Longitudinal Joint Modelling of Ordinal and Overdispersed Count Outcomes: A Bridge Distribution for the Ordinal Random Intercept

Table 8

Simulation study results with 0.8 correlation between the random intercepts and Bridge distribution for the random intercept of the ordinal outcome.

				MSE			MSE			MSE
		Mean	AVB		Mean	AVB		Mean	AVB
Count process
	50	2.5839	0.0161	0.0012	2.5893	0.0107	0.0011	2.5819	0.0181	0.0013
	200	2.6180	0.0180	0.0008	2.5957	0.0043	0.0005	2.6011	0.0011	0.0004
	500	2.6078	0.0078	0.0005	2.6011	0.0011	0.0004	2.6008	0.0008	0.0004
	50	-0.5976	0.0024	<0.0001	-0.5974	0.0026	<0.0001	-0.5949	0.0051	<0.0001
	200	-0.6018	0.0018	<0.0001	-0.5971	0.0029	<0.0001	-0.6031	0.0031	<0.0001
	500	-0.5979	0.0021	<0.0001	-0.5997	0.0003	<0.0001	-0.5991	0.0009	<0.0001
	50	-0.3636	0.0364	0.0014	-0.3810	0.0190	0.0004	-0.3952	0.0048	0.0001
	200	-0.4123	0.0123	0.0002	-0.3844	0.0156	0.0002	-0.4105	0.0105	0.0001
	500	-0.3466	0.0534	0.0029	-0.3863	0.0137	0.0002	-0.3981	0.0019	<0.0001
NBP	50	1.0100	0.0100	0.0001	5.5579	0.5579	0.3113	152.8764	2.8764	8.2737
	200	0.9912	0.0088	0.0002	5.0522	0.0522	0.0028	151.9130	1.9130	3.6597
	500	1.0010	0.0010	<0.0001	4.9405	0.0595	0.0035	150.9005	0.9005	0.8109
	50	0.1291	0.0291	0.0009	0.1240	0.0240	0.0006	0.0852	0.0148	0.0002
	200	0.1210	0.0210	0.0004	0.1273	0.0273	0.0008	0.0892	0.0108	0.0001
	500	0.1033	0.0033	0.0001	0.1088	0.0088	0.0001	0.0945	0.0055	0.0001
Ordinal process
	50	0.6450	0.0450	0.0020	0.6208	0.0208	0.0004	0.6439	0.0439	0.0019
	200	0.5931	0.0069	<0.0001	0.5853	0.0147	0.0002	0.5861	0.0139	0.0002
	500	0.5989	0.0011	<0.0001	0.6098	0.0098	0.0001	0.6001	0.0001	<0.0001
	50	0.0982	0.0018	<0.0001	0.1657	0.0657	0.0043	0.1239	0.0239	0.0006
	200	0.1429	0.0429	0.0018	0.1528	0.0528	0.0028	0.1117	0.0117	0.0001
	500	0.1207	0.0207	0.0006	0.1178	0.0178	0.0005	0.1036	0.0036	0.0002
	50	-0.8440	0.1560	0.0243	-0.8705	0.1295	0.0168	-0.8993	0.1007	0.0102
	200	-0.9305	0.0695	0.0048	-0.9355	0.0645	0.0042	-0.9409	0.0591	0.0035
	500	-0.9266	0.0734	0.0054	-0.9940	0.0060	<0.0001	-0.9885	0.0115	0.0001
	50	0.8827	0.1173	0.0138	0.8660	0.1340	0.0180	0.8386	0.1614	0.0261
	200	0.9797	0.0203	0.0004	0.8951	0.1049	0.0110	0.8671	0.1329	0.0177
	500	1.0117	0.0117	0.0002	0.9452	0.0548	0.0030	1.0256	0.0256	0.0007
	50	1.3427	0.0427	0.0018	1.3512	0.0512	0.0026	1.2490	0.0510	0.0026
	200	1.3840	0.0840	0.0071	1.3740	0.0740	0.0055	1.2982	0.0018	<0.0001
	500	1.3820	0.0820	0.0067	1.3769	0.0769	0.0059	1.2994	0.0006	<0.0001
	50	0.7599	0.0401	0.0016	0.7888	0.0112	0.0001	0.8147	0.0147	0.0002
	200	0.8051	0.0051	<0.0001	0.8197	0.0197	0.0004	0.8189	0.0189	0.0004
	500	0.8195	0.0195	0.0004	0.7749	0.0251	0.0006	0.7997	0.0003	<0.0001

NBP: negative binomial parameter; AVB: the absolute value of biases; MSE: mean square error.