Table 4.

Results of comparison of various methods, including Zhao et. al. [12] (Zhao), Spinka et al. [9] using grid-search (Spinka, grid) or supplementary information on Pr(D = 1) (Spinka, suppl.), and the proposed multinomial logistic regression method (Proposed)

	Zhao			Spinka, grid			Spinka, suppl.			Proposed
	βX	βhap	βint	βX	βhap	βint	βX	βhap	βint	βX	βhap	βint
α = -3, βX = 0.3, βhap = 0.1, βint = 0
biasa	0.002	0.025	0.028	0.002	-0.010	0.015	0.002	-0.020	-0.005	0.002	-0.021	-0.016
SEb	0.066	0.269	0.254	0.065	0.188	0.155	0.060	0.189	0.155	0.059	0.170	0.142
$\stackrel{\_}{\text{SE}}$c	0.064	0.260	0.268	0.063	0.187	0.159	0.063	0.183	0.153	0.063	0.175	0.143
coverd	0.948	0.958	0.975	0.955	0.957	0.965	0.943	0.947	0.952	0.970	0.947	0.955
sizee	-	-	0.025	-	-	0.035	-	-	0.048	-	-	0.045
α = -3, βX = 0.3, βhap = 0.1,βint = 0.3
biasa	0.001	0.022	0.029	0.000	-0.009	0.029	-0.006	-0.017	0.005	0.001	-0.028	-0.019
SEb	0.064	0.269	0.289	0.063	0.197	0.182	0.061	0.193	0.152	0.064	0.187	0.137
$\stackrel{\_}{\text{SE}}$c	0.064	0.265	0.277	0.063	0.193	0.161	0.063	0.189	0.154	0.063	0.181	0.137
coverd	0.950	0.952	0.936	0.948	0.958	0.923	0.954	0.948	0.950	0.954	0.948	0.956
powerf	-	-	0.198	-	-	0.524	-	-	0.480	-	-	0.513

^aSimulation mean of the parameter estimates minus the true value.

^bSimulation standard error of the parameter estimates.

^cSimulation mean of the estimated standard errors.

^dCoverage probability of 95% confidence interval.

^eSize of Wald test for testing H₀ : β_int = 0.

^fPower of Wald test for testing H₀ : β_int = 0.