Calculating SE and 95% CI for phi

[micah]

I am seeking some clarification on a previous topic (Confidence intervals for phi (interaction) parameter).
It appears that the site estimate of phi is the exponentiated beta coefficient, but it is not clear how the SE and CI are derived.
According to the previous post “To compute the 95% confidence interval, take the beta estimate for phi, add/subtract 1.96 times it's std.err., then transform those values (using exp function)”.
Thus, if my output for the beta coefficient of phi and its SE is as below, I calculate a 95% CI of 1.127 – 2.283:
Beta Coefficients:
occupancy phi 0.473085 (0.180002)

However these are not the CI values that appear in PRESENCE, copied below:
Individual Site Estimate of phi:
site survey phi std.err 95% conf. interval
Bear_Cr 1-1 1.6049 0.2899 1.5062 – 3.0501
I'm hoping to obtain clarification on how the SE and CIs are being calculated in PRESENCE for this value of phi, as they do not appear to be simple exponentiated values of the confidence interval surrounding the beta coefficient as would occur in simple logistic regression.

Thanks for your help.

[jhines]

The confidence interval can be computed by transforming the beta values using the link function, but I don't understand why you're using the exp link function. This function does not limit the occupancy estimate to be between zero and one. Normally, the logit link function (exp(Beta0+beta1)/(1+exp(beta0+beta1)) is used. Did you intentionally choose the exp link function?

The method above will give the 95 % confidence interval, but it probably won't be centered around the estimate. To get a standard error of the transformed phi, the delta method can be used. With this standard error, you can compute a 95% confidence interval around the occupancy estimate which is 'centered'.

Jim

[cooch]

The confidence interval can be computed by transforming the beta values using the link function, but I don't understand why you're using the exp link function. This function does not limit the occupancy estimate to be between zero and one. Normally, the logit link function (exp(Beta0+beta1)/(1+exp(beta0+beta1)) is used. Did you intentionally choose the exp link function?

The method above will give the 95 % confidence interval, but it probably won't be centered around the estimate. To get a standard error of the transformed phi, the delta method can be used. With this standard error, you can compute a 95% confidence interval around the occupancy estimate which is 'centered'.

Jim

Following Jim's response, the calculation of the 95% CI on the back-transformed betas (for psi, lets say) is discussed in some detail in the second appendix of the 'MARK book':

http://www.phidot.org/software/mark/docs/book/

See especially example (3), starting on p. 15.