Questions regarding secr.test, hazard-rate detection function and extracting variance estimates from a fitted model

[Jai Thomas]

Hi,

I have three questions that I am hoping someone could answer for me.

Firstly, are the results from the secr.test interpreted the same as the bootstrapped GOF test in program MARK? (e.g. the lower the value of P, the more you have to worry about lack of fit (page 5-22 in Program MARK –a gentle introduction-).

 

Is it ever ok to use the hazard rate detection function? When I use AIC to compare models with differnt detection functions, the models with hazard rate or exponential detection functions always have the smallest AIC values. In most of the stuff I have read, using hazard rate is discouraged unless there is some kind of boundary. The population I am studying is on an island. Is it therefore ok to use the hazard rate detection function? I only ask because the density estimates are considerably different depending on which detection function is used.  

Lastly, I would like to calculate population change (lambda= Dt+1/Dt) and the associated standard error (SE(lambda_i) =  ).

 Is there any way that I can extract the variance estimate for density from a fitted model so that I can calculate SE(lambda_i)?

Cheers

Jai

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Jai Thomas

PhD Candidate, Terrestrial Ecology Research Group
School of Veterinary and Life Sciences
Murdoch University, Western Australia

____________________________________________

[Murray Efford]

Firstly, are the results from the secr.test interpreted the same as the bootstrapped GOF test in program MARK? (e.g. the lower the value of P, the more you have to worry about lack of fit (page 5-22 in Program MARK –a gentle introduction-).

I don't know MARK that well, but I expect the answer is Yes

 

Is it ever ok to use the hazard rate detection function? When I use AIC to compare models with differnt detection functions, the models with hazard rate or exponential detection functions always have the smallest AIC values. In most of the stuff I have read, using hazard rate is discouraged unless there is some kind of boundary. The population I am studying is on an island. Is it therefore ok to use the hazard rate detection function? I only ask because the density estimates are considerably different depending on which detection function is used. 

The main problem with the hazard-rate function, andalso  the reason it may fit better than say halfnormal, is its long tail, which accommodates occasional long movements. A long tail means that very distant animals have a chance to get caught and the population at risk of detection is enormous. On an island there will be a natural boundary rather than an arbitrary cutoff, so this is less of a worry. The exponential function serves nearly the same purpose but is better behaved in the tail. If the different detection functions result in very different estimates I would be careful - those long movements may be having far too much influence.

Lastly, I would like to calculate population change (lambda= Dt+1/Dt) and the associated standard error (SE(lambda_i) =  ).

 Is there any way that I can extract the variance estimate for density from a fitted model so that I can calculate SE(lambda_i)?

I don't quite get the question. 'secr' reports SE for density. If you are interested in multiplicative population change between sessions then the beta coefficient D.Session of a model with D ~ Session (not capital S) is log(lambda) (assuming the default log link for density). So lambda-hat = exp(beta-hat) and SE(lambda-hat) = exp(beta-hat) * sqrt(exp(sebeta-hat^2)-1) (the standard delta approximation used in 'secr'). For the ovenbird example in 'secr'

beta <- coef(ovenbird.model.D)['D.Session', 'beta']

sebeta <- coef(ovenbird.model.D)['D.Session', 'SE.beta']
exp(beta)
[1] 0.9381417
exp(beta) * sqrt(exp(sebeta^2)-1)
[1] 0.06589315
# 95% CI by backtransforming limits on log scale
exp(coef(ovenbird.model.D)['D.Session', c('lcl','ucl')])
                lcl     ucl
D.Session 0.8176272 1.07642

Murray

[Murray Efford]

Taking this further...

For session-specific estimates of finite population increase (lambda) I found a way to use a different coding of the 'session' factor. This requires a tweak to secr - now included in release 3.1.1 submitted to CRAN a few minutes ago and available in the meantime as Windows binary secr_3.1.1.zip or source secr_3.1.1.tar.gz. The tweak allows users to specify the contrasts used in coding factor predictors (such as 'session').

The idea is spelled out in the 'Trend across sessions' section of secr-multisession.pdf.

Murray

[Jai Thomas]

Thanks a million Murray 👍. 

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Jai Thomas

PhD Candidate, Terrestrial Ecology Research Group
School of Veterinary and Life Sciences
Murdoch University, Western Australia

____________________________________________

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From: secr...@googlegroups.com <secr...@googlegroups.com> on behalf of Murray Efford <murray...@gmail.com>
Sent: Thursday, 30 November 2017 4:25:28 AM
To: secr
Subject: Re: Questions regarding secr.test, hazard-rate detection function and extracting variance estimates from a fitted model

 

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[Murray Efford]

No worries - I hope it's useful. Note that the links to pre-release secr 3.1.1 in my earlier email are now obsolete (and won't work): use the new version from CRAN (3.1.3.

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