IPW (MLE) on the Kim et al. (2021) DGP

Inverse probability weighting (MLE) on the data-generating process from Kim, Park, Chen & Wu (2021), JRSSA 184(3). The DGP draws x ~ N(2, 1) and three outcomes constructed so that all three have theoretical population mean 5. The non-probability sample oversamples the lower tail of x (70% from strata == TRUE, 30% from strata == FALSE).

nonprobsvy version: 0.3.0  |  R: 4.6.0  |  run: 2026-05-24 08:12:39  |  commit: 4b2ba9a

target_var	var_method	num_boot	alpha	n_reps	bias	rmse	mc_se	mean_se	coverage	ci_width
y1	analytic	NA	0.05	500	-0.026	0.105	0.005	0.110	0.956	0.432
y1	bootstrap	200	0.05	500	-0.026	0.105	0.005	0.112	0.952	0.440
y2	analytic	NA	0.05	500	-0.012	0.081	0.004	0.084	0.952	0.331
y2	bootstrap	200	0.05	500	-0.012	0.081	0.004	0.086	0.958	0.336
y3	analytic	NA	0.05	500	-0.025	0.125	0.005	0.129	0.948	0.506
y3	bootstrap	200	0.05	500	-0.025	0.125	0.005	0.132	0.952	0.517

Notes

• y1 = 1 + 2 x + e is linear in x — the propensity model is correctly specified for this outcome.
• y2 = 3 + x + 2 e is also linear in x but with a different scale.
• y3 = 2.5 + 0.5 x^2 + e is non-linear in x. The propensity adjustment still corrects the design bias, but residual coverage behaviour can differ — see the rows.

Source: ncn-foreigners/software-tutorials/codes/2021-kim-et-al-jrssa.R.