I am using the randomForest package in R with categorical co-variates. The documentation advises against the formula interface for large data. Following this advice, I prepare the outcome variable and a model.matrix object, M.
My question is does the algorithm treat the columns of M independently, so the mtry variables chosen may be biased to selecting from a factor with many levels? Or is the original factor (available via terms(M)) used when selecting the mtry variables?
I am familiar with cforest and the papers by Strobl et al. that address the bias in randomForest based on the domain of the variables. My question is does the choice of arguments (formula vs matrix) in randomForest exacerbate this bias.