# Model Evaluation

library(bayesrules)

For Bayesian model evaluation, the bayesrules package has three functions prediction_summary(), classification_summary() and naive_classification_summary() as well as their cross-validation counterparts prediction_summary_cv(), classification_summary_cv(), and naive_classification_summary_cv() respectively.

Functions Response Model
prediction_summary()
prediction_summary_cv()
Quantitative rstanreg
classification_summary()
classification_summary_cv()
Binary rstanreg
naive_classification_summary()
naive_classification_summary_cv()
Categorical naiveBayes

## Prediction Summary

Given a set of observed data including a quantitative response variable y and an rstanreg model of y, prediction_summary() returns 4 measures of the posterior prediction quality.

1. Median absolute prediction error (mae) measures the typical difference between the observed y values and their posterior predictive medians (stable = TRUE) or means (stable = FALSE).

2. Scaled mae (mae_scaled) measures the typical number of absolute deviations (stable = TRUE) or standard deviations (stable = FALSE) that observed y values fall from their predictive medians (stable = TRUE) or means (stable = FALSE).

3. and 4. within_50 and within_90 report the proportion of observed y values that fall within their posterior prediction intervals, the probability levels of which are set by the user. Although 50% and 90% are the defaults for the posterior prediction intervals, these probability levels can be changed with prob_inner and prob_outer arguments. The example below shows the 60% and 80% posterior prediction intervals.

# Data generation
example_data <- data.frame(x = sample(1:100, 20))
example_data$y <- example_data$x*3 + rnorm(20, 0, 5)

# rstanreg model
example_model <- rstanarm::stan_glm(y ~ x,  data = example_data, refresh = FALSE)

# Prediction Summary
prediction_summary(example_model, example_data,
prob_inner = 0.6, prob_outer = 0.80,
stable = TRUE)
mae mae_scaled within_60 within_80
1 2.405058  0.8680121       0.6       0.9

Similarly, prediction_summary_cv() returns the 4 cross-validated measures of a model’s posterior prediction quality for each fold as well as a pooled result. The k argument represents the number of folds to use for cross-validation.

prediction_summary_cv(model = example_model, data = example_data,
k = 2, prob_inner = 0.6, prob_outer = 0.80)
$folds fold mae mae_scaled within_60 within_80 1 1 2.848569 0.5061318 0.7 1.0 2 2 2.732608 0.5569211 0.6 0.9$cv
mae mae_scaled within_60 within_80
1 2.790589  0.5315264      0.65      0.95

## Classification Summary

Given a set of observed data including a binary response variable y and an rstanreg model of y, the classification_summary() function returns summaries of the model’s posterior classification quality. These summaries include a confusion matrix as well as estimates of the model’s sensitivity, specificity, and overall accuracy. The cutoff argument represents the probability cutoff to classify a new case as positive.

# Data generation
x <- rnorm(20)
z <- 3*x
prob <- 1/(1+exp(-z))
y <- rbinom(20, 1, prob)
example_data <- data.frame(x = x, y = y)

# rstanreg model
example_model <- rstanarm::stan_glm(y ~ x, data = example_data,
family = binomial, refresh = FALSE)

# Prediction Summary
classification_summary(model = example_model, data = example_data, cutoff = 0.5)
$confusion_matrix y 0 1 0 9 1 1 2 8$accuracy_rates

sensitivity      0.80
specificity      0.90
overall_accuracy 0.85

The classification_summary_cv() returns the same measures but for cross-validated estimates. The k argument represents the number of folds to use for cross-validation.

classification_summary_cv(model = example_model, data = example_data, k = 2, cutoff = 0.5)
$folds fold sensitivity specificity overall_accuracy 1 1 0.6 1.0 0.8 2 2 1.0 0.8 0.9$cv
sensitivity specificity overall_accuracy
1         0.8         0.9             0.85

## Naive Classification Summary

Given a set of observed data including a categorical response variable y and a naiveBayes model of y, the naive_classification_summary() function returns summaries of the model’s posterior classification quality. These summaries include a confusion matrix as well as an estimate of the model’s overall accuracy.

# Data
data(penguins_bayes, package = "bayesrules")

# naiveBayes model
example_model <- e1071::naiveBayes(species ~ bill_length_mm, data = penguins_bayes)

# Naive Classification Summary
naive_classification_summary(model = example_model, data = penguins_bayes, y = "species")
$confusion_matrix species Adelie Chinstrap Gentoo Adelie 95.39% (145) 0.00% (0) 4.61% (7) Chinstrap 5.88% (4) 8.82% (6) 85.29% (58) Gentoo 6.45% (8) 4.84% (6) 88.71% (110)$overall_accuracy
 0.7587209

Similarly naive_classification_summary_cv() returns the cross validated confusion matrix. The k argument represents the number of folds to use for cross-validation.

naive_classification_summary_cv(model = example_model, data = penguins_bayes,
y = "species", k = 2)
$folds fold Adelie Chinstrap Gentoo overall_accuracy 1 1 0.9634146 0.09375 0.8965517 0.7790698 2 2 0.9428571 0.00000 0.9242424 0.7383721$cv
Gentoo  6.45%   (8) 2.42% (3) 91.13% (113)