no. of parameters, logit link vs. sin link

[jj]

The MARK “gentle introduction” (Chapter 6, p. 41) instructs the reader to create the general model using design matrix rather than PIMs.

I am trying this with a dataset, and started with a general, time-dependent model, using PIMs (step 1). Then I used the design matrix approach (step 2), manipulating the design matrix instead of using the PIM. However, the PIM model (sin link) and the design matrix model (logit link) do not have the same no. of parameters. As stated in the text with step 2, the deviances were the same but the no. of parameters differed slightly. No surprise there.

But what about adjusting no. of parameters?
Which would be more correct, to a) adjust no of parameters for the logit models so they have the same no. of parameters as the corresponding sin model? b) use the logit models with the no. of estimable parameters as they come?

[cooch]

The MARK “gentle introduction” (Chapter 6, p. 41) instructs the reader to create the general model using design matrix rather than PIMs.

I am trying this with a dataset, and started with a general, time-dependent model, using PIMs (step 1). Then I used the design matrix approach (step 2), manipulating the design matrix instead of using the PIM. However, the PIM model (sin link) and the design matrix model (logit link) do not have the same no. of parameters. As stated in the text with step 2, the deviances were the same but the no. of parameters differed slightly. No surprise there.

But what about adjusting no. of parameters?
Which would be more correct, to a) adjust no of parameters for the logit models so they have the same no. of parameters as the corresponding sin model? b) use the logit models with the no. of estimable parameters as they come?

You should manually adjust the number of parameters to reflect the number that are individual estimable given the structure of the general model. So, of the two you suggest, the former, but....remember that although the sin link does a better job with estimating parameters near the boundaries, it can still 'get it wrong' on occasion (for particular combination of models and data sets....). As such, it is preferred to adjust the number of parameters to reflect what *should* be estimable, given the model structure (and independent of the data, short of particular constraints).

[dhewitt]

You should manually adjust the number of parameters to reflect the number that are individual estimable given the structure of the general model. So, of the two you suggest, the former, but....remember that although the sin link does a better job with estimating parameters near the boundaries, it can still 'get it wrong' on occasion (for particular combination of models and data sets....). As such, it is preferred to adjust the number of parameters to reflect what *should* be estimable, given the model structure (and independent of the data, short of particular constraints).

I'd say it's necessary, not just preferred. Counting parameters can be tricky (unless you're blessed with a dense dataset with all estimates "far" away from boundaries), but inferences based on model selection depend on getting the counts right.