I am fitting forest biomass data to a modified version of the Chapman-Richards function using the nlsLM() function. I am curious about the impact of multiple binary predictor variables on the model. The two binary variables are "thinned" and "planted." I have a good sense of how to test the effect of a single binary variable: I can stratify the model by both levels of the predictor, and then use goodness-of-fit tests to determine if the stratified model is better than the simple model. This has been covered in a previous answer: How to test the effect of a grouping variable with a non-linear model?
However, I am unsure how to correctly test the additive and interactive effects of both binary predictor variables in the same model. For instance, what is the effect of "thinned" given "planted"?
I can create a model (let's call it model1) stratified by all four possible combinations of the predictors:
thinned=Y & planted=Y
thinned=Y & planted=N
thinned=N & planted=Y
thinned=N & planted=N
And compare this to a model (let's call it model2) where I stratify by levels of "planted" only:
planted = Y
planted = N
Using goodness-of-fit testing, I can determine if model1 is a better fit than model2. However, I am uncertain what I've just tested. Did I test for the additive effect of "thinned", or the interactive effect of "thinned"? If I tested for the additive effect of "thinned", how would I test for the interactive effect (or vice versa)?
