Comparing models estimated by sin & logit link functions

[jlehmkuhl]

Can I compare AIC values for PIM-based models estimated with the sin link function with related design-matrix covariate models estimated with a logit link function? I am modeling Huggins closed-capture data.

I searched The Book and did not find the answer; but, I found a cryptic note from my long-ago 2004 CSU MARK class that comparable models must use the same link function. The sin link generally estimated more parameters than the logit link for PIM-based models; hence, my desire to compare sin & logit link models of the data.

[ganghis]

You should be okay comparing AIC between SIN and LOGIT link functions, provided that the number of parameters has been entered correctly. One issue that happens with the logit link is that when parameters are estimated on the boundary (zooming off to + or - infinity on the beta scale), MARK decides that it can't estimate a parameter and thus the AIC value you get will be off. In this case you're supposed to realize what is happening and adjust the number of parameters manually. This doesn't happen with the SIN link, but of course the trade off is that you can't do stuff with most individual covariates with the SIN link.