library(party)
irisct <- ctree(Species ~ ., data = iris)
print(irisct)
tb <- with(iris, table(cut(Petal.Length, c(0, 1.9, Inf)), Species))
print(tb)
print(chisq.test(tb))
How does the package get the "statistic = 140.264"? the chisq.test get "X-squared = 150", It's not the same. What does "criterion" mean?
Function ctree does not use $\chi^2$ tests, it uses conditional inference tests. These are implemented in package libcoin, functions LinStatExpCov and doTest. For more details, you can consult their help files, or Strasser and Weber (1999). As mentioned above, you can also consult the ctree vignette, or you can read Hothorn et al. (2006).
If you use ctree from package partykit instead of party, you can easily recover the test statistics computed for all potential partitioning variables in every terminal node. For example for the root node (node 1):
irisct <- partykit::ctree(Species ~ ., data = iris)
irisct[[1L]]$node$info$criterion
## Sepal.Length Sepal.Width Petal.Length Petal.Width
## statistic 9.218715e+01 5.971664e+01 1.402644e+02 1.384036e+02
## p.value 3.835958e-20 4.312762e-13 1.393271e-30 3.532723e-30
## criterion -3.835958e-20 -4.312762e-13 -1.393271e-30 -3.532723e-30
What ctree does internally to compute these statistics, for example for
Sepal.Length in the first node, is as follows:
Y <- model.matrix( ~ Species, data = iris)
X <- iris$Sepal.Length
lev <- libcoin::LinStatExpCov(X = X, Y = Y)
tst <- libcoin::doTest(lev, teststat = "quadratic", pvalue = TRUE,
lower = TRUE, ordered = FALSE, log = TRUE,
minbucket = 7)
tst$TestStatistic
## [1] 140.2644
The printed value of criterion is 1 minus the p-value for each splitting node, see also party::ctree_control. When using partykit::ctree, the misclassification error in each terminal node will be printed.
This probably does not answer all your questions, but hopefully provides some pointers.
Hothorn, T., Hornik, K., & Zeileis, A. (2006). Unbiased recursive partitioning: A conditional inference framework. Journal of Computational and Graphical statistics, 15(3), 651-674.
Strasser, H. and Weber, C. (1999). On the asymptotic theory of permutation statistics. Mathematical Methods of Statistics 8(2), 220–250.
ctreestatistic is calculated (the default is "quad"). $\endgroup$