Non-estimable parameters and alternatives

[lhabib]

Hi everybody,

I have a series of Occupancy Estimation models based on presence/absence data of various bird species as determined by point counts. I am running a separate MARK analysis for each of the commonly-detected species (found at >5% of the points). I am using 3 treatment groups and a covariate (shrub cover) which may influence detectability and/or occupancy. Because of this though, I must use the logit link function in MARK. For most species, the best model (as determined by AICc) has at least one non-estimable parameter. Since I have a covariate and had to create my models from the design matrix, I don't have the option of using the sin link function.

I just finished reading the marathon discussion between Evan and Gary regarding parameter counts from the old forum (which doesn't appear to be available any longer, but is cached by Google here if anyone's interested): http://tinyurl.com/434nk

My question is, can I still use these models that have non-estimable parameters? Are they totally invalid, or can I still use them to draw conclusions as to what is affecting detectability and occupancy? An alternate route would be to use my data in a logistic regression-type analysis, but that would be totally discounting detectability which I would rather avoid.

Any advice would be fantastic!

Thanks a lot,

Lucas Habib.

University of Alberta
Edmonton AB
Canada

[darryl]

Hi Lucas
What parameter is being indicated as unestimable? Also, what is the point estimate for that parameter? Perhaps as Gary suggests in that series of postings, it's tending to a boundry value so on the logistic scale its large with either positive or negative sign.

Cheers
Darryl

[lhabib]

Thanks for the reply Darryl!

The parameter(s) that are inestimable vary depending on which species I'm modelling. The example below shows my real parameter estimates for the best model for one species I am looking at (American Redstart):



As you can see, in this case 4 of the parameters have SEs of 0.000 (although MARK is telling my that only parameter 5 is inestimable for reasons unknown). However, this is not constant across species; the inestimable parameters vary depending on species and model. For some models I get SEs of 0, for some I get SEs of 8000, and for some all the parameters are estimable. I really don't know what to make of it.

If you would like some more info please let me know!
Thanks,
Lucas.

[darryl]

Lucas,
So what is the model you're trying to fit here? You have 3 groups and want occupancy to vary between groups, with detection probability to be constant across groups, by vary with a covariate 'shrub'? What does your design matrix look like? Are the 'Intercept' and 'Constant' terms related to the same or different real parameters?

Darryl

[lhabib]

Basically, I am doing point counts of birds in areas with variable background noise. I am trying to determine if noise affects a) detectability and b) presence/absence of certain species. For the purposes of MARK I have categorized background noise into 3 groups (low, med, high). For each species I ran a series of about 20 models for different combinations of how detectability and occupancy may be affected by noise category and shrub cover (covariate).

In this example, the model that best fits the data says that detectability varies with shrub cover and occupancy varies by noise category. The design matrix for this model:


Lucas.

[darryl]

Ok, I think I see your problem. One of your beta parameters related to psi looks redundant; you're trying to estimate 3 psi's with 4 parameters. If you remove one of B3-B6 then your identifiability problem should go away and you should still get the same log-likelihood values etc. The choice of which one to remove is up to you and impacts upon how you would interpret the beta parameter estimates. I think it's all detailed in the MARK bible.

Good luck!
Darryl

[lhabib]

Argh! It was all so simple. I was trying to follow the Bible to a T but I suppose I got mixed up somewhere along the way. All 5 of my parameters are now being estimated. However, as a follow-up (and just to make sure that I'm interpreting this correctly...)

My design matrix now looks like this:


and my beta estimates like this:


So, (after I transform them from logits to real numbers) parameters 3, 4, and 5 represent the occupancy estimates for each group, right?

Too bad all the CIs are overlapping!!!

Thanks for the help Darryl,
Lucas.

[darryl]

Perfect!