Introduction
Method
Shrinkage parameter
Hypothesis testing about regression coefficients
Numerical study
Intimate partner violence
Variable | \(\hat {\beta }\) | \(SE(\hat {\beta })\) | Odds ratio | P−value | |
---|---|---|---|---|---|
MELM | Group: Control | 0.08 | 0.53 | 1.08 | 0.874 |
Intervention(Ref) | |||||
Time | -0.36 | 0.43 | 0.69 | 0.396 | |
Financial | 0.36 | 0.26 | 1.43 | 0.161 | |
Sexual | 0.13 | 0.24 | 1.13 | 0.605 | |
Physical | 0.14 | 0.13 | 1.14 | 0.304 | |
Psychological | 0.09 | 0.05 | 1.10 | 0.079 | |
RMELM | Group: Control | 0.44 | 0.10 | 1.55 | < 0.0001 |
Intervention(Ref) | |||||
Time | -0.86 | 0.11 | 0.42 | < 0.0001 | |
Financial | 0.87 | 0.10 | 2.37 | < 0.0001 | |
Sexual | 0.64 | 0.09 | 1.90 | < 0.0001 | |
Physical | 0.38 | 0.05 | 1.46 | < 0.0001 | |
Psychological | 0.13 | 0.02 | 1.13 | < 0.0001 |
Simulation study
Discussion and conclusions
MELM | RMELM | |||||||
---|---|---|---|---|---|---|---|---|
n | ICC | ρ | \(\hat \beta _{1}\) | \(\hat \beta _{2}\) | \(\hat \beta _{3}\) | \(\hat \beta _{1}\) | \(\hat \beta _{2}\) | \(\hat \beta _{3}\) |
30 | 0.2 | 0.7 | 1.04 (25) | 1.03 (17) | 0.14 (3) | 0.09 (-35) | 0.12 (-30) | 0.05 (-43) |
0.8 | 1.38 (5) | 1.36 (12) | 0.13 (7) | 0.10 (-30) | 0.14 (-52) | 0.05 (-43) | ||
0.9 | 2.41 (15) | 2.45 (2) | 0.12 (0) | 0.11 (-25) | 0.15 (-55) | 0.05 (-43) | ||
0.95 | 2.33 (25) | 2.46 (-2) | 0.12 (0) | 0.12 (-25) | 0.14 (-57) | 0.05 (-43) | ||
0.5 | 0.7 | 1.51 (10) | 1.55 (12) | 0.18 (0) | 0.09 (-45) | 0.14 (-60) | 0.06 (-53) | |
0.8 | 2.16 (75) | 1.95 (-15) | 0.18 (-3) | 0.10 (-25) | 0.15 (-65) | 0.06 (-53) | ||
0.9 | 3.75 (-50) | 3.73 (47) | 0.18 (-3) | 0.08 (-45) | 0.12 (-57) | 0.06 (-53) | ||
0.95 | 6.93 (-10) | 7.38 (27) | 0.20 (-3) | 0.08 (-30) | 0.13 (-62) | 0.06 (-53) | ||
0.8 | 0.7 | 3.06 (-30) | 3.16 (25) | 0.29 (-10) | 0.09 (-65) | 0.15 (-72) | 0.08 (-70) | |
0.8 | 4.34 (35) | 4.15 (7) | 0.29 (-7) | 0.09 (-55) | 0.16 (-72) | 0.08 (-67) | ||
0.9 | 7.56 (5) | 7.68 (10) | 0.32 (-13) | 0.08 (-60) | 0.15 (-75) | 0.08 (-67) | ||
0.95 | 15.12 (25) | 15.07 (20) | 0.30 (3) | 0.06 (-45) | 0.14 (-72) | 0.07 (-63) | ||
50 | 0.2 | 0.7 | 0.35 (0) | 0.39 (7) | 0.08 (0) | 0.05 (-35) | 0.09 (-50) | 0.04 (-43) |
0.8 | 0.60 (-15) | 0.61 (12) | 0.07 (3) | 0.06 (-35) | 0.09 (-47) | 0.03 (-43) | ||
0.9 | 1.16 (-20) | 1.09 (15) | 0.08 (0) | 0.07 (-35) | 0.09 (-50) | 0.04 (-43) | ||
0.95 | 2.21 (10) | 2.23 (2) | 0.07 (-3) | 0.06 (-15) | 0.10 (-55) | 0.04 (-43) | ||
