I had asked a general question about conditional inference trees via party a while back and gotten a great reply.
I am revisiting this procedure and trying to make sense of the linear statistic that is being used (Hothorn et al., Unbiased Recursive Partitioning: A Conditional Inference Framework, Research Report Series, 2004, page 4, equation (1)).
I am not at all clear how this statistic is calculated. Can anyone help?
Here is what it seems to me that if
- $g(\cdot)$ and $h(\cdot)$ are the identity functions
- and there is a predictor $x$ and a response $y$, both numeric, the statistic is simply a scalar. This is not what is shown, so I am wrong :)
Example data:
x<-c(1,3,4,67,32,23,3,12,4)
y<-c(43,23,45,22,12,465,6,54,3)
w<-rep(1,9)
T<-0
for (i in 1:length(y))
{
T<-T+(w[i]*x[i]*y[i])
}
T #13523
I THINK the result needs to be a vector of length 81.