## 5 Principal Component Regression Analysis
### Causality Analysis Using Principal Component Regression (PCR)
However, MARS models often obscure the temporal dynamics of parameter influence due to their focus on nonlinear interactions, whereas PCR explicitly quantifies the progressive dominance of PC1 (from 68.7% to 83.0% for R\({}^{2}\) improvement). In contrast, support vector regression (SVR) studies by [PERSON] et al. [70] report higher predictive accuracy (R\({}^{2}\) > 0.90) but fail to resolve the mechanistic hierarchy of variables, highlighting PCR's unique strength in causal inference. The observed curing-time dependency of PC1 (increasing from \(\beta=-76.84\) at 7 days to \(\beta=-170.70\) at 28 days) corroborates findings from time-series functional principal component analysis (FPCA) [26], which links prolonged curing to microstructural densification. However, FPCA typically requires dense temporal sampling, whereas PCR achieves comparable insights with fewer time points (7, 14, 28 days). The diminishing role of PC2 (stiffness) over time contrasts with kernel-based PCR approaches [70], which model nonlinear dosage-response relationships but may overemphasize early-stage stiffness contributions due to kernel weighting biases. The PCR model's R\({}^{2}\) improvement (68.7% to 83.0%) and RMSE reduction (11.2 kPa to 7.8 kPa) align with elastic net PCR studies [70], which similarly report enhanced stability in later curing stages. However, elastic net PCR often incorporates regularization to mitigate multicollinearity [26], whereas this study's reliance on variance decomposition avoids coefficient constraints that might obscure causal relationships. The consistent significance of PC1 (\(p<0.001\)) across all curing stages contrasts with traditional multiple regression, where collinearity frequently destabilizes parameter estimates, underscoring PCR's robustness in handling correlated predictors. The negative influence of PC3 (presconsolidation stress, \(\beta=-0.32\)) in this study contrasts with landslide susceptibility models, where pre-consolidation stress positively correlates with strength. While PCR provides interpretable causal hierarchies, its linear framework may overlook nonlinear interactions captured by random forest or gradient-boosting models. Hybrid approaches combining PCR with functional data analysis could reconcile these limitations by modeling temporal trajectories as continuous functions. Additionally, the PCR-identified threshold of 20-30% lime-cement content for diminishing returns aligns with response surface methodology (RSM) studies, suggesting opportunities for integrating PCR with RSM to optimize additive dosages. This PCR analysis offers a nuanced understanding of UCS causality in stabilized soils, particularly the time-dependent dominance of compressibility over stiffness parameters. While non-PCR methods like SVR or MARS may achieve marginally higher predictive accuracy, they lack PCR's ability to decompose variance and trace mechanistic pathways. Future work should explore geographically weighted PCR to account for spatial variability in soil properties, enhancing the generalizability of these findings. This research investigates high-plasticity clay stabilization from Kano, Nigeria, using lime (0-30%) and cement (0-8%) additives. The study employs PCA and PCR to examine relationships between stabilizer content, curing time (7-28 days), and geotechnical properties including UCS, void ratio, porosity, compression index, pre-consolidation stress, and compressibility modulus. The research successfully evaluates lime-cement stabilization efficacy, estab \begin{table}
\begin{tabular}{l l l} \hline
**Curing Time** & **R\({}^{2}\) (Model Fit)** & **Significant Principal Components (\(p<0.05\))** & **Most Influential Factor** \\ \hline
7 Days & 0.687 (68.7\%) & PC1 (\(-76.84\), \(p<0.001\)) & Soil Compressibility and Porosity \\ \hline
14 Days & 0.688 (68.8\%) & PC1 (\(-139.96\), \(p<0.001\)) & Porosity and Stiffness \\ \hline
28 Days & 0.830 (83.0\%) & PC1 (\(-170.70\), \(p<0.001\)) & Soil Strength and Compaction \\ \hline \end{tabular}
\end{table}