## 5 Conclusions  
With advances in computational linguistics, NLP, and AI, scholars have provided thought-provoking insights on incorporating feature-based approaches and machine learning algorithms into AES tasks. However, little has been done to explore the relationship between deep-level linguistic features and different constructs of expository writing quality. Additionally, the inner workings of linguistic features in the black box are still unknown. The present study takes full advantage of the interdisciplinary fields combining corpus linguistics, NLP, and XAI. It also provides insightful perspectives on developing linear and non-linear models to examine the relationship between linguistic features and essay scores from holistic and analytic rating scales.  
With cutting-edge computational analytic tools and PCA, deep-level linguistic features were extracted to condense and reduce the noise, thereby eliminating redundancy and enhancing data quality. The results demonstrated that the micro-feature and combined feature approach provided a robust basis for characterizing writing quality compared to the aggregated feature approach. Furthermore, linear and non-linear AES models were constructed to explore the complex relationship between linguistic features and writing quality. The results indicated that the proposed non-linear AES model with Random Forest Regression outperformed the QWK score by 4.8% over the benchmark Qe-C-LSTM, which offered support to the idea that the relationship between linguistic features and writing quality was complicated as multi-dimensional constructs were involved. Lastly, SHAPvalues were plotted to identify the most powerful linguistic features per rating trait, thereby improving the explainability of the proposed model. Linguistic features for different constructs of writing quality can provide diagnostic feedback for writing instruction and revision. Teachers can also carry out diversified and individualized teaching according to the feedback of linguistic features, characterizing the writing quality through holistic and analytic rating traits.  
While our findings contribute to the development of more sophisticated, fair, and transparent AES systems, they also highlight the need for a broader representation of writing genres and a more diverse range of educational backgrounds. Broadening the scope of the datasets would enhance the robustness and generalizability of the proposed AES models. This expansion is crucial for achieving a comprehensive understanding of multi-dimensional writing assessment across large-scale educational contexts. Furthermore, future studies could benefit from integrating large language models [7; 123], which promise further to improve the accuracy and generalization capabilities of AES systems. Such advancements are essential for keeping pace with the evolving demands of multi-dimensional assessment.  
Conceptualization, X.T., H.C. and D.L.; methodology, X.T. and D.L.; software, X.T. and D.L.; validation, X.T., H.C., D.L. and K.L.; writing--original draft preparation, X.T.; writing--review and editing, H.C., D.L. and K.L.; supervision, H.C., D.L. and K.L.; funding acquisition, X.T. All authors have read and agreed to the published version of the manuscript.  
This research was funded by China Postdoctoral Science Foundation under Grant Number 2023M740222.  
Not applicable.  
The raw data supporting the conclusions of this article will be made available by the authors on request.  
The authors declare no conflicts of interest.