Negative Likelihood Ratio

nlr.factor

R Documentation

Description

A generic function for the negative likelihood ratio in classification tasks. Use weighted.nlr() weighted negative likelihood ratio.

Usage

## S3 method for class 'factor'
nlr(actual, predicted, ...)

## S3 method for class 'factor'
weighted.nlr(actual, predicted, w, ...)

## S3 method for class 'cmatrix'
nlr(x, ...)

## Generic S3 method
nlr(...)

## Generic S3 method
weighted.nlr(
 ...,
 w
)

Arguments

actual	A vector of - of length \(n\), and \(k\) levels.
predicted	A vector of -vector of length \(n\), and \(k\) levels.
…	micro = NULL, na.rm = TRUE Arguments passed into other methods
w	A <numeric>-vector of length \(n\). NULL by default.
x	A confusion matrix created cmatrix().

Value

If micro is NULL (the default), a named <numeric>-vector of length k

If micro is TRUE or FALSE, a <numeric>-vector of length 1

Definition

Let \(\hat{\alpha} \in [0, \infty]\) be the likelihood of a negative outcome. The negative likelihood ratio of the classifier is calculated as,

\[ \hat{\alpha} = \frac{1 - \frac{\#TP}{\#TP + \#FN}}{\frac{\#TN}{\#TN + \#FP}} \]

Where:

• \(\frac{\#TP}{\#TP + \#FN}\) is the sensitivity, or true positive rate

• \(\frac{\#TN}{\#TN + \#FP}\) is the specificity, or true negative rate

Examples

# 1) recode Iris
# to binary classification
# problem
iris$species_num <- as.numeric(
  iris$Species == "virginica"
)

# 2) fit the logistic
# regression
model <- glm(
  formula = species_num ~ Sepal.Length + Sepal.Width,
  data    = iris,
  family  = binomial(
    link = "logit"
  )
)

# 3) generate predicted
# classes
predicted <- factor(
  as.numeric(
    predict(model, type = "response") > 0.5
  ),
  levels = c(1,0),
  labels = c("Virginica", "Others")
)

# 3.1) generate actual
# classes
actual <- factor(
  x = iris$species_num,
  levels = c(1,0),
  labels = c("Virginica", "Others")
)

# 4) evaluate model performance
# with class-wise negative likelihood ratios
cat("Negative Likelihood Ratio", sep = "\n")
nlr(
  actual    = actual, 
  predicted = predicted
)

cat("Negative Likelihood Ratio (weighted)", sep = "\n")
weighted.nlr(
  actual    = actual,
  predicted = predicted,
  w         = iris$Petal.Length/mean(iris$Petal.Length)
)