## 4 Investigation and Analysis
### Analysis of Influencing Factors Based on BPNN-DEMATEL Model
These factors deserve attention, as they are affected by other factors and induce their own influence. Therefore, \(F_{2}\), \(F_{7}\), \(F_{9}\), and \(F_{14}\) can be determined as key factors. Based on the above analysis of the four quadrants, from the perspective of centrality, the larger the value, the more important it is. From the perspective of causality, the larger the absolute value, the more important it is. Therefore, in order to express the comprehensive importance of influencing factors, the key influencing factors for the promotion of prefabricated housing in Hainan Province were comprehensively analyzed, and the \(\mathbf{D}\) value was introduced, that is, the distance from each influencing factor to the point (\(W_{i(\text{mean})}\), \(R_{i(\text{mean})}\)). The larger the distance, the higher the importance of the influencing factor. The calculation formula of \(\mathbf{D}\) is shown in Equation (16):  
\[D=\sqrt{\left(W_{i(mean)}-W_{i}\right)^{2}+\left(R_{i(mean)}-R_{i}\right)^{2}} \tag{16}\]  
where \(W_{i(\text{mean})}=\sum_{1}^{20}W_{i}/20\), \(R_{i(\text{mean})}=\sum_{1}^{20}R_{i}/20\). The comprehensive importance of each influencing factor was calculated and ranked according to Formula (16). The results are shown in Table 8.  
As shown in Table 8, \(F_{1}\), \(F_{2}\), \(F_{9}\), \(F_{14}\), and \(F_{17}\) rank in the top five. Based on the results of the four-quadrant causal relationship diagram, \(F_{1}\), \(F_{2}\), \(F_{6}\), \(F_{7}\), \(F_{9}\), \(F_{12}\), \(F_{13}\), \(F_{14}\), \(F_{16}\), \(F_{17}\), \(F_{18}\), \(F_{19}\), and \(F_{20}\) are the key factors affecting the promotion of prefabricated housing in Hainan, \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Influencing** & \(W_{i}\) & \(R_{i}\) & \(\mathbf{D}\) & \(\mathbf{D}\)-**Sort** \\
**Factors** & \(W_{i}\) & \(R_{i}\) & \(\mathbf{D}\) & \(\mathbf{D}\)-**Sort** \\ \hline \(F_{1}\) & 1.9175 & 1.2542 & 1.2821 & 5 \\ \(F_{2}\) & 1.9129 & \(-\)1.2470 & 2.2834 & 1 \\ \(F_{3}\) & 1.5740 & \(-\)0.5883 & 0.5934 & 14 \\ \(F_{4}\) & 1.4992 & \(-\)0.1232 & 1.2810 & 6 \\ \(F_{5}\) & 1.4483 & \(-\)0.2074 & 0.4861 & 19 \\ \(F_{6}\) & 1.6343 & 0.7377 & 1.1691 & 7 \\ \(F_{7}\) & 1.6843 & \(-\)0.8452 & 1.0636 & 11 \\ \(F_{8}\) & 1.4780 & \(-\)0.2123 & 0.5238 & 18 \\ \(F_{9}\) & 1.8430 & \(-\)1.1505 & 1.5306 & 3 \\ \(F_{10}\) & 1.6117 & \(-\)0.7368 & 0.5746 & 16 \\ \(F_{11}\) & 1.4989 & \(-\)0.1533 & 0.5463 & 17 \\ \(F_{12}\) & 1.5913 & 0.6340 & 1.1292 & 9 \\ \(F_{13}\) & 1.5592 & 0.5462 & 1.0991 & 10 \\ \(F_{14}\) & 1.8471 & \(-\)1.1413 & 1.2908 & 4 \\ \(F_{15}\) & 1.6077 & \(-\)0.6753 & 1.1619 & 8 \\ \(F_{16}\) & 1.5008 & 0.4580 & 0.3275 & 20 \\ \(F_{17}\) & 1.9489 & 1.3027 & 1.9121 & 2 \\ \(F_{18}\) & 1.6103 & 0.6816 & 0.7770 & 12 \\ \(F_{19}\) & 1.6343 & 0.7377 & 0.7175 & 13 \\ \(F_{20}\) & 1.6302 & 0.7284 & 0.5783 & 15 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Comprehensive ranking table of influencing factors. and the above five factors are all among the key factors. Comprehensive analysis shows that factors \(F_{1}\) (imperfect standards and specifications), \(F_{2}\) (imperfect incentives), \(F_{9}\) (lack of motivation for corporate strategic transformation), \(F_{14}\) (insufficient market demand), and \(F_{17}\) (unununified design product standards) are key influencing factors. Evolution Path of Factors Affecting the Promotion of Prefabricated Housing in Hainan Province Based on Key Factor Chain  
In order to explore the evolution path of influencing factors in the promotion of prefabricated housing in Hainan Province, the final screening indicators \(F_{1}\), \(F_{2}\), \(F_{9}\), \(F_{14}\), and \(F_{17}\) were taken as key factors, and a comprehensive correlation matrix \(Yf_{5\times 5}\) of key factors was established.