Figures and tables in Pooling Incomplete Data Sets | International Journal of Microsimulation

Abstract

Data needed in micro studies are not always available from just a single source. In such cases it might be possible to combine two or more independent samples. The problem studied in this paper is to estimate a linear function between y and x from one sample of y-observations and another of x-observations. This is feasible if there are common variables z which can be used to predict x. A two-stage least squares estimator is propounded, which, for the model considered, is also an ML estimator. Simulation experiments show that it has a good relative efficiency and virtually no small sample bias.

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Tables

Table 1. Results from seven simulation experiments

		γ₁	γ₂	γ₃	γ₄	γ₅	γ₆
Parameter values		3.594	0.400	0.040	-0.00043	0.644	-0.0723
Simulation 1:	TSLS
n_A	288
n_B	288
Replications	800
Relative bias(%)		0.42	-0.82	2.42	1.72	0.79	1.36
Relative		32.82	29.55	57.50	53.49	27.00	36.66
Relative sq. root mean
variance estimate (%)		33.46	30.30	56.00	53.49	27.83	38.59
Simulation 2:	LS, X₂=LDISP known
n_A	288
Replications	400
Relative		29.54	24.60	56.25	53.49	24.78	34.16
Relative sq. root mean
variance estimate (%)		28.54	24.75	54.75	51.16	26.89	37.48
Simulation 3:	TSLS
n_A	720
n_B	720
Replications	600
Relative bias (%)		-1.00	0.61	1.83	0.28	-0.14	-1.14
Relative		21.82	19.16	35.30	33.23	17.23	24.17
Relative sq. root mean
variance estimate (%)		21.22	19.21	35.54	33.53	17.64	24.45
Simulation 4:	LS, X₂=LDISP known
n_A	720
Replications	1000
Relative		17.57	15.05	34.83	32.94	16.62	23.49
Relative sq. root mean
variance estimate (%)		17.99	15.61	34.57	32.66	16.99	23.69
Simulation 5:	TSLS, wrong predictors
n_A	720
n_B	720
Replications	600
Relative bias (%)		1.62	-4.86	2.18	-0.22	9.13	-7.70
Relative		24.16	22.57	37.55	35.52	19.66	25.84
Relative sq. root mean
variance estimate (%)		24.02	21.56	36.22	34.28	17.38	24.51
Simulation 6:	TSLS
n_A	360
n_B	1080
Replications	400
Relative bias (%)		-1.37	2.24	-5.30	5.47	-1.65	3.02
Relative		31.11	31.31	59.01	56.01	28.78	42.99
Relative sq. root mean
variance estimate (%)		29.74	29.85	60.06	57.20	27.48	40.72
Simulation 7:	LS, X₂=LDISP known
n_A	360
Replications	400
Relative bias (%)
Relative		25.37	23.90	54.13	51.74	27.62	41.92
Relative sq. root mean
variance estimate (%)		24.91	23.56	56.28	53.79	26.59	39.77