Understanding Cross-Validation in Logistic Regression

A Deeper Dive into the Challenges of Implementing 10-Fold Cross-Validation in R

In the world of machine learning, cross-validation is a crucial technique used to evaluate the performance of models. It involves splitting the data into training and testing sets, training the model on the training set, and then using the testing set to evaluate its performance. In this article, we will explore the challenges of implementing 10-fold cross-validation in R, specifically focusing on a common issue encountered when using the sample function.

Background: Understanding Cross-Validation

Cross-validation is a resampling technique used to assess the performance of a model by training and testing it on multiple subsets of the data. The goal is to estimate how well the model will perform on unseen data. In logistic regression, cross-validation can be used to evaluate the model’s accuracy, precision, recall, F1 score, and other metrics.

The Challenge: Implementing 10-Fold Cross-Validation

In this article, we will focus on implementing 10-fold cross-validation in R using the sample function. However, before diving into the code, let’s first understand why 10-fold cross-validation is used. The idea behind 10-fold cross-validation is to divide the data into 10 subsets or “folds.” Each fold contains approximately 1/10th of the original data. During training, the model is trained on nine folds, and during testing, it is evaluated on the remaining one fold.

Code Review: The Issue with sample

The original code provided by the user attempts to implement 10-fold cross-validation using a for loop and the sample function. However, there are several issues with this approach:

• Incorrect usage of sample: The sample function is used incorrectly in the original code. Instead of specifying the data frame, it should be specified as the number of elements to sample.
• Inconsistent variable naming: The variable names used in the original code are inconsistent. This makes it difficult to understand and maintain the code.

A Corrected Implementation

Here’s a corrected implementation of 10-fold cross-validation using R:

## Load necessary libraries
library(caret)
library(dplyr)

## Read the dataset
SAdata = read.table("http://statweb.stanford.edu/~tibs/ElemStatLearn/datasets/SAheart.data", sep=",", head=T, row.names=1)

## Define the function for 10-fold cross-validation
log.fun <- function(x, y) {
    # Initialize an empty list to store the results
    results <- list()
    
    # Set the number of folds
    set.seed(123)
    fold = sample(1:10, nrow(SAdata), replace = TRUE)
    
    # Create a data frame with the folded data
    dframe = SAdata[, c("x", "y"),]
    names(dframe) = c("x", "y")
    dframe$fold = factor(fold)
    
    # Perform 10-fold cross-validation
    for (i in 1:10) {
        # Create a new data frame with the current fold as training and test sets
        train = dframe %>% filter(fold != i)
        test = dframe %>% filter(fold == i)
        
        # Fit the logistic regression model to the training data
        model <- glm(x ~ y, data = train, family = binomial)
        
        # Make predictions on the test data
        pred <- as.data.frame(predict(model, test[, c("x", "y")], type = "response"))
        
        # Append the predicted values to the results list
        results[[paste0("Fold", i)]]$train = train
        results[[paste0("Fold", i)]]$test = test
        results[[paste0("Fold", i)]]$model = model
        results[[paste0("Fold", i)]]$pred = pred
        
    }
    
    # Return the list of results
    return(results)
}

## Perform 10-fold cross-validation
your_results <- log.fun(SAdata$chd, SAdata$obesity)

## Print the first few predicted values for each fold
head(your_results[[1]]$prediction)

Explanation

The corrected code uses the caret library to perform 10-fold cross-validation. The sample function is used correctly to generate a random set of folds. Each fold contains approximately 1/10th of the original data.

The code also uses the dplyr library for data manipulation, specifically using the %>% operator to pipe the data from one step to another.

The results are stored in an empty list called results, which is populated with the training, testing, model fit, and predicted values for each fold. The final result is returned as a list of lists, where each inner list corresponds to a single fold.

Conclusion

In this article, we explored the challenges of implementing 10-fold cross-validation in R using the sample function. We also provided a corrected implementation that uses the caret library and the %>% operator from the dplyr library for data manipulation.

Last modified on 2025-03-02