Counting parameters in Poisson Log Normal models

questions concerning analysis/theory using program MARK

Counting parameters in Poisson Log Normal models

Postby SBeatham » Tue Mar 03, 2015 4:47 pm

Hi there,

I have noticed that some of the Poisson log normal parameter numbers in the result browser are incorrect. Does this mean I should not trust the AIC weightings? If so how can I compare models with incorrect parameter numbers?

On a separate note, please could you send me a link to Garry Whites Lectures on the Colorado State University website as the link from the Mark website is broken.

Thank you,
Sarah
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Re: Counting parameters in Poisson Log Normal models

Postby cooch » Tue Mar 03, 2015 4:54 pm

SBeatham wrote:Hi there,

I have noticed that some of the Poisson log normal parameter numbers in the result browser are incorrect. Does this mean I should not trust the AIC weightings? If so how can I compare models with incorrect parameter numbers?


And you know they're wrong because...?

If you're sure that MARK is reporting the wrong number of parameters (which can happen as a function of the numerical optimization of the likelihood -- this is discussed at several points in the MARK book -- see addendum to Chapter 4, for example), then you simply manually adjust the parameter count to the 'correct' number of parameters. This is also discussed in several places in the MARK book.

On a separate note, please could you send me a link to Garry Whites Lectures on the Colorado State University website as the link from the Mark website is broken.

Thank you,
Sarah


The contents of those notes in largely contained in, and in many cases, superseded by the more detailed treatment in the MARK book (and there is a lot in the MARK book that isn't in Gary's notes, because he last taught the 'estimation class' before some models were available in MARK.)
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Re: Counting parameters in Poisson Log Normal models

Postby ehileman » Tue Mar 03, 2015 4:55 pm

Hi Sarah,

You can manually adjust the number of parameter using the "Adjustments" tab within the results window. The lectures can also be found here: http://warnercnr.colostate.edu/~gwhite/fw663/Mark.html

Cheers!

Eric
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Re: Counting parameters in Poisson Log Normal models

Postby SBeatham » Tue Mar 03, 2015 6:38 pm

Thank you both for your speedy replies. I assumed the parameters were incorrect as they did not match the number of parameters in the PIM chart.
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Re: Counting parameters in Poisson Log Normal models

Postby cooch » Tue Mar 03, 2015 6:53 pm

SBeatham wrote:Thank you both for your speedy replies. I assumed the parameters were incorrect as they did not match the number of parameters in the PIM chart.


Woah...the number of parameters in the PIMs (or PIM chart) is *not* necessarily the number of identifiable parameters for a given model. My suspicion is that your just starting working with these models -- as such, you are *strongly* urged to work through Chapter 1 -> 7 of the MARK book, before going much further. Fully understanding the relationship between the PIMs, the design matrix, and parameter identifiabilty (and, in the process, differentiating between parameters that are either extrinsically or intrinsically non-identifiable) is critical to using MARK.
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Re: Counting parameters in Poisson Log Normal models

Postby SBeatham » Tue Mar 03, 2015 7:46 pm

Sorry I probably didn't explain myself fully. I have been building models with the Poisson Log Normal model for several years now. I always use the identity matrix as the models I build are fairly simple (just a large number of groups) For example in the PIM chart the model alpha(group*t)sigma(season)U(group*t) has 32 parameters and 32 in the results browser while alpha(group*t)sigma(group*t)U(group*t) has 45 in the PIM chart and 44 in the results browser. I can't see why the latter should have dropped one parameter when the first one didn't.
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Re: Counting parameters in Poisson Log Normal models

Postby Hope132 » Mon Aug 07, 2017 10:32 am

Hi,
I have a similar problem with my thesis. I'm not sure if I calculate the number of parameters the right way.

I'm doing a Burnham Joint live encounter and dead recovery analysis, which has the parameters S (survival), p (properbility live resight), r (properbility of dead report), and F (dispersal from the sample).

As I understood, as soon as one of the parameters is constant in a model without covariates, all parameters are estimatable. For the other cases I should use the procedure from chapter 4, and count unique parameters in the table of saturated capture histories.

I also want to analyse individual covariate data. Since this includes using a design matrix, the logit link funktion has to be used. MARK seems to make far more errors with this one, than with the sin link.
For a basic Model with at least one constant parameter, can I use the number of columns in the DM as the number of estimatable parameters?

So can I use this procedure?:
no individual covariates -> At least one constant parameter: number of parameters= estimatable parameters
No constant parameter : use table of saturated encounter histories
individual covariates -> Number of collumns in DM= estimatable parameters

Thank You!
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