R lm difference between interactions with category and one models per category [duplicate]

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.

Model 1

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 Species01, Species01:Env and Species01:Env_sq).

I wonder if this Model 1 is different from the following Model 2 inferred for each of the single species:

Model 2

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)?

• If you have categorical variable, the two models shouldn't be different. If you choose 1 particular species and simplify Model 1 by removing all of the other species you should end up with Model 2. I think your question is similar to this one: stats.stackexchange.com/questions/547577/… Jan 20, 2022 at 22:48
• Thank you, I was simply wondering if there was a difference in the inference of the parameters or something like this, I am happy to have a confirmation that both models are equivalent for a single species. Jan 25, 2022 at 12:40