Research Article
Longitudinal Joint Modelling of Ordinal and Overdispersed Count Outcomes: A Bridge Distribution for the Ordinal Random Intercept
Table 4
Simulation study results with zero correlation between the random intercepts and Bridge distribution for the random intercept of the ordinal outcome.
| | | | | Mean | AVB | MSE | Mean | AVB | MSE | Mean | AVB | MSE |
| Count process | | | | | | | | | | | | 50 | 2.7689 | 0.1689 | 0.0295 | 2.6292 | 0.0292 | 0.0018 | 2.5784 | 0.0216 | 0.0014 | 200 | 2.6464 | 0.0464 | 0.0026 | 2.6114 | 0.0114 | 0.0006 | 2.6120 | 0.0120 | 0.0006 | 500 | 2.6242 | 0.0242 | 0.0010 | 2.6107 | 0.0107 | 0.0005 | 2.6006 | 0.0006 | 0.0004 | | 50 | -0.5870 | 0.0130 | 0.0002 | -0.6024 | 0.0024 | <0.0001 | -0.6015 | 0.0015 | <0.0001 | 200 | -0.6054 | 0.0054 | <0.0001 | -0.6023 | 0.0023 | <0.0001 | -0.6045 | 0.0045 | <0.0001 | 500 | -0.5996 | 0.0004 | <0.0001 | -0.5986 | 0.0014 | <0.0001 | -0.5968 | 0.0032 | <0.0001 | | 50 | -0.3789 | 0.0211 | 0.0005 | -0.3757 | 0.0243 | 0.0006 | -0.3804 | 0.0196 | 0.0004 | 200 | -0.4297 | 0.0297 | 0.0009 | -0.4285 | 0.0285 | 0.0008 | -0.4055 | 0.0055 | <0.0001 | 500 | -0.4231 | 0.0231 | 0.0005 | -0.4116 | 0.0116 | 0.0001 | -0.4034 | 0.0034 | <0.0001 | NBP | 50 | 1.0230 | 0.0230 | 0.0006 | 5.3854 | 0.3854 | 0.1486 | 150.6349 | 0.6349 | 0.4031 | 200 | 1.0060 | 0.0060 | 0.0002 | 5.0512 | 0.0512 | 0.0027 | 150.7227 | 0.7227 | 0.5224 | 500 | 1.0010 | 0.0010 | <0.0001 | 5.0036 | 0.0036 | <0.0001 | 150.5830 | 0.5830 | 0.3399 | | 50 | 0.1318 | 0.0318 | 0.0010 | 0.1304 | 0.0304 | 0.0009 | 0.0754 | 0.0246 | 0.0006 | 200 | 0.1188 | 0.0188 | 0.0004 | 0.1255 | 0.0255 | 0.0007 | 0.0859 | 0.0141 | 0.0002 | 500 | 0.1088 | 0.0088 | 0.0001 | 0.1106 | 0.0106 | 0.0002 | 0.0971 | 0.0029 | <0.0001 | Ordinal process | | | | | | | | | | | | 50 | 0.582 | 0.0180 | 0.0003 | 0.6082 | 0.0082 | 0.0001 | 0.6254 | 0.0254 | 0.0007 | 200 | 0.5911 | 0.0089 | 0.0001 | 0.5823 | 0.0177 | 0.0003 | 0.6116 | 0.0116 | 0.0001 | 500 | 0.5942 | 0.0058 | <0.0001 | 0.6134 | 0.0134 | 0.0002 | 0.5925 | 0.0075 | 0.0001 | | 50 | 0.1428 | 0.0428 | 0.0018 | 0.0885 | 0.0115 | 0.0001 | 0.1243 | 0.0243 | 0.0006 | 200 | 0.1466 | 0.0466 | 0.0022 | 0.0906 | 0.0094 | 0.0001 | 0.1181 | 0.0181 | 0.0003 | 500 | 0.1158 | 0.0158 | 0.0005 | 0.0967 | 0.0033 | 0.0002 | 0.1088 | 0.0088 | 0.0003 | | 50 | -0.8847 | 0.1153 | 0.0133 | -0.8949 | 0.1051 | 0.0111 | -0.8568 | 0.1432 | 0.0205 | 200 | -0.8906 | 0.1094 | 0.0120 | -0.8994 | 0.1006 | 0.0101 | -0.9176 | 0.0824 | 0.0068 | 500 | -0.9401 | 0.0599 | 0.0036 | -0.9301 | 0.0699 | 0.0049 | -0.9395 | 0.0605 | 0.0037 | | 50 | 1.1429 | 0.1429 | 0.0204 | 0.7435 | 0.2565 | 0.0658 | 0.8873 | 0.1127 | 0.0127 | 200 | 1.0309 | 0.0309 | 0.0010 | 1.1412 | 0.1412 | 0.0199 | 1.1031 | 0.1031 | 0.0106 | 500 | 1.0697 | 0.0697 | 0.0049 | 0.9123 | 0.0877 | 0.0077 | 0.9001 | 0.0999 | 0.0100 | | 50 | 1.4381 | 0.1381 | 0.0191 | 1.4146 | 0.1146 | 0.0132 | 1.4271 | 0.1271 | 0.0162 | 200 | 1.3915 | 0.0915 | 0.0084 | 1.3219 | 0.0219 | 0.0005 | 1.3616 | 0.0616 | 0.0038 | 500 | 1.3734 | 0.0734 | 0.0054 | 1.3127 | 0.0127 | 0.0002 | 1.3212 | 0.0212 | 0.0005 | | 50 | 0.0476 | 0.0476 | 0.0023 | 0.0716 | 0.0716 | 0.0052 | 0.0419 | 0.0419 | 0.0018 | 200 | 0.0134 | 0.0134 | 0.0002 | 0.0407 | 0.0407 | 0.0017 | 0.0181 | 0.0181 | 0.0003 | 500 | 0.0059 | 0.0059 | <0.0001 | 0.0007 | 0.0007 | <0.0001 | 0.0009 | 0.0009 | <0.0001 |
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NBP: negative binomial parameter; AVB: the absolute value of biases; MSE: mean square error.
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