0.5 | 0.7 | 0.60 (-15) | 0.63 (15) | 0.10 (-3) | 0.07 (-45) | 0.10 (-52) | 0.05 (-50) | |
0.8 | 1.02 (35) | 0.96 (-15) | 0.11 (3) | 0.06 (-35) | 0.12 (-62) | 0.05 (-50) | ||
0.9 | 1.84 (20) | 1.81 (-2) | 0.09 (-3) | 0.06 (-35) | 0.11 (-60) | 0.05 (-50) | ||
0.95 | 3.7 (20) | 3.74 (0) | 0.12 (10) | 0.05 (-30) | 0.10 (-62) | 0.04 (-47) | ||
0.8 | 0.7 | 1.75 (15) | 1.79 (30) | 0.21 (3) | 0.07 (-60) | 0.13 (-67) | 0.06 (-60) | |
0.8 | 2.76 (30) | 2.56 (20) | 0.18 (-7) | 0.07 (-55) | 0.14 (-70) | 0.06 (-67) | ||
0.9 | 5.08 (-5) | 5.16 (22) | 0.20 (7) | 0.06 (-55) | 0.13 (-70) | 0.06 (-60) | ||
0.95 | 9.40 (-15) | 9.71 (22) | 0.18 (0) | 0.06 (-33) | 0.13 (-72) | 0.06 (-63) | ||
100 | 0.2 | 0.7 | 0.18 (5) | 0.18 (-5) | 0.03 (0) | 0.04 (-30) | 0.07 (-47) | 0.03 (-37) |
0.8 | 0.23 (5) | 0.24 (-5) | 0.03 (-7) | 0.04 (-25) | 0.07 (-47) | 0.03 (-40) | ||
0.9 | 0.44 (0) | 0.43 (-2) | 0.03 (-3) | 0.04 (-25) | 0.07 (-47) | 0.03 (-40) | ||
0.95 | 0.88 (15) | 0.88 (-15) | 0.03 (0) | 0.04 (-20) | 0.08 (-52) | 0.03 (-40) | ||
0.5 | 0.7 | 0.25 (-5) | 0.26 (5) | 0.04 (-3) | 0.05 (-45) | 0.07 (-50) | 0.03 (-46) | |
0.8 | 0.37 (15) | 0.37 (-2) | 0.04 (0) | 0.05 (-35) | 0.08 (-55) | 0.03 (-46) | ||
0.9 | 0.61 (-10) | 0.66 (7) | 0.04 (0) | 0.04 (-35) | 0.09 (-55) | 0.03 (-46) | ||
0.95 | 1.32 (-25) | 1.30 (7) | 0.04 (-6) | 0.04 (-35) | 0.08 (-57) | 0.03 (-50) | ||
0.8 | 0.7 | 0.82 (15) | 0.90 (15) | 0.10 (-6) | 0.05 (-55) | 0.11 (-65) | 0.05 (-66) | |
0.8 | 1.05 (35) | 1.15 (2) | 0.08 (0) | 0.05 (-50) | 0.12 (-67) | 0.05 (-63) | ||
0.9 | 2.05 (35) | 2.08 (-7) | 0.09 (6) | 0.05 (-50) | 0.12 (-70) | 0.05 (-60) | ||
0.95 | 3.95 (-10) | 3.88 (25) | 0.09 (0) | 0.05 (-50) | 0.11 (-67) | 0.05 (-60) |
MELM | RMELM | |||||||
---|---|---|---|---|---|---|---|---|
n | ICC | ρ | \(\hat \beta _{1}\) | \(\hat \beta _{2}\) | \(\hat \beta _{3}\) | \(\hat \beta _{1}\) | \(\hat \beta _{2}\) | \(\hat \beta _{3}\) |
30 | 0.2 | 0.7 | 0.05 | 0.08 | 0.10 | 0.80 | 0.82 | 0.90 |
0.8 | 0.04 | 0.06 | 0.09 | 0.77 | 0.79 | 0.88 | ||
0.9 | 0.05 | 0.06 | 0.11 | 0.75 | 0.76 | 0.91 | ||
0.95 | 0.04 | 0.04 | 0.10 | 0.75 | 0.73 | 0.90 | ||
0.5 | 0.7 | 0.04 | 0.06 | 0.08 | 0.77 | 0.80 | 0.88 | |
0.8 | 0.06 | 0.06 | 0.09 | 0.77 | 0.77 | 0.88 | ||
0.9 | 0.04 | 0.05 | 0.08 | 0.71 | 0.73 | 0.89 | ||
0.95 | 0.04 | 0.04 | 0.09 | 0.62 | 0.66 | 0.87 | ||
0.8 | 0.7 | 0.05 | 0.04 | 0.05 | 0.74 | 0.74 | 0.83 | |
