What is K in pcount?

[Adrián Naveda-Rodríguez]

Hi,

I am looking for a definition of K in pcount. In page 324 of AHM said Nmax is called K in unmarked functions pcount and gmultimix.

So, if N is the number of individuals available for sampling, is Nmax the carrying capacity?

Regards,

Adrian

[Kery Marc]

Dear Adrian,

K is not a model parameter and not anything of biological importance either. You can think of it as simply a tuning "parameter" of the likelihood maximisation, nothing more. Technically, it is the upper bound of the summation over the possible values of N in the integrated likelihood that is maximised to obtain the MLEs.

But K has to be made big enough that the results (i.e., the estimates) won't be affected by your choice (i.e., won't change appreciably for instance when you make K even bigger). When your estimates keep changing when you make K bigger, then this indicates that the parameters are not estimable for your data set. We don't usually find this problem with the Poisson or the ZIP mixtures, BUT IT IS FREQUENTLY A PROBLEM WITH THE NEGBIN MIXTURE. When fitting Nmix models (using gmultimix() and especially with pcount()) we should always make a couple of tests of whether our parameters are identifiable by refitting the model with a bigger value of K.

Attached is what Royle, in his Biometrics paper in 2004, says on this this (on page 110, top left, of the paper).

Best wishes  --  Marc

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