parameters on a boundary, sin link, design matrix

questions concerning analysis/theory using program MARK

parameters on a boundary, sin link, design matrix

Postby abreton » Wed Apr 26, 2006 3:25 pm

In the manual and eslewhere, we learn that the sin link does better than the logit when estimates of parameters are on a boundary (0 or 1). Given this, and the parm-specific option off the design matrix, it seems intuitively reasonable to do the following when complete convergence fails using only the logit: use the sin link to estimate parameters on a boundary and logit to estimate all others. But here is what is keeping me up at night: we are strongly cautioned in the manual not to use the sin link in the design matrix - the main reason being the multi-modal structure of the sin function and the risk of the estimate getting lost in 'sin space' (down one hill or mode, up another...etcetera). This leds to my question: when, if ever, is it appropriate with a design matrix to use the sin link?
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parameters on a boundary, sin link, design matrix

Postby gwhite » Wed Apr 26, 2006 6:03 pm

Andre:

You can use the sin link with the design matrix when only a single column is non-zero. However, you would also want to be sure that the beta for this column is not used elsewhere.

The way to figure out if you screwed up is to run the model with both the logit and then sin links, and if the estimates and deviance differ, you probably should not have been running the sin link.

Gary
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Postby abreton » Wed Apr 26, 2006 6:41 pm

Given the value of sin for estimating boundary estimates and especially (I suspect) for sparse datasets, I was hopeful that there was some hard to find, published or otherwise, solution that would allow me to use the sin in a design matrix - that is, outside of an identity matrix. Unfortunately, the dataset I'm working with at the moment is too sparse for an identity matrix. Thanks for your insights...and so Evan doesn't attach a "RTFM" to my name, *I've read the manual many times and MARK helpfile - I was just hopeful that another option existed! Cheers - andre
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