Table 3.
Predictive performance of models results from ten-fold cross-validation
| Models | GMAE | GMSE | Mean | Minimum | Maximum |
|---|---|---|---|---|---|
| Actual | 0.8279 | −0.3770 | 1 | ||
| Direct mapping | |||||
| Explanatory variable set 1 | |||||
| OLS | 0.1087 | 0.0290 | 0.8239 | 0.1714 | 1 |
| Tobit | 0.1153 | 0.0307 | 0.8221 | 0.0121 | 0.9521 |
| GLM | 0.1063 | 0.2766 | 0.8254 | −0.0919 | 0.9931 |
| CLAD | 0.1298 | 0.0296 | 0.8371 | 0.1087 | 1 |
| Betamix | 0.1107 | 0.0283 | 0.8243 | −0.1218 | 0.9843 |
| ALDVMM-2 part | 0.1074 | 0.0275 | 0.8257 | −0.1873 | 0.9935 |
| ALDVMM-3 part | 0.1102 | 0.0288 | 0.8240 | −0.1241 | 0.9914 |
| Explanatory variable set 2 | |||||
| OLS | 0.0991 | 0.0236 | 0.8132 | −0.1984 | 1 |
| Tobit | 0.0998 | 0.0261 | 0.8101 | −0.1005 | 0.9412 |
| GLM | 0.0989 | 0.0234 | 0.8204 | −0.2003 | 0.9941 |
| CLAD | 0.0995 | 0.0253 | 0.8282 | −0.1210 | 1 |
| Betamix | 0.1176 | 0.0234 | 0.8250 | −0.1996 | 0.9876 |
| ALDVMM-2 part | 0.0904 | 0.0235 | 0.8232 | −0.2138 | 0.9880 |
| ALDVMM-3 part | 0.0914 | 0.0252 | 0.8211 | −0.2023 | 0.9861 |
| Explanatory variable set 3 | |||||
| OLS | 0.0965 | 0.0239 | 0.8240 | 0.1991 | 1 |
| Tobit | 0.1105 | 0.0249 | 0.8158 | 0.0021 | 0.9631 |
| GLM | 0.0900 | 0.0232 | 0.8271 | −0.1267 | 0.9961 |
| CLAD | 0.1231 | 0.0215 | 0.8304 | 0.1279 | 1 |
| Betamix | 0.0987 | 0.0232 | 0.8259 | −0.1098 | 0.9941 |
| ALDVMM-2 part | 0.0995 | 0.0241 | 0.8269 | −0.1098 | 0.9972 |
| ALDVMM-3 part | 0.0989 | 0.0261 | 0.8248 | −0.1011 | 0.9925 |
| Explanatory variable set 4 | |||||
| OLS | 0.0980 | 0.0272 | 0.8273 | 0.1052 | 1 |
| Tobit | 0.0989 | 0.0279 | 0.8175 | 0.0175 | 0.9438 |
| GLM | 0.0988 | 0.0263 | 0.8201 | −0.1950 | 0.9962 |
| CLAD | 0.1000 | 0.0280 | 0.8383 | −0.0720 | 1 |
| Betamix | 0.0986 | 0.0273 | 0.8264 | −0.1983 | 0.9960 |
| ALDVMM-2 part | 0.0984 | 0.0257 | 0.8270 | −0.1996 | 0.9966 |
| ALDVMM-3 part | 0.0988 | 0.0277 | 0.8252 | −0.1967 | 0.9950 |
| Explanatory variable set 5 | |||||
| OLS | 0.0889 | 0.0242 | 0.8280 | −0.2914 | 1 |
| Tobit | 0.0897 | 0.0249 | 0.8201 | −0.1071 | 0.9532 |
| GLM | 0.0883 | 0.0240 | 0.8279 | −0.3335 | 0.9971 |
| CLAD | 0.0911 | 0.0251 | 0.8371 | −0.2941 | 1 |
| Betamix | 0.0888 | 0.0248 | 0.8279 | −0.2911 | 0.9970 |
| ALDVMM-2 part | 0.0882 | 0.0229 | 0.8279 | −0.3246 | 0.9972 |
| ALDVMM-3 part | 0.0893 | 0.0256 | 0.8301 | −0.2954 | 0.9958 |
| Indirect (response) mapping | |||||
| GLOGIT | 0.1010 | 0.0346 | 0.8413 | −0.2520 | 1 |
GMAE and GMSE were obtained from ten-fold cross-validation. Predicted utilities over one were truncated at one. Explanatory variables for set 1: seven PROMIS-29 domains T-scores, set 2: polynomial forms of seven PROMIS-29 domains T-scores, age and sex, set 3: seven domains of PROMIS-29 (as continuous variables), age, age squared and sex, set 4: the PROMIS-29 items, age, age squared and sex, set 5: the PROMIS-29 (as categorical variables), age, age squared and sex
ALDVMM adjusted limited dependent variable mixture model, ALDVMM-2 part ALDVMM model with two components, ALDVMM-3 part ALDVMM model with three components, Betamix Mixture beta regression model, GLM generalised linear model, CLAD censored least absolute deviation, GLOGIT generalised logistic regression, GMAE geometric mean absolute error, GMSE geometric mean squared error, OLS ordinary least square
The reported GMAE, GMSE, mean and maximum are after truncation