Why does sin link return logit-scale beta estimates?

questions concerning analysis/theory using program MARK

Why does sin link return logit-scale beta estimates?

Postby eng » Mon Sep 21, 2020 4:10 pm

I'm fitting pretty simple time-varying CJS models using the sin link function for all parameters. When I run my models, the .out file states "Link Function Used is SIN". However, the beta estimates returned by MARK appear to be logit link values (i.e., real estimates are the inverse logit of the beta estimates, rather than the arcsine of the beta estimates). Why is that? Am I missing something about how MARK uses the sin link function?
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Re: Why does sin link return logit-scale beta estimates?

Postby cooch » Mon Sep 21, 2020 4:24 pm

See p. 22-23 in Chapter 6. Note that it really should be called the 'arcsine' link, since the estimation of the model parameters are actually on that scale, then backtransformed using a sin transform to the probability scale. However, George Box originally called it a sin link, and that somewhat erroneous name has stuck.
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Re: Why does sin link return logit-scale beta estimates?

Postby eng » Mon Sep 21, 2020 6:30 pm

Ah perfect! Thank you for the page reference and the interesting bit of nomenclatural history.
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