Table 1.

Simulation results for Models (M1) and (M2) when $c\in \left\{1,4,8\right\}$ under both random and homogeneous pooling. The summary statistics for ${\beta }_1$, ${\beta }_2$, ${\beta }_3$ include average bias (Bias), square root of mean squared error (RMSE), sample standard deviation (SSD) of the 500 posterior median estimates, the average of the 500 estimates of the posterior standard deviation (ESE), and empirical coverage probability of 95% credible intervals (CP95).

			$c=1$	$c=4$		$c=8$
Model	Parameter	Summary	Individual	Random	Homogeneous	Random	Homogeneous
M1	${\beta }_1=0.5$	Bias× 100	0.106	−0.062	0.204	−0.347	−0.072
		RMSE(CP95)	0.055(0.951)	0.054(0.941)	0.029(0.948)	0.057(0.932)	0.022(0.934)
		SSD(ESE)	0.055(0.056)	0.054(0.055)	0.029(0.029)	0.057(0.055)	0.022(0.021)
	${\beta }_2=0.5$	Bias× 100	−0.030	−0.088	0.052	−0.677	−0.427
		RMSE(CP95)	0.060(0.949)	0.053(0.943)	0.051(0.955)	0.050(0.956)	0.054(0.949)
		SSD(ESE)	0.060(0.061)	0.053(0.054)	0.052(0.053)	0.049(0.052)	0.053(0.052)
	${\beta }_3=-0.5$	Bias× 100	0.172	0.167	0.023	−0.066	−0.112
		RMSE(CP95)	0.059(0.936)	0.055(0.935)	0.028(0.959)	0.057(0.943)	0.021(0.932)
		SSD(ESE)	0.059(0.056)	0.055(0.055)	0.028(0.029)	0.057(0.056)	0.021(0.021)
M2	${\beta }_1=0.5$	Bias× 100	0.206	−0.283	−0.005	−0.061	−0.044
		RMSE(CP95)	0.056(0.946)	0.055(0.944)	0.028(0.958)	0.055(0.946)	0.021(0.948)
		SSD(ESE)	0.056(0.056)	0.055(0.055)	0.028(0.029)	0.055(0.055)	0.021(0.021)
	${\beta }_2=0.5$	Bias× 100	−0.066	−0.281	−0.229	−0.374	−0.387
		RMSE(CP95)	0.059(0.964)	0.056(0.930)	0.054(0.941)	0.054(0.931)	0.052(0.943)
		SSD(ESE)	0.059(0.061)	0.056(0.054)	0.054(0.053)	0.054(0.052)	0.052(0.052)
	${\beta }_3=-0.5$	Bias× 100	0.293	0.412	0.030	0.127	0.007
		RMSE(CP95)	0.053(0.956)	0.055(0.939)	0.029(0.946)	0.055(0.946)	0.021(0.946)
		SSD(ESE)	0.053(0.056)	0.055(0.055)	0.029(0.029)	0.055(0.055)	0.021(0.021)