What is the Glmnet package in R?

Last Updated : 16 Apr, 2025

The glmnet package in R is a robust package for L1 and L2 regularized linear and logistic regression model fitting, useful for avoiding overfitting and enhancing the generalization of the models. Lasso (L1) and Ridge (L2) regression techniques add a penalty term to the objective function in the model to simplify the model. Here, we will show how to conduct regularized regression using the glmnet package, which involves fitting a Lasso model, cross-validation tuning, and prediction.

Regularized Regression

A type of regression that adds a penalty term to the cost function to reduce overfitting.

Lasso Regression: A type of regularized regression that adds an L1 penalty term to the cost function.
Ridge Regression: A type of regularized regression that includes an L1 penalty term in the cost function.
Elastic Net Regression: A type of regularized regression that includes an L2 penalty term in the cost function.

Syntax

glmnet(X, y, family = "gaussian", alpha = 1, lambda = NULL)

The main function in the glmnet package is glmnet(), which fits a regularized generalized linear model. The function accepts a number of important arguments:

x: The matrix of predictor variables.
y: The response variable.
alpha: Declares the type of regularization (Lasso: alpha = 1, Ridge: alpha = 0, Elastic Net: 0 < alpha < 1).
lambda: Regularization parameter that affects the strength of the penalty.
family: specifies the type of response variable (e.g., Gaussian, binomial, Poisson).

Example 1: Fitting a Lasso Regression Model

Step 1: Install and Load the `glmnet` Package

First, install and load the necessary package.

install.packages("glmnet") library(glmnet)

Step 2: Load and Prepare the Data

Here, we load the mtcars dataset from the R package and use its data on car models and their features.

data(mtcars)   # Select all columns except the first as predictors. X <- as.matrix(mtcars[, -1])  # Select the first column as the response. y <- mtcars[, 1]

Step 3: Fit a Lasso Regression Model

The following code fits a Lasso regression model, and the Summary(model) provides information on the fitted model, like the number of non-zero coefficients, the value of the regularization parameter lambda used, and the coefficients themselves.

# Fit a regularized linear regression model model = glmnet(X, y, family = "gaussian", alpha = 1) summary(model)

Output:

          Length Class     Mode   
a0         79    -none-    numeric
beta      790    dgCMatrix S4     
df         79    -none-    numeric
dim         2    -none-    numeric
lambda     79    -none-    numeric
dev.ratio  79    -none-    numeric
nulldev     1    -none-    numeric
npasses     1    -none-    numeric
jerr        1    -none-    numeric
offset      1    -none-    logical
call        5    -none-    call   
nobs        1    -none-    numeric

Step 4: Plot the model

plot(model) will plot the relationship between the regularization parameter lambda and the estimate coefficients.

plot(model, label = TRUE)

Output

L1 Norm vs Estimated coefficients- Geeksforgeeks — L1 Norm vs Estimated coefficients

In the above graph, each curve represents the path of the coefficients against the L1 norm as lambda varies.

Step 5: Get the model coefficients

coef(model, , s = 0.1)

Output:

1 x 1 sparse Matrix of class "dgCMatrix"
                     s1
(Intercept) 20.12070307
cyl         -0.21987003
disp         .         
hp          -0.01300595
drat         0.77162507
wt          -2.63787681
qsec         0.46074875
vs           0.11747113
am           2.11349978
gear         0.30437026
carb        -0.46452172

Step 6: Prediction

Predict values for new data using the predict function. For example, the following code predicts values for new data using the Lasso regression model:

# Predict the response variable (y) using the fitted model and the predictor variables (x). y_pred <- predict(model, X)

Example 2: Using Cross-Validation for Lasso Model

Step 1: Fit a Lasso Model with Cross-Validation

For more robust model selection, you can use cross-validation to find the optimal value of lambda. The cv.glmnet() function automatically performs k-fold cross-validation.

# Fit a Lasso model with cross-validation fit <- cv.glmnet(X, y, alpha = 1, nfolds = 5)  # Display a summary of the model summary(fit)

Output:

           Length Class  Mode     
lambda     79     -none- numeric  
cvm        79     -none- numeric  
cvsd       79     -none- numeric  
cvup       79     -none- numeric  
cvlo       79     -none- numeric  
nzero      79     -none- numeric  
call        5     -none- call     
name        1     -none- character
glmnet.fit 12     elnet  list     
lambda.min  1     -none- numeric  
lambda.1se  1     -none- numeric  
index       2     -none- numeric

Step 2: Plot Cross-Validation Results

You can plot the results of the cross-validation to visualize the selection of lambda.

# Plot the cross-validation results using the "plot" function. plot(fit)

Output

cross-validation - Geeksforgeeks — cross-validation

Step 3: Make Predictions and Plot Actual vs Predicted

Once the model is fitted, you can use it to make predictions and visualize the results.