Calculation of real parameter conf interval (stumped again)

[bmitchel]

I am trying to understand how MARK calculates confidence intervals (and S.E.) for real parameters. I have a number of linear constraint betas and a logit link. I can correctly generate the parameter estimate (p in this case) with:

logit(p) = sum of the betas*covariate values
p = exp[logit(p)]/(1+exp[logit(p)])

My understanding is that

variance of logit(p) = sigma_i (covariate value_i^2 * beta_i) + sigma_i sigma_k (2 * covariate value_i * covariate value_k * covariance_ik).

In this case, the variance of p is not particularly meaningful (because when converted to probability the distribution is no longer normal), but the confidence interval can be calculated:

lower CI = exp(logit(p) - 1.96*sqrt[var of logit(p)])/(1 + exp(logit(p) - 1.96*sqrt[var of logit(p)]))
The upper CI would be the same, but with + instead of the two - signs.

Unfortunately, the confidence intervals I calculate this way are much larger than MARK's.

I would appreciate any information on how MARK calculates the confidence interval of p, and whether the standard error is useful for anything.

Thanks, as usual!

Brian Mitchell

[bmitchel]

It turns out that my formula for calculating the variance of logit(p) is correct, and is the same one MARK uses. The problem was that I had an error in my calculations.

I am still very interested in hearing how MARK calculates the SE for real parameters. I was under the impression that SE's should not be used after any nonlinear transformation (i.e. any of MARK's link functions) because the nonlinearity makes them hard to interpret (and useless for building confidence intervals).

However, I have noticed that MARK uses the SE for real parameters when model averaging, and I am hoping that someone can point me towards some documentation for how these SE's were calculated and why they are suitable for model averaging.

Thanks!

Brian Mitchell