TABLE 1.

Results from 4000 simulated survey samples and nonprobability samples with low to high participation rates under various propensity score models

	Scenario 1 True propensity model for ALP					Scenario 2 True propensity model for CLW
	%RB	V (×105)	VR	MSE (×105)	CP5	%RB	V (×105)	VR	MSE (×105)	CP
fc = 0.5%
${\widehat{\mu }}^{\text{Naive}}$	−42.76	0.22	0.99			−42.61	0.22	1.00
${\widehat{\mu }}^{\text{TW}}$	−0.13	4.38	0.93	4.39	0.90	−0.12	4.38	0.93	4.38	0.90
${\widehat{\mu }}^{\text{RDW}}$	−0.29	3.73	0.93	3.75	0.87	−0.40	3.63	0.93	3.66	0.87
${\widehat{\mu }}^{\text{FDW}}$	−0.28	3.73	0.93	3.75	0.87	−0.40	3.63	0.93	3.66	0.87
${\widehat{\mu }}^{\text{ALP}}$	−0.07	3.70	0.93	3.77	0.88	−0.19	3.66	0.93	3.67	0.88
${\widehat{\mu }}^{\text{CLW}}$	0.05	3.87	0.93	3.87	0.89	−0.07	3.76	0.93	3.76	0.88
${\widehat{\mu }}^{\text{ALP}.S}$	−0.11	3.54	0.92	3.54	0.87	−0.21	3.45	0.92	3.45	0.87
fc = 5%
${\widehat{\mu }}^{\text{Naive}}$	−42.74	0.02	0.99			−41.21	0.02	1.01
${\widehat{\mu }}^{\text{TW}}$	−0.04	0.50	0.98	0.50	0.92	−0.02	0.46	1.00	0.47	0.93
${\widehat{\mu }}^{\text{RDW}}$	−2.15	0.56	1.00	1.29	0.66	−3.05	0.43	1.01	1.89	0.45
${\widehat{\mu }}^{\text{FDW}}$	−2.05	0.57	1.00	1.23	0.68	−2.95	0.43	1.01	1.81	0.47
${\widehat{\mu }}^{\text{ALP}}$	−0.01	0.62	1.00	0.62	0.94	−1.03	0.47	1.01	0.64	0.85
${\widehat{\mu }}^{\text{CLW}}$	1.29	0.84	1.00	1.10	0.95	0.01	0.61	1.01	0.61	0.94
${\widehat{\mu }}^{\text{ALP}.S}$	−0.05	0.45	1.00	0.45	0.92	−0.63	0.35	1.02	0.41	0.86
fc = 10%
${\widehat{\mu }}^{\text{Naive}}$	−42.74	0.01	1.11			−39.65	0.01	1.11
${\widehat{\mu }}^{\text{TW}}$	−0.01	0.25	1.02	0.25	0.94	−0.01	0.22	1.01	0.22	0.94
${\widehat{\mu }}^{\text{RDW}}$	−4.25	0.34	1.00	3.20	0.17	−5.62	0.22	0.99	5.20	0.02
${\widehat{\mu }}^{\text{FDW}}$	−3.87	0.35	1.00	2.71	0.24	−5.28	0.22	0.99	4.62	0.03
${\widehat{\mu }}^{\text{ALP}}$	0.01	0.42	1.00	0.42	0.95	−1.81	0.27	0.99	0.79	0.65
${\widehat{\mu }}^{\text{CLW}}$	2.94	0.80	1.00	2.16	0.76	0.03	0.42	0.99	0.42	0.95
${\widehat{\mu }}^{\text{ALP}.S}$	−0.03	0.27	1.02	0.27	0.94	−0.86	0.18	1.01	0.29	0.81
fc = 20%
${\widehat{\mu }}^{\text{Naive}}$	−42.75	0.00	1.26			−36.50	0.01	1.21
${\widehat{\mu }}^{\text{TW}}$	−0.02	0.15	0.93	0.15	0.93	−0.02	0.11	0.96	0.11	0.93
${\widehat{\mu }}^{\text{RDW}}$	−8.58	0.21	0.95	11.83	0.00	−9.59	0.10	0.97	14.60	0.00
${\widehat{\mu }}^{\text{FDW}}$	−7.15	0.23	0.96	8.29	0.01	−8.51	0.11	0.98	11.53	0.00
${\widehat{\mu }}^{\text{ALP}}$	0.00	0.32	0.96	0.32	0.95	−2.85	0.16	0.98	1.44	0.19
${\widehat{\mu }}^{\text{CLW}}$	7.80	1.67	0.92	11.27	0.06	0.01	0.33	0.98	0.33	0.95
${\widehat{\mu }}^{\text{ALP}.S}$	−0.03	0.19	0.96	0.19	0.94	−1.02	0.10	1.00	0.27	0.73

Abbreviations: ALP, adjusted logistic propensity; CP, coverage probability; MSE, mean squared error; VR, variance ratio.