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