| | |
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
|
Type-1 Error
|
MC Error Type-1 Error
|
Bias
|
MC error bias
|
Variance
|
MC error variance
|
Type-1 Error
|
MC Error Type-1 Error
|
Bias
|
MC error bias
|
Variance
|
MC error variance
|
Type-1 Error
|
MC Error Type-1 Error
|
Bias
|
MC error bias
|
Variance
|
MC error variance
|
Type-1 Error
|
MC Error Type-1 Error
|
---|
25
|
0.5
|
0.5
|
-6.22E-04
|
2.64E-04
|
1.40E-03
|
3.04E-05
|
0.048
|
0.002
|
-6.48E-04
|
2.72E-04
|
1.39E-03
|
3.04E-05
|
0.062
|
0.002
|
-6.43E-04
|
2.71E-04
|
1.38E-03
|
3.02E-05
|
0.063
|
0.002
|
-6.22E-04
|
2.64E-04
|
1.34E-03
|
2.98E-05
|
0.060
|
0.002
|
100
|
0.5
|
0.5
|
8.00E-06
|
1.32E-04
|
3.50E-04
|
7.51E-06
|
0.049
|
0.002
|
-2.97E-06
|
1.37E-04
|
3.61E-04
|
7.68E-06
|
0.055
|
0.002
|
-4.54E-07
|
1.37E-04
|
3.61E-04
|
7.66E-06
|
0.055
|
0.002
|
8.00E-06
|
1.32E-04
|
3.46E-04
|
7.47E-06
|
0.052
|
0.002
|
250
|
0.5
|
0.5
|
1.07E-04
|
8.33E-05
|
1.40E-04
|
3.02E-06
|
0.051
|
0.002
|
1.09E-04
|
8.60E-05
|
1.46E-04
|
3.10E-06
|
0.053
|
0.002
|
1.09E-04
|
8.59E-05
|
1.45E-04
|
3.10E-06
|
0.053
|
0.002
|
1.07E-04
|
8.33E-05
|
1.39E-04
|
3.01E-06
|
0.052
|
0.002
|
750
|
0.5
|
0.5
|
-3.01E-06
|
4.84E-05
|
4.67E-05
|
1.01E-06
|
0.051
|
0.002
|
-2.56E-06
|
4.99E-05
|
4.87E-05
|
1.03E-06
|
0.054
|
0.002
|
-2.57E-06
|
4.99E-05
|
4.87E-05
|
1.03E-06
|
0.054
|
0.002
|
-3.01E-06
|
4.84E-05
|
4.66E-05
|
1.01E-06
|
0.052
|
0.002
|
25
|
0.215
|
0.215
|
-4.46E-04
|
3.72E-04
|
2.74E-03
|
3.41E-05
|
0.051
|
0.002
|
-3.06E-04
|
2.80E-04
|
1.82E-03
|
3.12E-05
|
0.037
|
0.001
|
-3.94E-04
|
3.51E-04
|
2.19E-03
|
3.13E-05
|
0.072
|
0.002
|
-4.46E-04
|
3.72E-04
|
2.63E-03
|
3.34E-05
|
0.062
|
0.002
|
100
|
0.215
|
0.215
|
5.06E-05
|
1.85E-04
|
6.86E-04
|
8.38E-06
|
0.050
|
0.002
|
-2.96E-05
|
1.38E-04
|
4.64E-04
|
7.95E-06
|
0.030
|
0.001
|
5.99E-05
|
1.74E-04
|
5.63E-04
|
7.95E-06
|
0.061
|
0.002
|
5.06E-05
|
1.85E-04
|
6.79E-04
|
8.33E-06
|
0.053
|
0.002
|
250
|
0.215
|
0.215
|
1.18E-04
|
1.17E-04
|
2.74E-04
|
3.31E-06
|
0.051
|
0.002
|
1.19E-04
|
8.69E-05
|
1.86E-04
|
3.17E-06
|
0.030
|
0.001
|
1.08E-04
|
1.10E-04
|
2.26E-04
|
3.16E-06
|
0.060
|
0.002
|
1.18E-04
|
1.17E-04
|
2.73E-04
|
3.30E-06
|
0.053
|
0.002
|
750
|
0.215
|
0.215
|
-1.10E-05
|
6.78E-05
|
9.13E-05
|
1.11E-06
|
0.050
|
0.002
|
-1.93E-05
|
5.02E-05
|
6.20E-05
|
1.06E-06
|
0.029
|
0.001
|
-1.64E-06
|
6.37E-05
|
7.55E-05
|
1.06E-06
|
0.059
|
0.002
|
-1.10E-05
|
6.78E-05
|
9.12E-05
|
1.11E-06
|
0.050
|
0.002
|
- 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 (type-1 error experiments).
- Type-1 error refers to the proportion of null hypothesis rejected (expected 0.05).