[R] Classification Tree Prediction Error

[Bert Gunter]

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Bert Gunter

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On Mon, Aug 24, 2020 at 8:58 AM Xu Jun <junxu.r using gmail.com> wrote:

> 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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>
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