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