Regarding "Indeed, time spent is just one of the response we measured. there is another response value for the preference, i.e., LEDnum (num of birds under LED at night, as birds won't move at night, so we count number of birds in each cage, we have total 3 birds for each group). for time spent or proportion of time, the value is continous data, how about the number of birds (0,1,2, or 3) or the corresponding proportion? Can we use the same model to analyze it?":
The analysis of LEDnum should use a binomial distribution, which models proportion as number of "successes" out of number of "trials". "Success" is a bird under LED. Number of trials is 3. The beauty of the GLIMMIX procedure is that it offers different distributions (like beta and binomial), so to some extent the code is similar. Unfortunately, there are lots of ways that a binomial mixed model can go wrong: estimation problems, overdispersion, etc.
I don't have time to do much more right now, but see
https://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/viewer.htm#statug_glimmix_a00...
https://support.sas.com/resources/papers/proceedings15/SAS1919-2015.pdf
http://www.lexjansen.com/wuss/2006/Analytics/ANL-Dai.pdf
