Confidence intervals for the Royle-Nichols model in Presence

[matobler]

I have a few questions regarding the calculation of confidence intervals for lambda in the Royle-Nichols model. To start, Presence reports two different CI for lambda. The first one is in the "Site estimates" part. Unlike other parameters this does not seem to be estimated using +-1.96*SE on the betas. How are these CI estimated? Using a profile likelihood? In the Model parameters section the CI is calculated with +-1.96*SE on the real parameters.

My last question concerns the CI for the derrived parameter psi. Presence simply calculates it based on the estimate and SE of psi. This can result in upper CI >1 or lower CI<1. Wouldn't it be better to calculate the CI for psi based on the CI for lambda: CIpsi=1-exp(-CIlambda)? So for the example bellow the CI for psi would then be 0.656 - 0.923.

Thanks,

Mathias

Untransformed (beta) parameters:
Estimated parameter estimate std.err
-------------------------- -------- -------
beta0 = -2.5222 0.2440
beta1 = 0.1616 0.2234

Individual Site estimates of Lambda:
Site Survey Lambda Std.err 95% conf. interval
1 1 1 1-0: 1.1754 0.2626 1.0658 - 2.5588
============================================================
MODEL PARAMETERS:
Estimated parameter estimate std.err 95% confidence interval
-------------------------- -------- ------- ------------------------
Detection probability (r) = 0.0743 0.0168 0.0414 - 0.1072
Avg. abundance/sample unit(lambda) = 1.18 0.26 0.66 - 1.69

Derrived parameter estimate std.err 95% confidence interval
-------------------------- -------- ------- ------------------------
Occupancy (psi) = 0.6913 0.0811 0.5324 - 0.8502
Total Abundance (N) = 172.78 38.60 97.12 - 248.44

[darryl]

I have a few questions regarding the calculation of confidence intervals for lambda in the Royle-Nichols model. To start, Presence reports two different CI for lambda. The first one is in the "Site estimates" part. Unlike other parameters this does not seem to be estimated using +-1.96*SE on the betas. How are these CI estimated? Using a profile likelihood? In the Model parameters section the CI is calculated with +-1.96*SE on the real parameters.

I'm not 100% certain, but my best guess is that for teh first one Jim has calculated the limits as +/- 1.96*SE on the log scale (as 0<lamda<inf), then transformed those limits. In the second case he's done it on the real scale instead.

My last question concerns the CI for the derrived parameter psi. Presence simply calculates it based on the estimate and SE of psi. This can result in upper CI >1 or lower CI<1. Wouldn't it be better to calculate the CI for psi based on the CI for lambda: CIpsi=1-exp(-CIlambda)? So for the example bellow the CI for psi would then be 0.656 - 0.923.

This probably would be a better way to do it.

Cheers
Darryl

[stephanietodd]

Hello,
Neither of my lambda estimates seem to have a 95%CI that is calculated from +/- 1.96SE. I noticed that for the model parameter estimate of lambda, the upper CI limit is much further away from the estimate than the lower CI... isn't this because its assuming a Poisson dist, and +/- 1.96SE is for a Normal dist? in that case how to you calculate the 95% CI for a Poisson dist?
Also, for one of my models the estimate of lambda is actually below (outstide) the lower 95% CI... not sure why that is??? this is from the output:
estimate std.err 95% confidence interval
1.16 0.03 1.94 - 22.45
Also my SE for lambda is always 0.03 in every model regardless of the estimate and 95% CI's....

Any help much appreciated
Cheers,
Stephanie

[darryl]

Jim has updated the output since 2008. As noted in the previous post, the CI's a asymmetric because they are first calculated on the log scale as x -/+1.96*SE, then transformed onto the real scale (eg lower limit = exp(x - 1.96*SE)). Note that x and SE are for the beta parameters, not the acutal lambda estimates.

The lambda estimate should be between the limits of your CI, that it not suggests some sort of problem either with the data, the way you've set up the model, or PRESENCE. If it's only happening for one model that might suggest the middle option is most likely.

Cheers
Darryl

[stephanietodd]

Jim has updated the output since 2008. As noted in the previous post, the CI's a asymmetric because they are first calculated on the log scale as x -/+1.96*SE, then transformed onto the real scale (eg lower limit = exp(x - 1.96*SE)). Note that x and SE are for the beta parameters, not the acutal lambda estimates.

The lambda estimate should be between the limits of your CI, that it not suggests some sort of problem either with the data, the way you've set up the model, or PRESENCE. If it's only happening for one model that might suggest the middle option is most likely.

Cheers
Darryl

Hi Darryl,
Yes of course it would help to look at the post dates.

I tried running the model again, very carefully entering the covariates with the exact same result. The covariates in this model are used in other models and the output is fine. I'm tempted to say its a problem with the program, as I have had some other problems (different results in different projects with exact same data and models, the green 'repeat model type' button saying I have been doing a Royle Biometrics model when I have been using the R-N model type, model outputs disappearing although the model is still present....)

However a bad builder blames his tools, and I am by no means a good (model) builder.

Any idea why the SE for lambda is always 0.03?

cheers,
Steph

[darryl]

PRESENCE does have a few 'features' (some call them bugs), and this could be one of them. If you send me your PRESENCE files offlist I'll take a quick look at them for you.
Darryl

[stephanietodd]

Hi Darryl,
That would be fantastic. Thankyou.
Shall I email them to you?
Cheers,
Steph

[darryl]

FYI. Off list we determined that it was a PRESENCE 'feature' that has now been removed. Users might want to update to the new version. Note it only affected some of the derived parameters in the output, the beta parameter estimates were fine.
Cheers
Darryl