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

Meaney, Christopher; Moineddin, Rahim

doi:10.1186/1471-2288-14-14

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

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).

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ISSN: 1471-2288

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