# Tree-Structured Regression Model Using a Projection Pursuit Approach
## 4 Results
### Comparison of the Performance of Tree-Based Regression Methods
Even though the projection pursuit regression tree shows similar or slightly worse performance than randomForest, it is outperformed in these three data sets. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline  & & & \multicolumn{6}{c}{**Projection Pursuit Regression Tree**} & & Random \\
**Dataset** & **n** & **p** & **Model 1** & **Model 2** & **Model 3** & **Model 4** & **Model 5** & Rpart & Forest \\ \hline Abalone & 4177 & 8 & 1.206 & 1.218 & 1.192 & 1.199 & 1.200 & 1.096 & 0.214 \\ airfoil & 1503 & 5 & 1.263 & 1.234 & 1.253 & 1.266 & 1.281 & 0.719 & 0.414 \\ ais & 202 & 10 & 1.631 & 1.679 & 1.303 & 1.034 & 1.151 & 1.129 & 0.297 \\ alcohol & 2467 & 17 & 1.215 & 1.183 & 1.244 & 1.230 & 1.235 & 1.022 & 0.471 \\ autompg & 392 & 7 & 1.074 & 1.083 & 0.841 & 0.755 & 0.883 & 0.798 & 0.182 \\ baseball & 263 & 18 & 1.396 & 1.379 & 1.337 & 1.227 & 1.327 & 0.829 & 0.186 \\ boston & 506 & 13 & 1.222 & 1.277 & 0.845 & 0.694 & 0.809 & 0.699 & 0.110 \\ budget & 1729 & 9 & 0.818 & 0.897 & 0.479 & 0.320 & 0.465 & 0.235 & 0.007 \\ cane & 3775 & 23 & 1.380 & 1.378 & 1.113 & 1.091 & 1.097 & 1.074 & 0.266 \\ mussels & 82 & 4 & 3.289 & 3.481 & 1.147 & 0.992 & 1.119 & 1.232 & 0.423 \\ ozone & 330 & 9 & 1.530 & 1.545 & 1.011 & 0.922 & 1.059 & 0.715 & 0.168 \\ parkinsons & 5875 & 20 & 1.341 & 1.333 & 1.162 & 1.130 & 1.126 & 1.125 & 0.122 \\ price & 159 & 15 & 1.947 & 2.053 & 1.661 & 1.525 & 0.975 & 1.043 & 0.221 \\ strikes & 628 & 4 & 1.084 & 1.055 & 1.115 & 1.105 & 1.104 & 0.800 & 0.377 \\ tecator & 240 & 22 & 7.412 & 7.692 & 3.820 & 0.500 & 2.049 & 5.867 & 1.056 \\ wine-red & 1599 & 11 & 1.275 & 1.274 & 1.327 & 1.325 & 1.323 & 0.938 & 0.168 \\ wine-white & 4898 & 11 & 1.356 & 1.299 & 1.467 & 1.441 & 1.440 & 1.006 & 0.137 \\ yachtdata & 308 & 6 & 0.189 & 0.200 & 0.027 & 0.009 & 0.020 & 0.063 & 0.108 \\ \hline \end{tabular}
\end{table} 
Table 7: Comparison of 1m, rpart, randomForest, and the projection pursuit regression tree with various data sets; the mean MSE/MSE(1m)of 200 iterations for the training dataset. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline  & & & \multicolumn{6}{c}{**Projection Pursuit Regression Tree**} & & Random \\
**Dataset** & **n** & **p** & **Model 1** & **Model 2** & **Model 3** & **Model 4** & **Model 5** & Rpart & Forest \\ \hline abalone & 4177 & 8 & 1.166 & 1.179 & 1.157 & 1.158 & 1.161 & 1.162 & 0.912 \\ airfoil & 1503 & 5 & 1.281 & 1.248 & 1.264 & 1.276 & 1.294 & 0.860 & 0.580 \\ ais & 202 & 10 & 1.735 & 1.760 & 1.540 & 1.403 & 1.365 & 1.474 & 1.221 \\ alcohol & 2467 & 17 & 1.208 & 1.175 & 1.240 & 1.237 & 1.233 & 1.017 & 1.057 \\ autompg & 392 & 7 & 1.089 & 1.100 & 0.873 & 0.822 & 0.934 & 1.127 & 0.695 \\ baseball & 263 & 18 & 1.206 & 1.177 & 1.312 & 1.190 & 1.152 & 1.052 & 0.679 \\ boston & 506 & 13 & 1.255 & 1.287 & 0.914 & 0.813 & 0.874 & 0.972 & 0.471 \\ budget & 1729 & 9 & 0.832 & 0.903 & 0.493 & 0.354 & 0.478 & 0.258 & 0.034 \\ cane & 3775 & 23 & 1.383 & 1.391 & 1.137 & 1.118 & 1.130 & 1.215 & 0.870 \\ mussels & 82 & 4 & 2.841 & 2.996 & 1.052 & 1.113 & 1.120 & 1.873 & 1.186 \\ ozone & 330 & 9 & 1.507 & 1.510 & 1.010 & 0.979 & 1.061 & 1.163 & 0.801 \\ parkinsons & 5875 & 20 & 1.326 & 1.320 & 1.162 & 1.143 & 1.135 & 1.158 & 0.681 \\ price & 159 & 15 & 1.646 & 1.683 & 1.560 & 1.625 & 1.067 & 1.007 & 0.525 \\ strikes & 628 & 4 & 1.075 & 1.046 & 1.102 & 1.097 & 1.094 & 1.082 & 0.935 \\ tecator & 240 & 22 & 6.180 & 6.328 & 4.100 & 1.336 & 2.720 & 6.411 & 2.918 \\ wine-red & 1599 & 11 & 1.275 & 1.275 & 1.325 & 1.330 & 1.323 & 1.089 & 0.817 \\ wine-white & 4898 & 11 & 1.349 & 1.294 & 1.461 & 1.439 & 1.435 & 1.020 & 0.673 \\ yachtdata & 308 & 6 & 0.209 & 0.234 & 0.032 & 0.017 & 0.026 & 0.061 & 0.207 \\ \hline \end{tabular}
\end{table} 
Table 8: Comparison of 1m, rpart, randomForest, and the projection pursuit regression tree with various data sets; the mean MSE/MSE(1m)of 200 iterations for the test dataset. Sometimes the performance of Model 5 is better than the performance of Model 4. The reason is mainly due to the overfitting.