I try to find "best" linear models with continuous and categorical covariables with Interaction Effect by BIC. The continuous covariables should have a quadratic effect on the response variable.
Additional to that, I want to extract the significant covariates from the full model by the following rule:
- If $Covariable_1*Covariable_i !=0$ for one of the i Covariates, then Covariates_1 and Covariates_i remain in the model (i.e also if just the first order term of the polynomial is significant wrt. p-value then we include also the quadratic term), also all significant interactions - If $Covariates_1*Covariates_i==0$ for all i then we exlude this Interaction Term and look at the maineffects of covariate_1: if there is no effect at all, then we remove this covariate.
Does this rule make any sense?
I wonder whether the step function in R considers this rule automatically and if not, whether there is any procedures/methods to this in R.
How would you start and find the best linear model with polynomial effect if you had to choose?