Generating contingency tables with fixed marginal probabilities and dependence structures described by loglinear models

Figures & data

Table 1. Simulation results for dual systems estimation with inclusion probabilities ${\pi }_A$ and ${\pi }_B$, sizes of odds ratios (OR), the mean and median of the estimates, the 95% confidence interval of the mean, the relative bias and coefficient of variation (CV), where the fitted model is [A][B].

N	${\pi }_A$	${\pi }_B$	OR	Mean	Median	95%CI		rbias%	CV
1000	0.8	0.7	1	1000.3	1000.0	979.5,	1020.6	0.027	0.011
1000	0.9	0.8	1	1000.0	1000.0	989.8,	1010.0	−0.005	0.005
2000	0.8	0.7	1	2000.1	2000.2	1971.3,	2029.1	0.005	0.007
2000	0.9	0.8	1	2000.1	2000.1	1985.2,	2014.6	0.007	0.004
1000	0.8	0.7	1.1	994.5	994.5	973.9,	1015.2	−0.545	0.011
1000	0.9	0.8	1.1	998.0	998.1	986.9,	1008.4	−0.197	0.005
2000	0.8	0.7	1.1	1989.9	1989.1	1960.3,	2018.0	−0.553	0.007
2000	0.9	0.8	1.1	1996.1	1996.0	1980.9,	2010.2	−0.197	0.004
1000	0.8	0.7	2	957.8	957.8	937.5,	978.9	−4.215	0.011
1000	0.9	0.8	2	984.4	984.6	972.3,	995.9	−1.560	0.006
2000	0.8	0.7	2	1915.6	1915.7	1886.4,	1943.8	−4.219	0.008
2000	0.9	0.8	2	1968.6	1968.7	1950.8,	1985.5	−1.571	0.004

Table 2. Simulation results for triple systems estimation with inclusion probabilities ${\pi }_A$ = 0.8, ${\pi }_B$ = 0.7 and ${\pi }_C$ = 0.9, with different sizes of odds ratios (OR), specified models, the mean and median of the estimates, the 95% confidence interval of the mean, the relative bias and coefficient of variation (CV).

N	OR (AB,AC,BC)	Model	Mean	Median	95%CI		rbias%	CV
1000	(1, 1, 1)	[A][B][C]	1000.0	1000.2	994.7	1004.6	0.002	0.003
1000	(1, 1, 1)	[AB][AC][BC]	1000.2	1000.1	993.5	1007.6	0.020	0.004
2000	(1, 1, 1)	[A][B][C]	2000.1	2000.1	1992.9	2007.1	0.003	0.002
2000	(1, 1, 1)	[AB][AC][BC]	2000.2	2000.1	1991.3	2010.6	0.012	0.002
1000	(1.5, 2, 1)	[A][B][C]	993.7	993.9	986.7	1000.1	−0.627	0.003
1000	(1.5, 2, 1)	[AB][AC][BC]	1000.4	1000.0	990.0	1013.0	0.036	0.006
1000	(1.5, 2, 1)	[AB][AC]	1000.2	1000.0	991.2	1009.4	0.018	0.005
1000	(1.5, 2, 1)	[A][BC]	993.0	993.2	986.0	999.4	−0.704	0.004
2000	(1.5, 2, 1)	[A][B][C]	1987.4	1987.4	1977.7	1996.9	−0.629	0.002
2000	(1.5, 2, 1)	[AB][AC][BC]	2000.2	1999.6	1985.8	2017.9	0.009	0.004
2000	(1.5, 2, 1)	[AB][AC]	2000.1	2000.2	1987.6	2014.0	0.007	0.003
2000	(1.5, 2, 1)	[A][BC]	1985.9	1985.9	1976.2	1995.5	−0.706	0.003