Table 3.

The table displays the bias, root mean square error (RMSE, both as a percentage of the true value) and the coverage probabilities for the pollution–health relationship estimated by the naïve ecological model (4) and the aggregate model (5), as both the true risk and the within‐area variation in pollution vary under different assumptions about $E_{\mathrm{ki}}^{*}$

Risk (α)		Pollution	Bias		RMSE		Coverage
			Model (4)	Model (5)	Model (4)	Model (5)	Model (4)	Model (5)
Constant $E_{\mathrm{ki}}^{*}$
1.05		SD = 1, independent	−0.31	−0.29	6.06	6.08	95.3	95.5
1.05		SD = 1, linear	−0.16	−0.22	5.85	5.83	96.2	96.4
1.05		SD = 10, independent	0.11	0.10	5.69	5.67	95.7	95.5
1.05		SD = 10, linear	0.45	−0.17	5.81	5.74	94.8	95.6
1.5		SD = 1, independent	−0.22	−0.34	14.06	13.92	95.4	94.4
1.5		SD = 1, linear	17.96	0.47	23.00	10.56	73.4	95.4
1.5		SD = 10, independent	−1.17	−0.64	7.87	5.35	92.6	94.3
1.5		SD = 10, linear	20.72	−0.09	23.57	2.37	44.6	95.9
Variable $E_{\mathrm{ki}}^{*}$
1.05		SD = 1, independent	−0.07	−0.06	5.79	5.80	95.4	95.6
1.05		SD = 1, linear	0.40	0.33	5.80	5.78	94.8	94.4
1.05		SD = 10, independent	0.25	0.23	5.65	5.64	95.6	95.6
1.05		SD = 10, linear	0.91	0.26	5.71	5.54	95.0	95.0
1.5		SD = 1, independent	0.18	0.35	14.71	13.34	95.0	96.2
1.5		SD = 1, linear	17.21	−0.46	22.75	10.19	73.0	94.2
1.5		SD = 10, independent	−0.70	−0.44	8.61	4.47	91.4	96.0
1.5		SD = 10, linear	21.33	−0.02	24.98	2.04	46.6	97.0