| | |
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
|
- Response variables were generated from a discrete multinomial distribution with probability mass observed only on points in (0,1). Multinomial response probabilities for this experiment are given in Table 2 above.
- ∆ = 0.10 (power experiments).
- Power refers to the proportion of null hypothesis rejected.