Table 2.

Simulation results for fitting CPMs with exchangeable working correlation with equal-quantile binned and rounded response data based on the primary setting. For equal-quantile binning, we show results of ${ℳ}_b=25,50,100$ and 200. Results of rounding to 0 and 1 decimal place are also shown.

Scenario	Metric	${\beta }_X$	${\beta }_T$	$E(Y\mid X=1,T=0.2)$	$Q(0.5\mid X=1,T=0.2)$	$F(5\mid X=1,T=0.2)$
Binning ${ℳ}_b=25$	Bias(%)	0.171	0.548	−1.064	−2.258	0.142
	RMSE	0.052	0.068	1.205	1.107	0.170
	Empirical SE	0.052	0.067	0.134	0.132	0.018
	Average SE	0.053	0.067	0.129	-	0.016
	Coverage	0.956	0.945	0.889	0.881	0.901
Binning ${ℳ}_b=50$	Bias(%)	0.174	0.757	−0.039	−0.053	−0.233
	RMSE	0.052	0.068	1.205	1.166	0.171
	Empirical SE	0.052	0.068	0.135	0.131	0.016
	Average SE	0.053	0.067	0.133	-	0.016
	Coverage	0.958	0.942	0.929	0.923	0.935
Binning ${ℳ}_b=100$	Bias(%)	0.187	1.193	−0.316	−0.493	−0.174
	RMSE	0.052	0.069	1.217	1.181	0.171
	Empirical SE	0.052	0.068	0.135	0.130	0.016
	Average SE	0.053	0.067	0.135	-	0.016
	Coverage	0.957	0.936	0.945	0.948	0.953
Binning ${ℳ}_b=200$	Bias(%)	0.208	2.069	−0.197	−0.311	−0.112
	RMSE	0.052	0.071	1.223	1.189	0.170
	Empirical SE	0.052	0.068	0.135	0.131	0.015
	Average SE	0.053	0.067	0.136	-	0.016
	Coverage	0.957	0.924	0.946	0.952	0.958
Rounding 0 decimal place	Bias(%)	0.196	0.799	−0.015	−7.316	−20.965
	RMSE	0.052	0.070	1.231	0.940	0.222
	Empirical SE	0.054	0.069	0.136	0.155	0.014
	Average SE	0.053	0.068	0.139	-	0.014
	Coverage	0.959	0.937	0.952	0.244	0.004
Rounding 1 decimal place	Bias(%)	0.210	3.180	−0.123	−0.693	−2.147
	RMSE	0.052	0.076	1.229	1.175	0.176
	Empirical SE	0.052	0.070	0.136	0.130	0.015
	Average SE	0.053	0.067	0.138	-	0.016
	Coverage	0.957	0.907	0.953	0.942	0.943