Table 1.
Simulation results for high-dimensional data with clustered binary outcome generated from balanced and unbalanced designs.
| Balanced Design | |||||
| Estimate | TRUE | GMIFS/glmer | LASSO/glmer | glmmLasso | LASSO |
| σ21 | 2 | 2.46 | 2.46 | 1.14 | - |
| σ22 | 1 | 1.11 | 1.11 | 0.52 | - |
| (Intercept) | 0 | −0.60(0.30) | −0.60(0.30) | −0.45 | −0.36(0.13) |
| β2 | 1 | 0.97(0.27) | 0.97(0.27) | 0.67 | 0.53(0.22) |
| β3 | −1 | −1.08(0.19) | −1.08(0.19) | −0.41 | −0.70(0.09) |
| β4 | 1 | 1.14(0.19) | 1.14(0.19) | 0.46 | 0.77(0.05) |
| β5 | −1 | −0.95(0.18) | −0.95(0.18) | −0.32 | −0.60(0.16) |
| Prediction Error | 0.123 | 0.123 | 0.118 | 0.310 | |
| True Positives | 5 | 5 | 5 | 5 | |
| Time(sec) | 5710.93 | 1887.87 | 6495.28 | 22.43 | |
| Unbalanced Design | |||||
| Estimate | TRUE | GMIFS/glmer | LASSO/glmer | glmmLasso | LASSO |
| σ21 | 2 | 3.78 | 3.43 | 1.86 | - |
| σ22 | 1 | 1.17 | 1.15 | 0.56 | - |
| (Intercept) | 0 | −0.63(0.35) | −0.63(0.40) | −0.52 | −0.41(0.17) |
| β2 | 1 | - | - | 0.30 | - |
| β3 | −1 | −0.77(0.18) | −0.77(0.05) | −0.19 | −0.48(0.27) |
| β4 | 1 | 1.18(0.20) | 1.10(0.01) | 0.49 | 0.68(0.10) |
| β5 | −1 | −0.82(0.17) | −0.78(0.05) | −0.27 | −0.47(0.28) |
| β415 | 0 | - | −0.46(0.21) | −0.05 | −0.29(0.08) |
| β440 | 0 | - | - | −0.02 | - |
| β751 | 0 | 0.58(0.17) | - | 0.09 | - |
| Prediction Error | 0.137 | 0.127 | 0.149 | 0.310 | |
| True Positives | 4 | 4 | 5 | 4 | |
| Time(sec) | 5121. 20 | 1303.38 | 9559.24 | 25.82 | |
TRUE indicates the underlying parameter value; GMIFS logistic model with random effects (GMIFS/glmer), LASSO logistic model with random effects (LASSO/glmer), glmmLasso, LASSO indicate the parameter estimates (and standard error if possible) in the optimal model using four approaches, respectively. The optimal model for GMIFS logistic model with random effects glmer, LASSO logistic model with random effects and LASSO were selected according to the ‘elbow criterion’ in BIC and the optimal model for glmmLasso was selected according to the minimal BIC.