Table 1.

Parameter estimates from 500 replications with sample size 400 assuming conditional independence on both measurements y and x.

Truth	β0	β1	β2	γ0	γ1	py1	qy1	py2	qy2	px1	qx1	px2	qx2
	−0.700	1.500	1.500	−0.850	1.500	0.800	0.850	0.850	0.750	0.900	0.750	0.700	0.950
Ideal analysis
EST	−0.712	1.576	1.551	−0.860	1.526
BIAS	−0.012	0.076	0.051	−0.010	0.026
SE	0.227	0.422	0.212	0.182	0.161
SD	0.239	0.439	0.222	0.175	0.159
CP	0.944	0.948	0.948	0.960	0.954
Naive analysis
EST	−0.412	0.427	0.475	0.118	0.473
BIAS	0.288	−1.073	−1.025	0.968	−1.027
SE	0.177	0.253	0.065	0.114	0.057
SD	0.173	0.238	0.077	0.112	0.070
CP	0.616	0.014	0.000	0.000	0.000
Model assuming conditional independence (M1)
EST	−0.737	1.639	1.781	−0.900	1.646	0.797	0.846	0.844	0.746	0.892	0.746	0.695	0.945
BIAS	−0.037	0.139	0.281	−0.050	0.146	−0.003	−0.004	−0.006	−0.004	−0.008	−0.004	−0.005	−0.005
SE	0.435	0.886	0.491	0.305	0.305	0.034	0.030	0.030	0.035	0.029	0.033	0.043	0.019
SD	0.435	0.767	0.450	0.308	0.316	0.032	0.031	0.030	0.033	0.029	0.034	0.042	0.018
CP	0.948	0.968	0.938	0.938	0.928	0.964	0.936	0.958	0.956	0.946	0.964	0.958	0.944
Model assuming conditional dependence (M2)
EST	−0.839	1.881	2.027	−0.952	1.891	0.783	0.838	0.834	0.735	0.875	0.734	0.675	0.936
BIAS	−0.139	0.381	0.527	−0.102	0.391	−0.017	−0.012	−0.016	−0.015	−0.025	−0.016	−0.025	−0.014
SE	0.527	1.077	0.625	0.370	0.421	0.035	0.031	0.032	0.035	0.033	0.033	0.044	0.021
SD	0.480	0.825	0.474	0.357	0.326	0.033	0.031	0.031	0.034	0.030	0.033	0.042	0.019
CP	0.956	0.976	0.922	0.938	0.882	0.924	0.942	0.934	0.932	0.896	0.928	0.924	0.926

CP: coverage probability.