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Table 5 Mean estimates from 20000 replicate simulations of bias (MC error of bias), variance (MC error of variance) and type-1 error (MC error type-1 error), from the fitted linear, beta, variable-dispersion beta and fractional logit regression models estimated on the multinomial distributed response data (Type-1 error 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 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
  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 (type-1 error experiments).
  3. Type-1 error refers to the proportion of null hypothesis rejected (expected 0.05).