. I am wondering if Sawtooth Software is able to produce each of these four models.  

Also, my dataset is a balanced fractional factorial design with over 1000 participants who were randomly assigned one of 999 different surveys generated by Sawtooth - so I won't have to worry about sparse data.

---

OK, this helps.  Within our SSI Web program one can run a fixed effects MNL model.  We offer hierarchical Bayesian MNL instead of the random or mixed effects model.  Our programs do not estimate MNP models.