Standard error values for Averaged estimates

[nawintiwary]

Running a single season occupancy model with covariates in Presence we get occupancy estimates for each site along with std error and CI values. If we are interested in overall site occupancy we average the psi estimates. What is the best way of getting the std error values for the averaged occupancy estimates.

[stephanietodd]

I was wondering the exact same thing.... It seems strange that Presence doesn't include an average psi and SE for that model in the output, seeing as that's what you're supposed to report

[stephanietodd]

Its ok, I know how to do this now. If anyone else wants to know:

-To do the average standard error you have to change the SE into variance first before changing it back into the SE
-First take the square of each Standard error (SE^2) (this assumes that the SE is a known quantity) and this will create the variance for each site
- Add this together (all the variance you just created) to create an total variance
- Divide this with the square of the number of observations (sites^2), this will give you the average of the total variance
- With the average of the total variance take the square root, this will give you the standard error

Cheers,
Steph

[darryl]

Steph,
This only holds if the estimates are independent, which they're not. You need to calculate the full variance-covariance (VC) matrix for the psi estimates (not given in the output, but can be determined from the VC matrix for the regression coefficients/beta parameters which is an optional output). Bigger question though is exactly what is meant by 'overall' occupancy. Is it for just your sample (places that were surveyed), or the population of sites? Is it an average probability or the proportion of sites occupied? There's some subtle, but important, distinctions here that people need to work through.
Cheers
Darryl

[stephanietodd]

Steph,
This only holds if the estimates are independent, which they're not. You need to calculate the full variance-covariance (VC) matrix for the psi estimates (not given in the output, but can be determined from the VC matrix for the regression coefficients/beta parameters which is an optional output). Bigger question though is exactly what is meant by 'overall' occupancy. Is it for just your sample (places that were surveyed), or the population of sites? Is it an average probability or the proportion of sites occupied? There's some subtle, but important, distinctions here that people need to work through.
Cheers
Darryl

Hi Darryl,
Ahhh no.
I'm going off published occupancy studies, who have reported a single occupancy estimate for each of their top models. Also, assuming that there was no one 'top' model (model weight >0.9), these estimates were also averaged (weighted) to give one estimate across sites and models. I know the 'model averaged' option gives you weighted averages across the top models, but this is still by site. The precision of site estimates is also much poorer.

I saw Jim Hines suggested using the null model to report this figure, but if it isn't ranked highly why would you do this? shouldn't the top models with give a more accurate estimate?

If you don't recommend this then what estimates do you recommend reporting? I don't have a priori concept of what I would like to report, I want to report whatever information I have from running the models.

Cheers,
Steph

[darryl]

Well, if you don't know what you want to report, noone here will be able to help you very much...

Higher-ranked models are likely better because the added covariates are explaining some important source of variation in the data. That doesn't necessaryily mean that a simpler model is going to give you the wrong answer if you ignore that covariate and are just after an 'overall' (whatever you mean by that) number. I've looked at it by simulation once and if you have a good sampling design (eg random), then there's no systematic bias introduced by ignoring that important covariate (at least for the scenarios considered).

Here's an analogy. Suppose I wanted to estimate the average height of people in the room, I could take the simple average, or I could build a regression model using gender, age, hair colour, etc. as covariates and use that to predict the average height. Even though the regression model might describe people's individual heights better, there's probably going to be very little difference compared to the simpler approach if I'm only interested in what the average height of people in the room is. If I want to extrapolate to people outside of the room, then if sample can be considered representative of the wider population, again, little is likely gained by taking a more complex approach. Where the more complex approach is worthwhile, is if the traits of the people of the room are not representative (eg suppose 80% of the people in the room were male) in which case you can use the model to predict the height for each person in the population (supposing their traits are known) and calculate an average that way.

That's not to say that simpler is always ok. If there's variation in p that's not being explained by a covariate, that's a form of hetergeneity that can cause a bias in estimated occupancy.

Darryl