Stata 16: Lasso for Prediction and Model Selection

Overview

• New feature in Stata 16: Lasso for prediction and model selection.
• Includes three estimators:
  • Lasso
  • Square-root lasso
  • Elastic net
• Models that can be fitted:
  • Linear
  • Logit
  • Probit
  • Poisson

Features

• Utilizes cross-validation, adaptive lasso plugins, and user-specified criteria.
• After fitting a lasso model, you can:
  • Create cross-validation function plots.
  • Generate coefficient path plots.
  • Select different lambda values.
  • Create tables listing variable entry/exit.
  • Tabulate measures of fit by lambda.
  • Compare fit across multiple lasso models.

Using the Lasso Dialog Box

• Accessed under Statistics > Lasso.
• Allows specification of:
  • Dependent variable
  • Variables to always include in the model
  • List of variables for lasso selection
  • Selection method
  • Cross-validation options

Example with Fake Survey Data

• Dataset: web use fake survey
• Contains responses to 161 questions + demographic data.
• Objective: Select variables predicting response to Question 104.
• Traditional variable selection is challenging with 160 questions.

Variable Grouping

• Use VL commands to define variable groups:
  • VL set identifies categorical and continuous variables.
  • Categorical: variables with 4 or fewer unique values.
  • Continuous: variables with more than 4 unique values.
  • Use uncertain zero option to omit uncertain groups.
• Output:
  • 115 categorical variables
  • 47 continuous variables
• Global macros created:
  • VL_categorical
  • VL_continuous

Fitting Lasso Models

1. Split Sample
   • Split data into training (group one) and testing (group two) datasets.
2. Fit Linear Lasso Model
   • Command: lasso linear for dependent variable q104.
   • Specify covariates using global macros.
   • Include if sample == 1 for training data fitting.
   • Set a random number seed for reproducibility.
3. Model Fit
   • Default lasso fits 23 models with varying lambda values.
   • Model 19: Largest out-of-sample R-squared and smallest cross-validation mean prediction error.
   • Best prediction: lambda = 0.17.
4. Visualizations
   • Use CV plot to create graph of lambda vs. cross-validation function.
   • Confirm minimum at lambda = 0.17.

Model Selection and Evaluation

• Store model results: estimates store CV.
• Use lasso knots to create a model information table:
  • Model number
  • Lambda value
  • Nonzero coefficients count
  • Out-of-sample R-squared
  • BIC value.
• Selection: Choose model with lowest BIC (Model 14).
• View cross-validation plot for selected model using CV plot.

Adaptive Lasso Model

• Fit adaptive lasso model with selection adaptive:
  • Selected model 78 for best fit based on smallest CV mean prediction error.
  • Store results as adaptive.
• Use lasso Co F to view selected variables across models.

Goodness of Fit Assessment

• Use lasso gof to evaluate fit on training vs. testing samples:
  • Sample 1: Training data
  • Sample 2: Testing data
• Results indicate minimum BIC model has smallest mean squared error and largest R-squared in testing data.

Additional Resources

• For more information on lasso for prediction and model selection, access the manual on the website.