Page 442 - Applied Statistics with R

442 CHAPTER 17. LOGISTIC REGRESSION

Instead we’ll have to use estimated probabilities. So to create a classifier that
seeks to minimize misclassifications, we would use,

̂
̂
(x) = argmax [ = ∣ X = x].

In the case of a binary response since ̂(x) = 1 − ̂(x), this becomes

̂
(x) = { 1 ̂ p(x) > 0.5
0 ̂ p(x) ≤ 0.5
Using this simple classification rule, we can turn logistic regression into a clas-
sifier. To use logistic regression for classification, we first use logistic regression
to obtain estimated probabilities, ̂(x), then use these in conjunction with the

above classification rule.
Logistic regression is just one of many ways that these probabilities could be
estimated. In a course completely focused on machine learning, you’ll learn
many additional ways to do this, as well as methods to directly make classifica-
tions without needing to first estimate probabilities. But since we had already
introduced logistic regression, it makes sense to discuss it in the context of
classification.

17.4.1 spam Example

To illustrate the use of logistic regression as a classifier, we will use the spam
dataset from the kernlab package.

# install.packages("kernlab")
library(kernlab)
data("spam")
tibble::as.tibble(spam)

## Warning: `as.tibble()` was deprecated in tibble 2.0.0.
## Please use `as_tibble()` instead.
## The signature and semantics have changed, see `?as_tibble`.

## # A tibble: 4,601 x 58
## make address all num3d our over remove internet order mail receive
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0 0.64 0.64 0 0.32 0 0 0 0 0 0
## 2 0.21 0.28 0.5 0 0.14 0.28 0.21 0.07 0 0.94 0.21
## 3 0.06 0 0.71 0 1.23 0.19 0.19 0.12 0.64 0.25 0.38
## 4 0 0 0 0 0.63 0 0.31 0.63 0.31 0.63 0.31