Multivariate classification RF - splitting rule clarification

[larajan67]

I appreciate your work in developing the R package – randomForestSRC. The capacity to create multivariate random forest models via the package’s functions has been ideal for my work in modeling taxa distributions simultaneously. However, I would appreciate some clarification on the splitting rule implemented for the multivariate classification random forest. I have read the vignette on various multivariate splitting rules from your website as well as your paper “Random Forest missing data algorithms". Specifically, I would like to know the following:

1. In the case of the averaged standardized Gini splitting rule for multivariate random forest, are the best splits determined by maximizing this extended Gini split-statistic or only maximizing the Gini split statistic for each coordinate? It seems that the maximizing happens to the extended Gini split-statistic, as suggested in Equation 2 of “Random forest missing data algorithms”, but I would like to confirm.
2. Is the multivariate nature of the response matrix (multiple response variables) accounted for only through the calculation of the extended Gini split statistic? The vignette suggests that correlation among coordinates is ignored, as it states “A disadvantage is that it’s an additive independence rule that works over the Y coordinates separately, and as such it does not take into account correlation. If this is the case, when I discuss the method, should I state that it accommodates multivariate structure (via the extended Gini split statistic) but not multivariate correlation?

[ishwaran]

Thank you for your questions, here are my responses:

1. We maximize the extended Gini split-statistic. For concreteness, suppose there are two coordinates Y(1), Y(2). Then for a proposed split there are Gini statists G(1) and G(2), the extended split-statistic is the average G=[G(1)+G(2)]/2. This value G is what is being maximized.
2. Yes, the multivariate nature of the response value Y(1),...,Y(q) is only accounted for through the calculation of the extended split-statistic. When you are referring to this statistic, something like the following is appropriate "the multivariate-extended split-statistic is able to accommodates the multivariable nature of the responses without directly modeling correlation"