Table 5.
Simulated parameters |
Estimated parameter values
|
σ | r2 | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Genetic main effects (G)
|
Environmental effects (E) and G × E
|
||||||||||||||||||||
Homozygous
|
Heterogygous
|
Epistatic
|
E | Homozygous
|
Heterozyous
|
Epistatic
|
|||||||||||||||
dA | dB | hA | hB | iAB | jAB | jBA | lAB | βm | βdA | βdB | βhA | βhB | βiAB | βjAB | βjBA | βlAB | |||||
1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | .5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |||||
Data | Method | ||||||||||||||||||||
True latent trait | Normal errors | θ | 0.989 | 0.959 | 0.023 | 0.028 | 0.017 | 0.024 | 0.019 | 0.009 | 0.501 | 0.002 | 0.008 | −0.004 | −0.006 | −0.004 | −0.003 | −0.003 | −0.002 | 1.006 | 0.554 |
t | 30.39 | 29.47 | 0.50 | 0.61 | 0.52 | 0.53 | 0.42 | 0.13 | 78.63 | 0.36 | 1.22 | −0.43 | −0.67 | −0.55 | −0.28 | −0.29 | −0.18 | − | – | ||
Normal errors | θ | 0.981 | – | −0.010 | – | – | – | – | – | 0.494 | 0.006 | – | 0.004 | – | – | – | – | – | 1.230 | 0.332 | |
t | 89.48 | – | −0.25 | – | – | – | – | – | 89.48 | 1.11 | – | 0.47 | – | – | – | – | – | – | – | ||
Normal errors | θ | 1.006 | 1.001 | – | – | – | – | – | – | 0.496 | – | – | – | – | – | – | – | – | 1.006 | 0.554 | |
t | 223.0 | 222.8 | – | – | – | – | – | – | 156.3 | – | – | – | – | – | – | – | – | – | – | ||
Logistic regression | θ | 2.558 | 2.785 | −0.403 | −0.329 | −0.449 | 1.251 | 0.896 | 1.084 | 1.068 | −0.094 | −0.140 | 0.060 | 0.019 | 0.037 | −0.155 | −0.118 | −0.099 | – | – | |
t | 3.15 | 3.43 | −0.43 | −0.34 | −0.55 | 1.30 | 0.96 | 1.00 | 8.46 | −0.74 | −1.11 | 0.42 | 0.13 | 0.29 | −1.03 | −0.82 | −0.59 | – | – | ||
Equal item parameters | Sum score | θ | 0.730 | 0.634 | −0.611 | −0.646 | 1.864 | −0.563 | −0.606 | −0.365 | 1.401 | 0.423 | 0.442 | 0.043 | 0.049 | −0.164 | 0.160 | 0.164 | 0.021 | 3.658 | 0.464 |
t | 6.16 | 5.36 | −3.68 | −3.86 | 15.74 | −3.36 | −3.64 | −1.55 | 60.39 | 18.22 | 19.07 | 1.34 | 1.49 | −7.05 | 4.87 | 5.03 | 0.46 | – | – | ||
Square root transformation | θ | 0.583 | 0.532 | −0.150 | −0.179 | 0.483 | 0.059 | 0.091 | −0.087 | 0.352 | 0.031 | 0.041 | 0.025 | 0.030 | −0.081 | 0.008 | 0.001 | 0.014 | 0.933 | 0.470 | |
t | 19.31 | 17.60 | −3.53 | −4.20 | 15.97 | 1.38 | 2.14 | −1.45 | 59.39 | 5.25 | 6.92 | 3.05 | 3.55 | −13.73 | 0.96 | 0.06 | 0.88 | – | – | ||
Logistic regression | θ | 2.462 | 2.466 | 0.371 | 0.615 | −0.741 | 0.079 | 0.176 | −0.151 | 0.961 | −0.112 | −0.112 | −0.054 | −0.084 | 0.082 | −0.029 | −0.020 | 0.039 | – | – | |
t | 6.16 | 6.17 | 0.82 | 1.38 | −1.85 | 0.18 | 0.17 | −0.30 | 15.11 | −1.76 | −1.77 | −0.74 | −1.17 | 1.28 | −0.40 | −0.28 | 0.47 | – | – | ||
Variable item parameters | Sum score | θ | 2.771 | 2.801 | −0.246 | −0.195 | 0.847 | 0.147 | 0.040 | −0.082 | 1.309 | −0.011 | −0.019 | 0.057 | 0.042 | −0.175 | −0.002 | 0.023 | 0.011 | 3.206 | 0.484 |
t | 26.70 | 26.98 | −1.69 | −0.13 | 8.16 | 1.00 | 0.27 | −0.40 | 64.37 | −0.53 | −0.95 | 2.00 | 1.47 | −8.63 | −0.06 | 0.81 | 0.27 | – | – | ||
Square root transformation | θ | 0.653 | 0.655 | 0.034 | −0.000 | −0.020 | 0.003 | −0.002 | −0.008 | 0.230 | −0.037 | −0.038 | 0.002 | −0.000 | −0.011 | 0.000 | 0.002 | 0.001 | 0.561 | 0.470 | |
t | 35.93 | 36.07 | 1.32 | −0.08 | −1.11 | 0.10 | −0.09 | −0.22 | 64.66 | −10.29 | −10.54 | 0.37 | −0.08 | −3.23 | 0.06 | 0.34 | 0.10 | – | – | ||
Logistic regression | θ | 2.919 | 2.857 | 0.622 | 0.418 | −0.946 | −0.002 | −0.264 | −0.240 | 0.964 | −0.185 | −0.173 | −0.078 | −0.046 | 0.091 | −0.014 | 0.027 | 0.049 | – | – | |
t | 5.29 | 5.18 | 1.03 | 0.69 | −0.17 | −0.00 | −0.44 | −0.36 | 11.28 | −2.17 | −2.02 | −0.83 | −0.49 | 1.05 | −0.15 | 0.28 | 0.46 | – | – |
The sample size for each model is 100,000 independent observations. For the analytical method, “Normal errors” are true latent trait regression with normal errors, “Logistic Regression” is logistic regression of dichotomized outcome with binomial errors, “Sum Scores” are the regression of sum score with normal errors and “Square-Root Transformation” is the regression of square-root transformed sum score with normal errors