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Thank you Kjetil for your suggestion. If overdispersion is the problem, then negative binomial would also be suitable to use? I'm searching for the convergence warnings and found this page: rstudio-pubs-static.s3.amazonaws.com/…. Now I'm guessing that the random effect (site) I added is causing the problem. The results of M1 shows site has the variance of 2.460e-12 (very close to zero). I deleted the random effect (site) in M1 and got two significant fixed effects and no warning. However is this the true reason and how to explain this?
