comparing models with and without fixed parameters.

[caspar]

Dear MARK list,

Would a CJS {say, Phi(.)p(t)} model in which we fix a parameter, say p3=1, be comparable to a model (Phi(.)p(.)) in which we do not fix p3? Do these models still share the same likelihood?

Thanks in advance for your thoughts,

Caspar

[dhewitt]

Caspar,

We don't have enough information to answer your question.

If you're asking whether models with fixed parameters can be compared to ones without fixed parameters, the answer is yes as long as the "fixing" is appropriate and the parameter counts don't include the fixed ones. MARK will not be estimating these so they should not be counted. (Whether "fixing" is appropriate is subjective except in cases where it is necessary to get the model structure right, and this will require some potentially serious thought on your part. Opinions may differ.)

The question of whether models are comparable and the question about whether they share the same likelihood are different. The two models you mention are not the same (but see below) so they don't have the same likelihood. But, that doesn't mean they cannot be compared. Maybe there is a nuance I'm missing.

One issue in your question is that a Phi(.)p(.) with p3 "not fixed" doesn't make sense. p3 will be the same as all other p because you're telling MARK to estimate one p for all occasions. Maybe you meant Phi(.)p(t) with and without p3 fixed? If so, return to serious thinking!