evaluating temporal covariates from beta values

[howeer]

I'm able to reconstitute real parameter estimates (capture probabilities) from beta values using the equations for the linear model and link functions, but what I'd like to do is get the slopes associated with temporal covariates ("real covariates" in the gentle intro) into the same scale as the real parameter estimates. Since parameters are estimated on (in my case) the logit scale, slopes (beta values) are also on that scale, right?. Is there a way to back-transform the beta values for temporal covariates to yield slopes such that a positive slope means a positive relationship between the temporal covariate and capture probabilities and vice versa?
Thanks

[jlaake]

If it is linear in the logit space, it is non-linear in the real space so there is no concept of a single slope. You can get the slopes function by taking the derivative of the inverse logit transformation with respect to the covariate of interest. For example, if it is

p(T)=exp(beta0+beta1*T)/(1+exp(beta0+beta1*T)=1/(1+exp(-beta0-beta1*T)

you can take the derivative of p(T) with respect to T to get slope equation in real space.

For any slope of a continuous covariate T the derivative for the real space is

p(T)*(1-p(T))*Beta

where Beta is the parameter for the continuous covariate. From this you can see that the sign of beta determines both the sign of the slope in the logit and real spaces because p(T)*(1-P(T)) will always be positive. Try it out by computing a numerical slope for a set of real parameters and comparing it to this value.

--jeff