parameter specific link and design matrix

[caspar]

Dear all,

Is it a valid approach to specify a sin link for the part of the design matrix that is identity (so only one nonzero element in a column for each parameter), and a logit for the remaining part (the non identity)? For example, consider a multistrata model where S is a function of stratum, p as well, but psi constrained along pairwise distances between strata irrespective of direction, then, suppose 3 strata and the following design matrix:

10000000 S1
01000000 S2
00100000 S3
00010000 p1
00001000 p2
00000100 p3
00000013 Psi1:2=Psi2:1
00000017 Psi1:3=Psi3:1
00000015 Psi2:3=Psi3:2

can I use the sin link for parameters 1:6, and logit for 7:8 by using the "parameter specific link" option? The results I'm getting seem reasonable (after providing initial betas). This would be helpful when trying to avoid numerical convergence of parameters that approach boundary(S in my case), but still allow my psi estimates to be constrained along a continuous covariate.

Thanks in advance

Caspar

[gwhite]

Caspar:
You can apply different links to different rows of the design matrix, and for the case you describe, the resulting model will work fine. Where you can get in trouble is applying the sin link to rows that include a continuous covariate (and hence not have a monotonic relationship -- but maybe you want a hump in the relationship). However, you probably never want to apply different links to rows that have a common beta column. The resulting model would be non-sensical. because the beta value would be used in different links.

I often do exactly what you proposed to try to evaluate the correct number of parameters being estimated when some of them are on the boundary.

Gary