Mlogit and time dependence

[npseudacris]

In my multistrata robust model I want to constrain Psi by time or time related covariates. My question is on setting up the mlogit in the parameter specific links. I have three states and thus 6 Psi and 14 time periods. When time is not in the model I set it up as L to M and L to P Mlogit (1), M to L and M to P as Mlogit (2), and P to L and P to M as Mlogit (3). For the model under time constraints would I set each Psi pair to the same Mlogit for each time period, e.g. L to P and L to M Mlogit (1) for time 1, Mlogit (2) for time two etc?

I also have three transitions that are set to 0 in the fixed parameters because they cannot occur, M to L, M to P and P to L. I was thinking for the M Psis I could leave out the time dependence in the PIMs and then use the same tier Mlogit link for both. Although, P to L cannot occur P to M can (although with low frequency). Do I need to set up time dependence for both Ps in the PIMs so I can set the Mlogits or is it possible to not set up time dependence for P to L? If that is possible, what would I set the Mloigt to for the single P to L relative to the time dependant P to M Psis?

Thanks,
Nicole

[Bill Kendall]

I don't think you need to use the mlogit transformations to help you with the constraint process. First, if you use PIM's to carry out the constraints (i.e., only one set of psi's for all time periods), you will see that you will get only one set of psi's when you pull up the parm-specific transformation screen. If you use the design matrix to carry out the constraints, it is OK to leave the mlogit set up as is, because your use of the beta's will enforce the constraint. In other words, the transformation separately assures that psi's for state P in times 1 and 2 add to one. However, because of the constraints imposed in the design matrix the estimation process causes the psi's for times 1 and 2 to be estimated in lock step.

This brings up a side issue of convenience. If you use the PIM's for constraints you will need to repeat the process of setting up the mlogit specifications (either manually or by cutting and pasting from a spreadsheet) each time you run a new model. However, if you use the design matrix instead the PIM's do not change and therefore the tranformation specifications remain as is.

Finally, for your state M is appears that transitions out of that state are precluded, and therefore the mlogit transformation is not needed. Similarly, if for any state the number of possible transitions does not exceed 2 (e.g., for your state P the animal can only stay where it is or go to M), the mlogit collapses to a regular logit and therefore can be treated like any other parameter driving a binary outcome.

Good luck!,
Bill