## 3 Results
### Incremental Predictive Power of Factor Groups
#### 3.3.2. Incremental Predictive Power of Factor Groups: Triplets  
Next, we investigated whether using three psychological factors could increase the predictive power in comparison with the predictive power of their subsets. Out of the 1140 triplets, an improvement was measured in only 21 cases (1.8%). On the other hand, we observed no significant improvement to the best performing pair from the previous section, namely the combination of the UES, coping, and EPI at the 0.1 level, while 11 triplets showed significant improvement to the UES solely. The best performing one was the triplet of coping, EPI, and PERMA health, which gained an AUC of 0.810. In Table 3 the \"Number of triplets\" column indicates the number of triplets with (significant) incremental predictive power that the given factor contributes to. In this case, the coping and PERMA negativity factors were prominently included in triplets with incremental predictive power, in more than 52% of all. In addition, EPI and PI self-control were also present in many triplets, namely 8 and 6 (38% and 29%, respectively, of all 21 groups). Some of the PERMA factors (positivity, meaning, happiness, relationship), EQ factors (stress-management, interpersonal part), and PI subsystems (monitoring and mobilizing) were included in a few groups (less than 3%). Table 4 shows the predictive power of the five best triplets according to the AUC scores. \begin{table}
\begin{tabular}{c c} \hline \hline
**Groups** & **AUC (with UES)** \\ \hline coping, EPI, PERMA health & 0.810 \\ coping, EPI, PERMA negativity & 0.809 \\ coping, EPI, PERMA positivity & 0.806 \\ coping, PERMA meaning, PERMA negativity & 0.790 \\ coping, grit, PI self-control & 0.789 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The predictive power of the five best triplets. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Factor** & **Number of Pairs** & **Number of Triplets** & **Number of Quadruplets** & **Number of Quintuplets** & **Number of** **Sextuplets** & **Ratio in All \({}^{*}\)** \\ \hline PERMA negativity & \(3/1\) & \(11/4\) & \(12/7\) & \(21/13\) & 0 & \(54.5\%/61.0\%\) \\ coping & \(7/7\) & \(11/11\) & \(7/7\) & \(12/12\) & 0 & \(43.2\%/92.7\%\) \\ PI self-control & \(4/1\) & \(6/2\) & \(7/3\) & \(20/11\) & 0 & \(43.2\%/41.5\%\) \\ EPI & \(7/1\) & \(8/3\) & \(6/3\) & \(10/4\) & 0 & \(36.4\%/26.8\%\) \\ PERMA health & \(2/0\) & \(3/2\) & \(7/2\) & \(10/7\) & 0 & \(26.1\%/26.8\%\) \\ EQ intrapersonal & \(1/0\) & \(4/0\) & \(7/1\) & \(8/2\) & 0 & \(22.7\%/7.3\%\) \\ PERMA accomplishment & \(4/1\) & \(3/2\) & \(5/1\) & \(7/1\) & 0 & \(21.6\%/12.2\%\) \\ PERMA engagement & \(2/0\) & \(2/0\) & \(3/0\) & \(6/0\) & 0 & \(14.8\%/0.0\%\) \\ EQ adaptation & \(1/1\) & \(4/4\) & \(2/2\) & \(4/4\) & 0 & \(12.5\%/26.8\%\) \\ PERMA happiness & \(1/0\) & \(0/0\) & \(1/1\) & \(7/4\) & 0 & \(10.2\%/12.2\%\) \\ PERMA loneliness & \(0/0\) & \(2/0\) & \(1/0\) & \(6/4\) & 0 & \(10.2\%/9.8\%\) \\ PERMA meaning & \(1/1\) & \(1/1\) & \(3/1\) & \(4/2\) & 0 & \(10.2\%/12.2\%\) \\ Grit & \(1/1\) & \(4/3\) & \(2/2\) & \(1/1\) & 0 & \(10.2\%/17.1\%\) \\ PERMA positivity & \(0/0\) & \(1/1\) & \(3/1\) & \(3/2\) & 0 & \(8.0\%/9.8\%\) \\ EQ interpersonal & \(0/0\) & \(0/0\) & \(2/1\) & \(3/2\) & 0 & \(5.7\%/7.3\%\) \\ PERMA relationship & \(0/0\) & \(0/0\) & \(2/0\) & \(2/1\) & 0 & \(4.5\%/2.4\%\) \\ EQ mood and motivation & \(1/0\) & \(2/0\) & \(1/0\) & \(0/0\) & 0 & \(4.5\%/0.0\%\) \\ EQ stress-management & \(0/0\) & \(1/0\) & \(1/0\) & \(1/0\) & 0 & \(3.4\%/0.0\%\) \\ PI mobilizing & \(1/0\) & \(0/0\) & \(0/0\) & 0/0 & 0 & \(1.1\%/0.0\%\) \\ PI monitor & \(0/0\) & \(0/0\) & \(0/0\) & 0/0 & 0 & \(0.0\%/0.0\%\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The number of groups (pairs, triplets, quadruplets, quintuplets, sextuplets) and the ratio of all groups with additional incremental predictive power where the given factor contributes to.