Table 3.

Simulation Results: MSE (SE). Uncorrelated predictors. “Full” is the full regression model that includes all predictors and interactions. “lasso” is the lasso model without any constraints. “Res. lasso” is the lasso model where the main effects are not penalized. “Dir. lasso” is the directed lasso. The boldfaced results are the best for a particular model.

	Dir. lasso	SHIM	Lasso	Res. lasso	Full
n=100, cor=0
Model 1	0.229	0.509	0.502	0.506	0.511
	0.004	0.008	0.008	0.009	0.009
Model 2	0.352	0.366	0.435	0.508	0.527
	0.006	0.006	0.008	0.010	0.010
Model 3	0.380	0.475	0.357	0.458	0.527
	0.007	0.009	0.007	0.008	0.009
Model 4	0.245	0.296	0.315	0.368	0.513
	0.004	0.005	0.005	0.005	0.008
Model 5	0.166	0.219	0.197	0.308	0.517
	0.004	0.005	0.004	0.006	0.008
Model 6	0.322	0.475	0.428	0.514	0.524
	0.005	0.008	0.007	0.009	0.009
Model 7	0.252	0.306	0.405	0.481	0.525
	0.004	0.005	0.007	0.008	0.009
Model 8	0.491	0.713	0.932	1.840	2.590
	0.008	0.028	0.015	0.075	0.127
n=75, cor=0
Model 1	0.325	0.793	0.815	0.826	0.901
	0.006	0.015	0.017	0.019	0.038
Model 2	0.516	0.528	0.680	0.771	0.888
	0.012	0.011	0.017	0.023	0.027
Model 3	0.562	0.667	0.492	0.655	0.856
	0.009	0.011	0.008	0.011	0.018
n=500, cor=0
Model 1	0.044	0.071	0.071	0.071	0.071
	0.001	0.001	0.001	0.001	0.001
Model 2	0.051	0.060	0.065	0.069	0.072
	0.001	0.001	0.001	0.001	0.001
Model 3	0.052	0.059	0.055	0.065	0.071
	0.001	0.001	0.001	0.001	0.001
Model 8	0.065	0.086	0.102	0.131	0.138
	0.001	0.001	0.001	0.001	0.001
n=500, cor=0.3
Model 1	0.042	0.075	0.072	0.072	0.072
	0.001	0.001	0.001	0.001	0.001
Model 2	0.055	0.058	0.060	0.068	0.071
	0.001	0.001	0.001	0.001	0.001
Model 3	0.055	0.057	0.049	0.063	0.069
	0.001	0.001	0.001	0.001	0.001