A Survey Design for a Sensitive Binary Variable Correlated with Another Nonsensitive Binary Variable

Table 5

Comparison of the efficiency of the proposed combination questionnaire model with that of the hidden sensitivity model of Tian et al. [8] (i.e., the main questionnaire model only) with (𝑝₁,𝑝₂,𝑝₃)=(1/3,1/3,1/3).

Parameter	True value	The combination questionnaire model				The hidden sensitivity model
		(𝑁=𝑛+𝑚=50+50)				(𝑁=𝑛+𝑚=100+0)
		MLE	Bias	Variance	MSE	MLE	Bias	Variance	MSE
𝜃1	0.10	0.1013	0.0013	0.0113	0.0113	0.1010	0.0010	0.0064	0.0064
𝜃2	0.50	0.4985	−0.0015	0.0089	0.0089	0.4975	−0.0025	0.0041	0.0041
𝜃3	0.20	0.2008	0.0008	0.0037	0.0037	0.2001	0.0001	0.0029	0.0029
𝜃4	0.20	0.1994	−0.0006	0.0026	0.0026	0.2014	0.0014	0.0016	0.0016
𝜃1	0.20	0.1957	−0.0043	0.0090	0.0090	0.1985	−0.0015	0.0055	0.0055
𝜃2	0.30	0.2999	−0.0001	0.0070	0.0070	0.2999	−0.0001	0.0034	0.0034
𝜃3	0.40	0.4038	0.0038	0.0040	0.0040	0.4025	0.0025	0.0037	0.0037
𝜃4	0.10	0.1006	0.0006	0.0017	0.0017	0.0991	−0.0009	0.0009	0.0009
𝜃1	0.30	0.3021	0.0021	0.0107	0.0107	0.3026	0.0026	0.0081	0.0081
𝜃2	0.25	0.2483	−0.0017	0.0077	0.0077	0.2499	−0.0001	0.0039	0.0039
𝜃3	0.15	0.1474	−0.0026	0.0042	0.0042	0.1476	−0.0024	0.0032	0.0032
𝜃4	0.30	0.3021	0.0021	0.0033	0.0033	0.2999	−0.0001	0.0021	0.0021

Note: Bias(𝜃_𝑖)=𝐸(𝜃_𝑖)−𝜃_𝑖 and MSE(𝜃_𝑖)=[Bias(𝜃_𝑖)]²+Var(𝜃_𝑖).