Understanding the Problem with Drawing a Graph of MSE Error for Ridge Model in R
In this blog post, we will delve into the issues surrounding the task of visualizing the Mean Squared Error (MSE) error for a ridge model built using the glmnet package in R. The problem arises from the incorrect handling of data splitting and model predictions.
Background on Ridge Regression Models
Ridge regression is a type of linear regression that adds a penalty term to the loss function to prevent overfitting. This penalty term, also known as the L2 regularization term, is proportional to the magnitude of the model coefficients. The glmnet package in R provides an implementation of ridge regression using the lasso method, which combines the benefits of both linear and L1 regularization.
Creating the Training and Validation Data Sets
The training data set is created by randomly sampling from the entire dataset with a 2:1 split between the two sets. However, it’s essential to ensure that both the training and validation sets are complete cases.
# Load the necessary libraries
library(glmnet)
library(caret)
# Load the Hitters data
data(Hitters, package = "ISLR")
# Limit the dataset to only include complete cases
Hitters <- Hitters[complete.cases(Hitters), ]
Building and Training the Model
The model is built using the glmnet function, which takes in the predictor variables, response variable, penalty parameter, and other parameters. In this case, we’re using a ridge regression model with no intercept term (alpha = 0).
# Create the model matrix
x <- Hitters[, c("AtBat", "Hits", "HmRun", "Runs", "RBI", "Walks",
"Years", "CAtBat", "CHits", "CHmRun", "CRuns", "CRBI",
"CWalks", "PutOuts", "Assists", "Errors")]
# Scale the predictor variables
x <- scale(x)
# Create a sequence of penalty parameters (lambda)
lambda_seq <- 10^seq(10, -2, length = 100)
# Build and train the model using cross-validation
ridge_model <- glmnet(x, Hitters$Salary, alpha = 0,
lambda = lambda_seq)
cv_ridge <- cv.glmnet(x, Hitters$Salary, alpha = 0)
lambda_optimal <- cv_ridge$lambda.min
# Create a new model with the optimal penalty parameter
ridge_model_optimal <- glmnet(x, Hitters$Salary, alpha = 0,
lambda = lambda_optimal)
Predicting on New Data and Calculating RMSE
The caret package provides a function for calculating the root mean squared error (RMSE). However, in this case, we can calculate it manually by taking the square root of the average of the squared differences between predicted and actual values.
# Create new data sets for training and validation
set.seed(1)
train_test <- sample(1:2, nrow(x), TRUE, prob = 2:1)
train <- as.data.frame(cbind(Hitters$Salary[train_test == 1], x[train_test == 1,]))
valid <- as.data.frame(cbind(Hitters$Salary[train_test == 2], x[train_test == 2,]))
# Create the model matrix for training and validation
x_train <- model.matrix(Hitters$Salary ~ ., data = train)[,-1]
y_train <- train$Salary
x_valid <- model.matrix(Hitters$Salary ~ ., data = valid)[,-1]
y_valid <- valid$Salary
# Predict on new data using the trained model
mse_ridge <- sqrt(mean((predict(ridge_model_optimal, newx = x_valid) - y_valid)^2))
# Alternatively, use caret to calculate RMSE
caret::RMSE(predict(ridge_model_optimal, newx = x_valid), y_valid)
Visualizing the Residuals
We can visualize the residuals by plotting the actual values against the predicted values. This will give us a better understanding of how well our model is performing.
# Plot the residual histogram
hist(predict(ridge_model_optimal, newx = x_valid) - y_valid,
main = "Residual histogram", xlab = "Predicted - Actual")
# Plot the actual versus predicted values
plot(x_valid[,"AtBat"], y_valid, xlab = "At Bat (normalized)",
ylab = "Salary", main = "Actual (black) versus predicted (red)")
points(x_valid[,"AtBat"], predict(ridge_model_optimal, newx = x_valid),
col = "red")
segments(x_valid[,"AtBat"], y_valid, col = "red",
y1 = predict(ridge_model_optimal, newx = x_valid))
Conclusion
In this blog post, we explored the challenges of visualizing MSE error for a ridge model built using glmnet in R. We identified issues with data splitting and model predictions and demonstrated how to create complete data sets, build and train models, predict on new data, and visualize residuals. By following these steps, you can effectively analyze your regression models and identify areas for improvement.
Last modified on 2023-12-26