Research Article
Longitudinal Joint Modelling of Ordinal and Overdispersed Count Outcomes: A Bridge Distribution for the Ordinal Random Intercept
Table 7
Simulation study results with 0.8 correlation between the random intercepts and normal distribution for the random intercept of the ordinal outcome.
| | | MSE | | MSE | | MSE | Mean | AVB | Mean | AVB | Mean | AVB |
| Count process | | | | | | | | | | | | 50 | 2.6422 | 0.0422 | 0.0027 | 2.6220 | 0.0220 | 0.0014 | 2.6250 | 0.0250 | 0.0016 | 200 | 2.5805 | 0.0195 | 0.0008 | 2.6140 | 0.0140 | 0.0006 | 2.6076 | 0.0076 | 0.0005 | 500 | 2.6019 | 0.0019 | 0.0004 | 2.6024 | 0.0024 | 0.0004 | 2.6038 | 0.0038 | 0.0004 | | 50 | -0.5816 | 0.0184 | 0.0003 | -0.6113 | 0.0113 | 0.0001 | -0.5882 | 0.0118 | 0.0001 | 200 | -0.5841 | 0.0159 | 0.0003 | -0.6058 | 0.0058 | <0.0001 | -0.5930 | 0.0070 | <0.0001 | 500 | -0.6006 | 0.0006 | <0.0001 | -0.6016 | 0.0016 | <0.0001 | -0.5998 | 0.0002 | <0.0001 | | 50 | -0.4181 | 0.0181 | 0.0004 | -0.3991 | 0.0009 | <0.0001 | -0.4105 | 0.0105 | 0.0001 | 200 | -0.3950 | 0.0050 | <0.0001 | -0.4099 | 0.0099 | 0.0001 | -0.4220 | 0.0220 | 0.0005 | 500 | -0.3840 | 0.0160 | 0.0003 | -0.4070 | 0.0070 | <0.0001 | -0.4050 | 0.0050 | <0.0001 | NBP | 50 | 1.0810 | 0.0810 | 0.0066 | 5.5362 | 0.5362 | 0.2875 | 148.4848 | 1.5152 | 2.2959 | 200 | 1.0517 | 0.0517 | 0.0028 | 5.4830 | 0.4830 | 0.2334 | 151.0433 | 1.0433 | 1.0886 | 500 | 1.0040 | 0.0040 | <0.0001 | 5.5855 | 0.5855 | 0.3428 | 150.8672 | 0.8672 | 0.7520 | | 50 | 0.0863 | 0.0137 | 0.0002 | 0.0871 | 0.0129 | 0.0002 | 0.0830 | 0.0170 | 0.0003 | 200 | 0.0892 | 0.0108 | 0.0001 | 0.0831 | 0.0169 | 0.0003 | 0.0861 | 0.0139 | 0.0002 | 500 | 0.0987 | 0.0013 | <0.0001 | 0.0967 | 0.0033 | 0.0001 | 0.0918 | 0.0082 | 0.0001 | Ordinal process | | | | | | | | | | | | 50 | 0.6606 | 0.0606 | 0.0037 | 0.6255 | 0.0255 | 0.0007 | 0.6603 | 0.0603 | 0.0036 | 200 | 0.6290 | 0.0290 | 0.0008 | 0.6231 | 0.0231 | 0.0005 | 0.6624 | 0.0624 | 0.0039 | 500 | 0.6055 | 0.0055 | <0.0001 | 0.6020 | 0.0020 | <0.0001 | 0.6294 | 0.0294 | 0.0009 | | 50 | 0.1803 | 0.0803 | 0.0064 | 0.1657 | 0.0657 | 0.0043 | 0.1645 | 0.0645 | 0.0042 | 200 | 0.1720 | 0.0720 | 0.0052 | 0.1615 | 0.0615 | 0.0038 | 0.1682 | 0.0682 | 0.0047 | 500 | 0.1693 | 0.0693 | 0.0050 | 0.1401 | 0.0401 | 0.0018 | 0.1512 | 0.0512 | 0.0028 | | 50 | -0.8495 | 0.1505 | 0.0227 | -0.8917 | 0.1083 | 0.0117 | -0.9167 | 0.0833 | 0.0070 | 200 | -0.9289 | 0.0711 | 0.0051 | -0.8916 | 0.1084 | 0.0118 | -0.9195 | 0.0805 | 0.0065 | 500 | -0.9529 | 0.0471 | 0.0022 | -0.9676 | 0.0324 | 0.0011 | -0.9785 | 0.0215 | 0.0005 | | 50 | 1.3728 | 0.3728 | 0.1390 | 1.3594 | 0.3594 | 0.1292 | 1.2142 | 0.2142 | 0.0459 | 200 | 1.1717 | 0.1717 | 0.0295 | 1.1962 | 0.1962 | 0.0385 | 1.0980 | 0.0980 | 0.0096 | 500 | 1.1056 | 0.1056 | 0.0112 | 1.0246 | 0.0246 | 0.0006 | 1.0090 | 0.0090 | 0.0001 | | 50 | 1.1966 | 0.1034 | 0.0107 | 1.2818 | 0.0182 | 0.0004 | 1.2796 | 0.0204 | 0.0004 | 200 | 1.2019 | 0.0981 | 0.0097 | 1.2015 | 0.0985 | 0.0097 | 1.2908 | 0.0092 | 0.0001 | 500 | 1.2260 | 0.0740 | 0.0055 | 1.2222 | 0.0778 | 0.0061 | 1.2923 | 0.0077 | 0.0001 | | 50 | 0.7068 | 0.0932 | 0.0087 | 0.7193 | 0.0807 | 0.0065 | 0.8492 | 0.0492 | 0.0024 | 200 | 0.7167 | 0.0833 | 0.0070 | 0.8135 | 0.0135 | 0.0002 | 0.7834 | 0.0166 | 0.0003 | 500 | 0.7297 | 0.0703 | 0.0049 | 0.7711 | 0.0289 | 0.0008 | 0.8293 | 0.0293 | 0.0009 |
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NBP: negative binomial parameter; AVB: the absolute value of biases; MSE: mean square error.
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