0.8 | 0.05 | 0.05 | 0.06 | 0.74 | 0.73 | 0.84 | ||
0.9 | 0.04 | 0.04 | 0.06 | 0.67 | 0.70 | 0.85 | ||
0.95 | 0.05 | 0.05 | 0.06 | 0.56 | 0.57 | 0.84 | ||
50 | 0.2 | 0.7 | 0.05 | 0.08 | 0.18 | 0.88 | 0.89 | 0.95 |
0.8 | 0.06 | 0.08 | 0.19 | 0.85 | 0.89 | 0.96 | ||
0.9 | 0.06 | 0.09 | 0.21 | 0.84 | 0.86 | 0.94 | ||
0.95 | 0.06 | 0.07 | 0.18 | 0.81 | 0.80 | 0.95 | ||
0.5 | 0.7 | 0.06 | 0.09 | 0.15 | 0.86 | 0.86 | 0.91 | |
0.8 | 0.08 | 0.07 | 0.14 | 0.84 | 0.87 | 0.93 | ||
0.9 | 0.06 | 0.08 | 0.17 | 0.83 | 0.81 | 0.93 | ||
0.95 | 0.05 | 0.05 | 0.18 | 0.75 | 0.76 | 0.94 | ||
0.8 | 0.7 | 0.06 | 0.07 | 0.10 | 0.85 | 0.85 | 0.90 | |
0.8 | 0.06 | 0.06 | 0.08 | 0.80 | 0.81 | 0.88 | ||
0.9 | 0.06 | 0.07 | 0.10 | 0.77 | 0.77 | 0.90 | ||
0.95 | 0.07 | 0.07 | 0.09 | 0.72 | 0.74 | 0.90 | ||
100 | 0.2 | 0.7 | 0.11 | 0.20 | 0.46 | 0.88 | 0.90 | 0.98 |
0.8 | 0.09 | 0.15 | 0.42 | 0.89 | 0.91 | 0.98 | ||
0.9 | 0.07 | 0.11 | 0.43 | 0.87 | 0.90 | 0.97 | ||
0.95 | 0.08 | 0.09 | 0.43 | 0.84 | 0.88 | 0.98 | ||
0.5 | 0.7 | 0.10 | 0.16 | 0.34 | 0.86 | 0.88 | 0.94 | |
0.8 | 0.10 | 0.13 | 0.36 | 0.87 | 0.88 | 0.96 | ||
0.9 | 0.08 | 0.10 | 0.37 | 0.82 | 0.87 | 0.95 | ||
0.95 | 0.07 | 0.08 | 0.32 | 0.78 | 0.81 | 0.95 | ||
0.8 | 0.7 | 0.10 | 0.12 | 0.20 | 0.82 | 0.84 | 0.88 | |
0.8 | 0.10 | 0.10 | 0.20 | 0.80 | 0.81 | 0.91 | ||
0.9 | 0.09 | 0.10 | 0.23 | 0.76 | 0.77 | 0.91 | ||
0.95 | 0.09 | 0.11 | 0.22 | 0.73 | 0.74 | 0.92 |
n | ICC | ρ | MELM | RMELM |
---|---|---|---|---|
30 | 0.2 | 0.7 | 35.51 | 16.23 |
0.8 | 55.82 | 16.39 | ||
0.9 | 31.61 | 16.39 | ||
0.95 | 37.85 | 16.39 | ||
0.5 | 0.7 | 90.42 | 41.83 | |
0.8 | 82.36 | 41.89 | ||
0.9 | 69.25 | 42.28 | ||
0.95 | 75.14 | 42.15 | ||
0.8 | 0.7 | 203.67 | 264.10 | |
0.8 | 170.74 | 264.49 | ||
0.9 | 186.09 | 264.64 | ||
0.95 | 169.43 | 262.87 | ||
50 | 0.2 | 0.7 | 10.81 | 16.44 |
0.8 | 17.38 | 16.54 | ||
0.9 | 13.68 | 16.49 | ||
0.95 | 15.07 | 16.52 | ||
0.5 | 0.7 | 26.21 | 42.02 | |
0.8 | 37.03 | 42.20 | ||
0.9 | 38.22 | 42.19 | ||
0.95 | 46.13 | 42.21 | ||
0.8 | 0.7 | 137.90 | 263.55 | |
0.8 | 149.56 | 261.40 | ||
0.9 | 148.32 | 261.48 | ||
0.95 | 120.76 | 263.8 | ||
100 | 0.2 | 0.7 | 5.04 | 16.15 |
0.8 | 5.28 | 16.41 | ||
0.9 | 4.70 | 16.39 | ||
0.95 | 5.07 | 16.45 | ||
0.5 | 0.7 | 15.11 | 41.08 | |
0.8 | 12.90 | 41.65 | ||
0.9 | 13.54 | 41.54 | ||
0.95 | 11.38 | 41.77 | ||
0.8 | 0.7 | 83.39 | 256.69 | |
0.8 | 78.19 | 256.61 | ||
0.9 | 67.40 | 257.31 | ||
0.95 | 73.20 | 259.98 |