## 4 Results and Discussion
### Comparison between Linear and Non-Linear AES Models in Capturing Writing Quality  
Both linear and non-linear methods were used to explore the relationship between linguistic features and essay scores across different rating traits. Table 5 demonstrates the performance of linear and non-linear AES models in delineating the relationship between linguistic features and the multifaceted constructs of writing quality. Following these tests, Random Forest Regression emerged as the most effective model, demonstrating superior performance across all rating traits and evaluation metrics. It achieved the highest (\(R^{2}\)) values, indicating a strong explanatory power for variations in writing quality, with notable scores in _Ideas_ (0.777), _Organization_ (0.769), _Style_ (0.740), _Conventions_ (0.725), and _Holistic_ (0.771). Additionally, this model outperformed others regarding QWK, with scores indicating a robust agreement between predicted and actual ratings, peaking at 0.863 in the holistic rating trait. Decision Tree Regression showed remarkable strength in Exact Agreement, particularly in the _Ideas_ and _Organization_, suggesting its capability to mirror the scoring patterns of human raters precisely. However, the Random Forest model excelled in the Exact-Plus-Adjacent Agreement metric across all the rating traits. The Random Forest Regression model stood out for its robust capability across multiple dimensions of writing quality, supported by high agreement rates with human raters. The results suggested that non-linear AES models better captured the relationship between linguistic features and writing quality across different rating traits, which could enhance the overall accuracy and reliability of AES tasks, ensuring a more systematic assessment of writing quality that mirrors the complex judgment process of human raters. The confusion matrices for each rating trait, illustrated in Figures 4 and 5, provided further insights into the accuracy of AES models, revealing the distribution of predictions across the scoring traits. These matrices are crucial for understanding where the model excels and where it may confuse certain score categories. With qualified micro-features, the proposed AES model not only achieves high accuracy but also aligns closely with the nuanced judgment of human raters across multiple dimensions of writing quality. Figure 4: Confusion matrix for the Holistic dimension. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Model** & **Ideas** & **Organization** & **Style** & **Conventions** & **Holistic** \\ \hline \multicolumn{5}{l}{**Bayesian Linear Regression**} \\ \(R^{2}\) & 0.629 & 0.556 & 0.592 & 0.547 & 0.680 \\ QWK & 0.767 & 0.679 & 0.731 & 0.670 & 0.806 \\ E & 0.481 & 0.506 & 0.576 & 0.481 & 0.178 \\ E + A & 0.892 & 0.917 & 0.975 & 0.936 & 0.503 \\ \multicolumn{5}{l}{**Linear Regression**} \\ \(R^{2}\) & 0.637 & 0.542 & 0.582 & 0.496 & 0.672 \\ QWK & 0.783 & 0.685 & 0.722 & 0.670 & 0.811 \\ E & 0.433 & 0.497 & 0.551 & 0.503 & 0.159 \\ E + A & 0.911 & 0.914 & 0.965 & 0.917 & 0.487 \\ \multicolumn{5}{l}{**Stochastic Gradient Descent Regression**} \\ \(R^{2}\) & 0.614 & 0.554 & 0.598 & 0.515 & 0.670 \\ QWK & 0.775 & 0.699 & 0.753 & 0.668 & 0.801 \\ E & 0.439 & 0.519 & 0.576 & 0.478 & 0.185 \\ E + A & 0.911 & 0.914 & 0.981 & 0.927 & 0.487 \\ \multicolumn{5}{l}{**Random Forest Regression**} \\ \(R^{2}\) & **0.777** & **0.679** & **0.740** & **0.725** & **0.771** \\ QWK & **0.863** & **0.778** & **0.832** & **0.819** & **0.863** \\ E & 0.646 & 0.640 & 0.720 & **0.659** & 0.280 \\ E + A & **0.952** & **0.949** & **0.987** & **0.965** & **0.643**We also compared the modeling results with other baseline models. Numerous scholars have conducted deep learning techniques to construct AES models for writing assessments. Table 6 shows the QWK scores at the holistic rating trait on the ASAP dataset 7. MN [119] utilizes a novel approach by evaluating the relationship between unlabeled essays and a repository of selected essays for score prediction.