I am having a little trouble verifying correct notation for a crossed factor nested mixed model anova using lme4 package in R. My data is experimental, I applied two crossed treatments (light and nutrients) and measured growth of algal cultures, and did so during 3 separate months. I would like to specify in the model that the light and nutrient factors are nested within month. This is not a three way crossed design because the algal communities were different each month. I'm considering month to be a fixed factor because it is temporally dependent, but light and nutrient application as random because high and low light or nutrient levels can be generalized to a broader range of natural conditions (although I know arguments could be made for the opposite).
Using lme4, my model for crossed random effects looks like this, although I'm not certain that this is the appropriate way to specify that nutrients and light are nested within Month:
lmer(growth.day ~ (1|Light:Nutrients) + (Month / Light:Nutrients), growth.dat)
something doesn't seem right in output. I've considered using
aov(), as follows, but I am not sure that notation is correct in describing
Month as fixed and
Light * Nutrients as random:
aov(growth.day ~ Error(Light * Nutrients) + (Month / (Light * Nutrients)), growth.dat)