Classification Tree Prediction Error

Dear all R experts,

I have a question about using cross-validation to assess results estimated
from a classification tree model. I annotated what each line does in the R
code chunk below. Basically, I split the data, named usedta, into 70% vs.
30%, with the training set having 70% and the test set 30% of the original
cases. After splitting the data, I first run a classification tree off the
training set, and then use the results for cross-validation using the test
set. It turns out that if I don't have any predictors and make predictions
by simply betting on the majority class of the zero-one coding of the
binary response variable, I can do better than what the results from the
classification tree would deliver in the test set. What would this imply
and what would cause this problem? Does it mean that classification tree is
not an appropriate method for my data; or, it's because I have too few
variables? Thanks a lot!

Jun Xu, PhD
Professor
Department of Sociology
Ball State University
Muncie, IN 47306
USA

Using the estimates, I get the following prediction rate (correct
prediction) using the test set. Or we can say the misclassification error
rate is 1-0.837 = 0.163

(tab[1,1] + tab[2,2]) / sum(tab)[1] 0.837

Without any predictors, I can get the following rate by betting on the
majority class every time, again using data from the test set. In this
case, the misclassification error rate is 1-0.85 = 0.15

table(h2.test)h2.test

1poorHlth 0goodHlth
      101       575 > 571/(571+101)[1] 0.85



R Code Chunk

# set the seed for random number generator for replication
set.seed(47306)
# have the 7/3 split with 70% of the cases allotted to the training set
# AND create the training set identifier
class.train = sample(1:nrow(usedta), nrow(usedta)*0.7)
# create the test set indicator
class.test = (-class.train)
# create a vector for the binary response variable from the test set
# for future cross-tabulation.
h2.test <- usedta$h2[class.test]
# count the train set cases
Ntrain = length(usedta$h2[class.train])
# run the classification tree model using the training set
# h2 is the binary response and other variables are predictors
tree.h2 <- tree(h2 ~ age + educ + female + white + married + happy,
                data = usedta, subset = class.train,
                control = tree.control(nobs=Ntrain, mindev=0.003))
# summary results
summary(tree.h2)
# make predictions of h2 using the test set
tree.h2.pred <- predict(tree.h2, usedta[class.test,], type="class")
# cross tab the predictions using the test set
table(tree.h2.pred, h2.test)
tab = table(tree.h2.pred, h2.test)
# calculate the ratio for the correctly predicted in the test set
(tab[1,1] + tab[2,2]) / sum(tab)
# calculate the ratio for the correctly predicted using the naive approach
# by betting on the majority category.
table(h2.test)[2]/sum(tab)

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