I am analysing a dataset of the performance of several species given an environmental variable.
To do so, I use a simple linear model with the lm function from the stats package.
formula_All_Species = Perf ~ -1 + Species + Species:Env + Species:Env_sq
Species is a factor,
Env is a numeric, as well as
Env_sq with Env_sq = Env^2.
I look at the results for a single species (for instance, I look at the coefficients
I wonder if this Model 1 is different from the following Model 2 inferred for each of the single species:
formula_Single_Species = 1 + Env + Env_sq
In summary, how is a model with interactions between categories and variables different from several models without interaction (one for each category)?