standard error in Pradel's lambda

[achatinella]

Hi folks,

I’m using Pradel models (survival and seniority specification) to estimate survival, recruitment, and realized lambda as a function of covariates. I wrote a program that uses the Delta method to calculate standard errors for each individual. I checked the accuracy of my program by comparing the SE I get from my program to those reported by Mark for the standardized mean. My estimates are identical (within rounding error) to those reported by Mark for survival and seniority. But to calculate the SE for lambda, I have to fit a separate model (survival and lambda specificaton), so that I can get the VC matrix for lambda. With this model, the SE’s I get for survival are also identical (within rounding error) to those reported by Mark, but the SE for lambda is much smaller than the one reported by Mark.

1. Does anyone know why SEs for lambda would be off when estimates for the other parameters are dead on?

2. Is it legitimate to use a separate model for estimates of the SE on lambda, or should I be calculating all parameters from a single model? If the latter, how does one calculate the SE of a ratio of random variables? That is,

lambda = survival / seniority

but what would be the precision of the estimate of lambda calculated in this way using the SE from survival and seniority?

Thanks in advance,

Jim