Table 6 Mean estimates from 20000 replicate simulations of bias (MC error of bias), variance (MC Error Variance), and Power (MC Error Power), from the fitted linear, beta, variable-dispersion beta and fractional logit regression models estimated on the multinomial distributed response data (Power experiments)
Linear regression model | Beta regression model | Variable dispersion beta regression model | Fractional logit regression model | |||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
N0 = N1 | E(Y0) | E(Y1) | Bias | MC error bias | Variance | MC error variance | Power | MC error power | Bias | MC error bias | Variance | MC error variance | Power | MC error power | Bias | MC error bias | Variance | MC error variance | Power | MC error power | Bias | MC error bias | Variance | MC error variance | Power | MC error power |
25 | 0.5 | 0.6 | -1.36E-04 | 2.63E-04 | 1.40E-03 | 3.04E-05 | 0.745 | 0.003 | 2.32E-03 | 2.76E-04 | 1.44E-03 | 3.22E-05 | 0.769 | 0.003 | 1.77E-03 | 2.73E-04 | 1.43E-03 | 3.20E-05 | 0.767 | 0.003 | -1.36E-04 | 2.63E-04 | 1.35E-03 | 2.98E-05 | 0.774 | 0.003 |
100 | 0.5 | 0.6 | -2.17E-04 | 1.33E-04 | 3.50E-04 | 7.54E-06 | 1.000 | 0.000 | 2.37E-03 | 1.39E-04 | 3.72E-04 | 8.18E-06 | 1.000 | 0.000 | 1.86E-03 | 1.38E-04 | 3.72E-04 | 8.16E-06 | 1.000 | 0.000 | -2.17E-04 | 1.33E-04 | 3.46E-04 | 7.50E-06 | 1.000 | 0.000 |
250 | 0.5 | 0.6 | -5.06E-05 | 8.32E-05 | 1.40E-04 | 3.02E-06 | 1.000 | 0.000 | 2.55E-03 | 8.73E-05 | 1.50E-04 | 3.29E-06 | 1.000 | 0.000 | 2.05E-03 | 8.64E-05 | 1.50E-04 | 3.28E-06 | 1.000 | 0.000 | -5.06E-05 | 8.32E-05 | 1.39E-04 | 3.01E-06 | 1.000 | 0.000 |
750 | 0.5 | 0.6 | -8.70E-05 | 4.85E-05 | 4.66E-05 | 1.01E-06 | 1.000 | 0.000 | 2.55E-03 | 5.08E-05 | 5.02E-05 | 1.10E-06 | 1.000 | 0.000 | 2.05E-03 | 5.04E-05 | 5.02E-05 | 1.10E-06 | 1.000 | 0.000 | -8.70E-05 | 4.85E-05 | 4.66E-05 | 1.01E-06 | 1.000 | 0.000 |
25 | 0.215 | 0.315 | 2.82E-04 | 3.70E-04 | 2.75E-03 | 3.42E-05 | 0.466 | 0.004 | 1.35E-02 | 2.96E-04 | 2.02E-03 | 3.04E-05 | 0.725 | 0.003 | 3.33E-03 | 3.55E-04 | 2.21E-03 | 3.07E-05 | 0.589 | 0.003 | 2.82E-04 | 3.70E-04 | 2.64E-03 | 3.35E-05 | 0.501 | 0.004 |
100 | 0.215 | 0.315 | 6.30E-06 | 1.84E-04 | 6.85E-04 | 8.36E-06 | 0.966 | 0.001 | 1.36E-02 | 1.46E-04 | 5.17E-04 | 7.65E-06 | 1.000 | 0.000 | 3.10E-03 | 1.77E-04 | 5.68E-04 | 7.71E-06 | 0.987 | 0.001 | 6.30E-06 | 1.84E-04 | 6.78E-04 | 8.32E-06 | 0.967 | 0.001 |
250 | 0.215 | 0.315 | 1.87E-05 | 1.17E-04 | 2.74E-04 | 3.31E-06 | 1.000 | 0.000 | 1.37E-02 | 9.28E-05 | 2.08E-04 | 3.04E-06 | 1.000 | 0.000 | 3.14E-03 | 1.12E-04 | 2.28E-04 | 3.07E-06 | 1.000 | 0.000 | 1.87E-05 | 1.17E-04 | 2.73E-04 | 3.30E-06 | 1.000 | 0.000 |
750 | 0.215 | 0.315 | 1.02E-04 | 6.74E-05 | 9.14E-05 | 1.10E-06 | 1.000 | 0.000 | 1.38E-02 | 5.33E-05 | 6.94E-05 | 1.02E-06 | 1.000 | 0.000 | 3.22E-03 | 6.45E-05 | 7.64E-05 | 1.03E-06 | 1.000 | 0.000 | 1.02E-04 | 6.74E-05 | 9.13E-05 | 1.11E-06 | 1.000 | 0.000 |