CJS phi & p time-specific, 6 occasions, why 10 parameters?

[simone77]

Hi,

I am dealing with a simple CJS model on a set of encounter histories like these:
/* [R3W] */ 100000 1 0.0000 0.1180 0.1880 0 0.0000 0.0000 1 3;
/* [R5V] */ 100000 1 0.0000 0.1110 0.0640 0 0.1220 0.0270 1 3;
...

I have 6 occasions and 8 (unstardized) covariates. The peculiarity of this data set is that all the individuals are marked at the first occasion (all histories start with a "1"). I run a simple CJS and I would expect to count 4 phi + 4 p + 1beta(phi5*p6) = 9 parameters.

Doing some trials it seems to me that if I use the sin link with the default 2nd part var. estimation I got the expected number of parameters (9). However, if I use the logit link or change to hessian the var. estimation, MARK counts 10 parameters.

Am I missing something?
I am using MARK version 7.2 on a Windows 7 Pro (x64).

[jlaake]

With the sin link the parameter count is fairly reliable but that is not the case with the logit link. I'm sure this is covered in the documentation. Not sure about the change in the Hessian. The parameter counting is a numerical technique. It is not perfect.

--jeff

[simone77]

Thanks Jeff for your prompt response.
I thought to remember that some extrinsically non-identifiable parameter might be overlooked because of some issue in your data and therefore the parameter counting in MARK results in less parameters than really should be. I didn't expect to find MARK counting more parameters than real.
Anyway, thank you because I was afraid I was doing some silly error in counting parameters in such a simple model.

[jlaake]

It certainly undercounts as well with the logit, which is why in RMark I always set parameter count to number of columns in the DM. In situations like Phi(t)p(t) that will overcount but I've found that undercounting is more problematic with logit link.

--jeff

[cooch]

Doing some trials it seems to me that if I use the sin link with the default 2nd part var. estimation I got the expected number of parameters (9). However, if I use the logit link or change to hessian the var. estimation, MARK counts 10 parameters.

And your motivation for using something other than the defaults is....what? If you read the relevant sections of Chapter 4, it covers what each option does, why you probably shouldn't be fooling them, and, if you read the Addendum, you'll know more about how MARK counts parameters than you probably want to.

I am using MARK version 7.2 on a Windows 7 Pro (x64).

That won't affect the issue you address in your question, but you should update. Version 7.2 is >1 year out of date.

[simone77]

And your motivation for using something other than the defaults is....what? If you read the relevant sections of Chapter 4, it covers what each option does, why you probably shouldn't be fooling them, and, if you read the Addendum, you'll know more about how MARK counts parameters than you probably want to.

I have read these sections several times in the last years and really appreciate them for the extent of information they provide. I just did not expect to find MARK counting more parameters than real and that's why I wondered if I was doing some silly error when counting parameters manually. Therefore, since the link function may play a role in the parameters counting, my motivation was just exploring how parameters counting varied (in case it did) under different settings. I know the Hessian is not reliable but I was curious to see hot it affected parameter counting in this case.

I am not used to find MARK counting more parameters than real, in case I have found the contrary and that makes sense because some extrinsical non-identifiability issue may exist. Sometimes the sin link tends to count parameters better because it is less affected, for example, by boundary estimates but...in this case?

Yes, I have to update the MARK version, thank you for saying.