I was looking at different link functions for binomial glms recently for
the same reason as you (more zeros than ones). I did a bit of reading up
on the various link functions and IIRC, you can use the cloglog link on
your data, just turn your 0's into 1's and vice versa. This was stated
in the one or two references I looked at as to why only one of cloglog
and loglog links is often provided in software

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