Use of alternative link functions in occupancy models

[patk]

I am exploring some additional link functions because some of my betas have SEs that are ugly in my top models (sparse dataset). I have run the occupancy estimation using alternative link functions and in some cases the betas improve but the deviance changes albeit not dramatically.

My questions are: 1) are all link functions available in MARK suitable for binomial models? For example, the log function does improve the betas but I am concerned that it is more appropriate for Poisson distributions.

2) I assume since the deviances change that I will have to run the set of models with the same link function.

Thanks for any feedback.
Pat

[sbonner]

Hi Pat,

1) are all link functions available in MARK suitable for binomial models? For example, the log function does improve the betas but I am concerned that it is more appropriate for Poisson distributions.

The simple answer to this question is no. For example, if you model a probability (p) using the log function as log(p)=beta then p is not bounded in [0,1]. If beta>0 then p>1. If the true p is close to 1 then you're likely to run in to problems in MARK because p will go above 1 during the optimization, and you are likely to get confidence intervals that extend above 1.

That said, you may get away with this in some cases. If p is small then log(p) and logit(p) are very close and the results should be very similar -- if p is small then and . Similarly, logit(p) is very close to linear if p is near .5, so you could get away with using an identity link in this case.

However, my general advice would be to stick with a link function that appropriately bounds the parameters in your model. If you are getting "ugly" SEs then this likely indicates that your parameter estimates are on the boundary (p near 0 or 1). In this case, you can use the profile likelihood interval option to compute more reasonable confidence intervals.

2) I assume since the deviances change that I will have to run the set of models with the same link function.

I wouldn't worry that the deviance has changed -- this simply indicates that changing the log function has changed the fit of the model -- improved the fit if the deviance is smaller and made it worse if the deviance is bigger. However, if you wanted to do model averaging then you would have to have the same link functions in all models since the interpretations of the beta parameters could be very different.

Cheers,

Simon

[patk]

Hi Simon: Thanks for the excellent feedback. I will try the profile interval likelihood option.
Have a good day.
Pat