Method | Stability of model selection | Incorporating model uncertainty | Computational efficiency (running time)a |
---|---|---|---|
I. STEPWISE REGRESSION METHODS | |||
Backward elimination (AIC) | Moderate | Do not incorporate model uncertainty in the estimation of regression coefficients and standard errors. | Model selection: 5.4 s |
Estimation of SE with bootstrapb: 30.9 s | |||
Backward elimination (BIC) | Very poor | Model selection: 5.6 s | |
Estimation of SE with bootstrapb: 15.0 s | |||
Backward elimination (LRT) | Moderate | Model selection: 5.1 s | |
Estimation of SE with bootstrapb: 19.2 s | |||
Forward selection (AIC) | Moderate | Model selection: 2.8 s | |
Estimation of SE with bootstrapb: 28.5 s | |||
Forward selection (BIC) | Very poor | Model selection: 1.9 s | |
Estimation of SE with bootstrapb: 13.8 s | |||
Forward selection (LRT) | Moderate | Model selection: 3.1 s | |
Estimation of SE with bootstrapb: 19.8 s | |||
II. PENALIZED REGRESSION METHODS | |||
Lasso | Poor (λmin) | Model uncertainty is partially incorporated into the estimation and inference procedure via λ tuning step, and estimation of standard errors using bootstrap. | Lasso algorithm: 0.02 s |
Good (λ1se) | 10-fold CV: 0.5 s | ||
Estimation of SE with bootstrapb: 394.0 s | |||
Adaptive lasso | Good (λmin) | Estimation of weights (ridge regression): 1.6 s | |
Good (λ1se) | Adaptive lasso algorithm: 0.02 s | ||
10-fold CV: 0.5 s | |||
Estimation of SE with bootstrapb: 411.2 s | |||
Adaptive elastic net | Good (λmin) | Estimation of weights (ridge regression): 1.6 s | |
Good (λ1se) | Estimation of λ for L2 penalty (elastic net): 1.2 s | ||
Adaptive elastic net algorithm: 0.2 s | |||
10-fold CV: 1.4 s | |||
Estimation of SE with bootstrapb: 3,265.3 s | |||
III. BAYESIAN MODEL AVERAGING | |||
Bayesian model averaging (using MCMC to search model space) | PIPs of regression covariates inform model selection. Bootstrap gave selection frequencies that were almost identical to PIPs (data not shown). | Model uncertainty is properly incorporated into the estimation of regression coefficients and their standard deviations (provided that MCMC chain converged and the algorithms managed to search the entire model space). | 250.8 s |
(1,000,000 iterations, chain converged) |