# Delving into Causal Discovery in Health-Related Quality of Life Questionnaires
## 4 Discussion
### Impact, Limitations, and Future Work
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**IA** & **DAG \#** & **1** & **2** & **3** & **4** & **5** & **6** & **7** \\ \hline  & \# of nodes & 5 & 10 & 11 & 15 & 21 & 26 & 26 \\ \hline Sample size \(n\) & \# of edges & 5 & 9 & 11 & 16 & 17 & 21 & 19 \\ \hline  & HD & 1.54 & 2.21 & 4.32 & 8.06 & 7.85 & 11.03 & 9.93 \\  & rHD & 0.31 & 0.25 & 0.39 & 0.50 & 0.46 & 0.53 & 0.52 \\
100 & 0’s in HD & 44 & 25 & 0 & 0 & 0 & 0 & 0 \\  & SHD & 3.66 & 5.68 & 8.72 & 12.79 & 11.17 & 16.72 & 14.32 \\  & rSHD & 0.73 & 0.63 & 0.79 & 0.80 & 0.66 & 0.80 & 0.75 \\  & 0’s in SHD & 25 & 2 & 0 & 0 & 0 & 0 & 0 \\ \hline  & HD & 0.27 & 0.37 & 1.05 & 1.73 & 2.79 & 4.14 & 3.01 \\  & rHD & 0.05 & 0.04 & 0.10 & 0.11 & 0.16 & 0.20 & 0.16 \\
500 & 0’s in HD & 747 & 665 & 280 & 124 & 23 & 15 & 37 \\  & SHD & 0.89 & 2.29 & 3.49 & 7.35 & 5.97 & 9.96 & 7.00 \\  & rSHD & 0.18 & 0.25 & 0.32 & 0.46 & 0.35 & 0.47 & 0.37 \\  & 0’s in SHD & 736 & 290 & 46 & 5 & 1 & 0 & 2 \\ \hline  & HD & 0.10 & 0.20 & 0.50 & 0.60 & 1.95 & 2.85 & 2.11 \\  & rHD & 0.02 & 0.02 & 0.05 & 0.04 & 0.11 & 0.14 & 0.11 \\
1000 & 0’s in HD & 898 & 819 & 589 & 553 & 122 & 36 & 118 \\  & SHD & 0.30 & 1.10 & 1.80 & 3.50 & 4.56 & 6.06 & 4.14 \\  & rSHD & 0.06 & 0.12 & 0.16 & 0.22 & 0.27 & 0.29 & 0.22 \\  & 0’s in SHD & 898 & 581 & 255 & 111 & 10 & 12 & 50 \\ \hline  & HD & 0.12 & 0.18 & 0.32 & 0.40 & 1.22 & 2.30 & 1.63 \\  & rHD & 0.02 & 0.02 & 0.03 & 0.03 & 0.07 & 0.11 & 0.09 \\
2000 & 0’s in HD & 887 & 837 & 713 & 655 & 271 & 69 & 202 \\  & SHD & 0.34 & 0.62 & 0.94 & 1.29 & 3.14 & 4.26 & 2.53 \\  & rSHD & 0.07 & 0.07 & 0.09 & 0.08 & 0.18 & 0.20 & 0.13 \\  & 0’s in SHD & 887 & 787 & 532 & 395 & 176 & 60 & 180 \\ \hline  & HD & 0.14 & 0.21 & 0.34 & 0.41 & 1.04 & 2.00 & 1.18 \\  & rHD & 0.03 & 0.02 & 0.03 & 0.03 & 0.06 & 0.10 & 0.06 \\
5000 & 0’s in HD & 867 & 808 & 694 & 665 & 325 & 90 & 250 \\  & SHD & 0.36 & 0.57 & 0.69 & 0.58 & 2.06 & 3.38 & 2.17 \\  & rSHD & 0.07 & 0.06 & 0.06 & 0.04 & 0.12 & 0.16 & 0.11 \\  & 0’s in SHD & 867 & 799 & 687 & 643 & 200 & 86 & 194 \\ \hline  & HD & 0.12 & 0.18 & 0.33 & 0.43 & 1.05 & 1.90 & 1.13 \\  & rHD & 0.02 & 0.02 & 0.03 & 0.03 & 0.06 & 0.09 & 0.06 \\
10,000 & 0’s in HD & 879 & 837 & 715 & 638 & 352 & 121 & 305 \\  & SHD & 0.30 & 0.48 & 0.63 & 0.60 & 1.60 & 2.30 & 1.63 \\  & rSHD & 0.06 & 0.05 & 0.06 & 0.04 & 0.09 & 0.11 & 0.09 \\  & 0’s in SHD & 879 & 834 & 713 & 633 & 308 & 113 & 310 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The mean Hamming distance (HD) across 1000 iterations, the mean relative HD (rHD) across 1000 iterations, the number of cases the HD was zero across 1000 iterations (0’s in HD), the mean structural Hamming distance (SHD) across 1000 iterations, the mean relative SHD (rSHD) across 1000 iterations, and the number of cases the SHD was zero across 1000 iterations (0’s in SHD) based on estimations with the Incremental Association (IA) algorithm are displayed. The notations DAG #1, 2, 3, 4, 5, 6, and 7 correspond to the seven synthetic directed acyclic graphs that are described in Section 2.2.1 and are displayed in Figure 1.