## 3 Method
### Research Procedures
#### 3.3.1 Feature Extraction and Selection  
Six computational analytic tools were used to extract linguistic features for model construction. The feature selection was a pivotal step in refining the array of linguistic attributes extracted from essays, guaranteeing that only the most relevant and robust features were incorporated into the model training process. Initially, an extensive set of 2044 features was extracted from each essay, utilizing advanced linguistic tools such as CRAT [99], TAALED [100], TAALES [66], TAASSC [101], TAACO [53], and GAMET [103]. The advantage of combining a great number of computational analytic tools was to ensure the richness and comprehensiveness of the linguistic features for measuring different constructs of writing quality. If these linguistic indices were directly included in the analysis, the model would be complicated and unstable, leading to over-fitting problems. Therefore, several methods were used to remove the redundant features and keep those that contribute the most to writing quality (see Table 3). The non-parametric Kolmogorov-Smirnov test was employed to assess the adherence of the data to a normal distribution. In addition, the variance threshold was used to remove the feature that did not vary much within itself (variance lower than 0.01) [8]. The variance threshold seeks to eliminate variables demonstrating negligible variation within the dataset on the premise that such features are improbable to yield significant revelations regarding paper quality. Figure 2: The flowchart of research procedures. The multicollinearity tests were conducted to overcome the overlapping problems between features. These tests aimed to identify instances where two or more indices exhibited a high degree of correlation. In scenarios where indices were found to be highly correlated (\(r>0.90\)), the index demonstrating the strongest correlation with the scores was retained for subsequent analysis, while redundant indices were excluded from the model [4]. After conducting filter methods, the number of linguistic features was reduced from 2044 to 362. The rigorous feature selection process honed the machine learning model's training on a refined feature set, ensuring precise and stable scoring of essays. PCA was used to condense the information of linguistic indices and keep those that contribute the most to the variance. Scholars have indicated three standard methods for determining the number of principal components. The first method was an eigenvalue-based method, which followed the Kaiser-Harris criterion and retained components with eigenvalues greater than 1 [108]. The second method was [PERSON]'s scree test [109]. By plotting the eigenvalues and principal components, the curve of the scree plot was displayed, and the principal components above the maximum change were retained. The last method was the parallel analysis method [110]. A principal component was considered significant and retained for further analysis if its eigenvalue surpassed the corresponding average eigenvalue derived from a collection of random matrices. The decision on the number of principal components to retain was informed by this eigenvalue criterion, in conjunction with the insights gained from the initial two methods employed in the analysis. To ensure the correlation of the indicators contained in each principal component, only the absolute value of the eigen loading greater than 0.35 was included for further analysis [4]. Figure 3 shows the proportion of the total data variance accounted for by each principal component. Seven principal components were retained by taking account of the first two methods [108; 109]. Among them, the first principal component explained 10.1% (74 micro-features) of the variance of the total data variation. The last six principal components explained 5.9% (52 micro-features), 4.9% (26 micro-features), 4.0% (14 micro-features), 3.3% (19 micro-features), 2.5% (6 micro-features), and 2.2% (3 micro-features), respectively.