I have a problem with my random effect definition. Lets say I have a mixed effect model predicting species richness (S) by precipitation (P) and temperature (T) in different places - different datasets together (dataset) (that is the random effect). I am also interested in interaction between temperature and precipitation.
Now I have a mixed effect model (actually it is more complicated but doesnt matter for this qustion) with variying both slope and intercept by datasets and I am not sure if the fixed effects (temperature and precipitation) should be in random effect also with interaction or just as a sum, i.e. (using lmer function in R)
S ~ T*P + (1+(T + P)|dataset)
S ~ T*P + (1+(T * P)|dataset)
Is it both possible with different interpretation or just one is correct?