How to specify a multilevel regression using lmer function in R? I am trying to analyse the effects of clipping (33% and 66%) and season (1, 2 and 3) on species richness.  I have a control (no clipping, in no season) that the values are nested in.  
I am having difficulty building the code for this.
This is what I have managed:
lmm1 <- lmer(Species_Richness ~ Seasonf + Clipf + (Seasonf|Controlf) + 
    (Clipf|Controlf), data = Data)

How can I specify my model?
 A: The code you've written fits the model that has Season and Clipf as fixed effects as well as a random intercept shared by those with the same value of Controlf, and a random slope in Seasonf and Clipf that is shared by those with the same value of Controlf.
But, based on this comment alone
I was intending to make the intercept shared by those with the same value of controlf a fixed effect, as they are nested values (if that makes sense?) and then the season and clip were supposed to be random effects? 
the code you want is: 
lmer(Richness ~ Controlf + (1|Seasonf) + (1|Clipf))

But, I have to say, I'm not really sure this model makes sense. This is saying that observations made in the same season are correlated and observations that have the same clipping value are correlated, while the variable Controlf, which you've described the observations as being "nested within", is being treated as a fixed effect. 
It seems to me that season is more naturally thought of as a fixed effect, since its effect its effect is likely to be systematic (e.g. say there is known to be more species richness in the summer), not by random chance (which is what specifying it as a random effect assumes, informally). Similarly, Clipf seems to be a fixed effect. 
If Controlf is some sort of grouping variable then this seems to be to be more naturally thought of as a random effect. Think of individuals within households - one wouldn't expect certain houses to produce systematically larger (or smaller) responses - the differences between households may be thought of as resulting from random effects. If your observations are nested within Controlf analogously to the way people are nested within households, then it should be a random effect. 
So, your model would be: 
lmer(Richness ~ Seasonf + Clipf + (1|Controlf)) 

But, from your statement control (no clipping, in no season), it makes it sound like Controlf is just another level of Clipf, in which case it should be a left out of the model, as it will be estimated by the intercept. At that point there aren't actually any random effects in the model, so you could just use lm() instead. 
A: I think you might rather want something like:
lmer (Richness ~ 1 + (1 | Seasonf) + (1 | Clipf), data=Data)

where Seasonf's levels are: Control, Season1, Season2, Season3, and Clipf's levels are: Control, P33, and P66.
I'd wait on upvotes to indicate if this is correct, though. I've used lmer a lot, but still don't understand some of the statistical issues involved.
P.S. I'm assuming you have no more data than you've specified. Do you have other data per observation? I'm also assuming that Seasonf and Clipf are factors, and Richness is continuous.
