I'm interested to study weather conditions on species diversity. To this end, I used a mixed model, where Julian-day, temperature, and precipitations are the fixed effects, while the month is used as a random effect. My question is: Is it a problem to use a random effect that is correlated with one of the variables in fixed term?
Random effects terms are used to account for correlations in grouped/clustered data. When you include a random effect for the grouping factor
month, then you postulate that species diversity measurements in the same month are correlated. The fixed effects are used to specify the mean of your outcome variable (i.e., species diversity).
When you put month as a grouping factor it is not treated as an ordered factor. Hence, if you have that month is January, February, March, and April, you could recode it to banana, apple, orange, and grape, and you would get the same results.