Calculating standard errors for co-variate functions...?

[DMills]

I am looking at survival of lobsters relative to size for different habitats, and have found my size co-variate to be an important descriptor of survival in many cases. I have followed the method outlined in chapter 12 to calculate a survival function relating size and survival. Clearly the model output provides SE for the mean sized lobster only.

Is there a way of calculating SEs for the entire function, or at least other points on the curve?

[ganghis]

Hi,

The quick and dirty way if you're only interested in a few points is to rerun the model in question and check the 'user-specified covariate' option on the run model screen... then enter whatever covariate you you want.

Alternatively, you can use the delta method (see Evan's new appendix or Gary's FW663 notes) to calculate the variance of your function at specific points. It's slightly involved because of the transformation (logit or sin) used to constrain survival to (0,1). In any case, you'd be pulling values off of the estimated beta variance/covariance matrix.

Hope that helps...

Cheers, Paul Conn

[cooch]

Hi,
Alternatively, you can use the delta method (see Evan's new appendix or Gary's FW663 notes) to calculate the variance of your function at specific points. It's slightly involved because of the transformation (logit or sin) used to constrain survival to (0,1). In any case, you'd be pulling values off of the estimated beta variance/covariance matrix.

Hope that helps...

Cheers, Paul Conn

The new appendix Paul is referring to is Appendix B (I just posted an updated version 5 minutes ago), which is a fairly thorough discussion of the 'Delta method, which is preciesly what you want to do. I'd recommend going through the whole appendix - before you dive into the examples at the end, one of which is quite close to the precise problem you're describing.

Also, if you wan to avoid the hassles of doing the calculation 'by hand' (or, getting Excel or some other application to do them), and you only want the SE for specific points, MARK gives you the option of using a 'User-specified covariate' value. MARK defaults to the mean covariate value, but you can actually have it give you a user-specified value (i.e., something other than the mean). This is mentioned in Chapter 12.