Mysterious MLogits and RMark

posts related to the RMark library, which may not be of general interest to users of 'classic' MARK

Mysterious MLogits and RMark

Postby jlaake » Wed May 16, 2007 2:40 pm

I thought I’d post a note to the list server about what I’ve learned of the mlogit link this past week and also to let users of RMark know that a new version has been posted. Parameters such as Psi for multistrata models and pent for POPAN are constructed such that the values sum to 1 and one of the values is computed by subtracting the estimated values from 1. Here is what I have learned:
1) If the sum of the estimated real parameters is greater than 1 then obviously the subtracted value is negative. In that case, the subtraction probability is set to 0 and a penalty is added to the likelihood to force the solution such that the sum is 1. So the LESSON here is to look at the penalty term if you are using logits are some other link for these types of parameters.
2) The mlogit is a useful link to constrain the real parameters such that the sum of the estimated real parameters is less than or equal to 1 such that the real parameter computed by subtraction will be greater than or equal to 0. Thus it will not depend on the penalty approach. Because the mlogit had that property I chose it as the default link for Psi and pent for models developed via RMark. What I didn’t know is that when it computes the mlogit link it does so based on the unique real parameters and not on all the real parameters in the mlogit set. So for example, if you had 5 strata (A to E) and you wanted to estimate 4 real parameters for transitions from A by constraining equality for D and E (PsiAB,PsiAC,PsiAD=PsiAE) you cannot do that by setting the parameter index to be the same for PsiAD=PsiAE if you are using the mlogit link. You MUST use separate parameter indices and use the design matrix to implement the constraint. So the LESSON here is to use the all-different PIMS for parameters that use the mlogit link and use ONLY the design matrix for constraints. Evan has changed the multistrata chapter in the book to make this clear.
3) The final lesson is that even if you made the mistake of setting the parameter indices the same in the above example, it will only affect the results if the constraint becomes important which means that the subtraction probability is close to 0. So hopefully this means that past users of RMark with the Multistrata design will not see much change in their results when they update to v1.6.6 which is now on the web. Initially I had used all-different PIMS for mlogit parameters but starting in April 2006 (v1.4.5) I added parameter simplification for mlogit parameters. In hindsight that was a mistake but I didn’t catch it because for my set of test examples it doesn’t make any difference because the subtraction probability is well away from 0.
I apologize for any problems this may have caused RMark users. I do try to validate my changes but please help me by closely examining your models and results. As I add more of the analysis models in MARK it will become more difficult to validate them all.
Regards --jeff
jlaake
 
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