I am trying to calculate SEs of real parameter estimates using Beta output from MARK. I am using multistrata modeling to estimate the effects of certain management actions on movement of cormorants among colonies. I know that I need to use the delta method to estimate variances. I've read Appendix B of Gentle Introduction and the documentation from Colorado State's FW663 class on the subject. I have replicated SE estimates for apparent survival and resight probability, that were modeled using the logit link. I can not figure out how to calculate SE for movement parameters that were estimated using the multinomial logit link. I have calculated the partial derivative of the mlogit equation in Mathematica D, and tried to calculate variance as:
var(Y) = DV transposeD, where V is the variance-covariance matrix.
Estimating SEs for movement rates based upon Beta estimates is an intermediate step in calculating certain effect sizes. I have included the effect of oiling cormorant eggs on movement as the proportion of the colony that was treated (in the design matrix). So the size of the effect of oiling eggs would the difference between movement rates with egg oiling and movement rates without egg oiling. Where each of these effects and their SEs are estimated from the Beta equation.
In an ideal world, we would have been able to apply a single new management option each year, so that we could simply calculate effect sizes as differences in real parameter estimates from one year to the next. Of course, this is assuming there is no annual variation. Unfortunately, I can not estimate the effect sizes in this manner.
Any help would be greatly appreciated.