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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)

From: A Monte Carlo simulation study comparing linear regression, beta regression, variable-dispersion beta regression and fractional logit regression at recovering average difference measures in a two sample design

    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
  1. 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.
  2. ∆ = 0.10 (power experiments).
  3. Power refers to the proportion of null hypothesis rejected.