Can fixed-effect model apply for unbalanced data?
I remembered it can but severeal things have to be noticed but I cannot find the website now
Yeah it can. The issue is that, in a multi-factor ANOVA setup, unbalanced data causes the sums of squares for the individual treatments to be dependent, so there gets to be some interpretation issues. Instead of getting to just look at the individual sums of squares on their own, you have to look at different sums of squares depending on what hypothesis you are testing (phrases like Type I or Type III sums of squares might ring a bell).