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1 Regularized Linear Modeling and Knockoff Filtering

Use the ALS (Case Study 15) data to:

  • Detect and impute missing value if any.

  • Use the ALSFRS_slope as a clinically relevant outcome variable.

  • Randomly split data into training (70%) and testing (30%) datasets.

  • Use the LASSO to fit a model with cross validation (with optimized regularization parameter) and visualize the result.

  • Similarly, train a ridge regression model.

  • Train OLS model and improve it with stepwise variable selection.

  • Report the coefficient estimates for OLS, Stepwise OLS with AIC, Ridge and LASSO.

  • Calculate the predicted values for all 4 models and report the models performance metircs (RMSE and \(R^2\)).

  • Apply knockoff filtering for variable selection, controlling the false discovery rate.

  • Compare the variables selected by Stepwise OLS, LASSO and knockoff.

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