# Representing Aspectual Meaning in Sentence: Computational Modeling Based on Chinese
## 2 Materials and Methods
### Statistical Validation of Classification Model
#### 2.2.2 Multinomial Logistic Regression  
After completing the sense mapping, you can construct the co-occurrence frequency matrix by using the word-POS pairs as the first column of keywords and the six aspectual markers as the first row of headers. The values in the matrix are filled with the co-occurrence frequencies of words and aspectual markers from the SINICA corpus. This forms the co-occurrence frequency matrix for statistical testing. It is worth noting that we applied min-max scaling for standardization but found that it did not positively impact the final results. Therefore, we ultimately used the raw frequencies for the multinomial logistic regression testing.  
Multinomial logistic regression (MLR) is a statistical technique used to model the relationship between a categorical dependent variable with more than two levels and one or more independent variables. Unlike binary logistic regression, which predicts dichotomous outcomes, MLR extends the framework to handle multi-class scenarios by estimating the probability of each category relative to a reference category.  
In this study, multinomial logistic regression (MLR) is employed for the statistical analysis of situation types due to its suitability for modeling categorical dependent variables with multiple unordered levels. Situation types, as the outcome variable, typically represent distinct categories (e.g., states, activities, accomplishments, achievements, etc.), which are inherently qualitative and cannot be meaningfully ordered. MLR is specifically designed for such scenarios, as it allows for the estimation of the probability of each situation type relative to a reference category while accounting for the influence of predictor variables (e.g., aspectual markers, lexical features, or contextual factors).  
The use of MLR is justified because it provides a robust framework to examine how independent variables affect the likelihood of different situation types occurring. For instance, it can reveal whether specific aspectual markers or linguistic features are more strongly associated with certain situation types. Additionally, MLR does not assume an ordinal relationship among the categories, making it ideal for analyzing situation types, which are often nominal in nature. By leveraging MLR, this study can systematically explore the complex interplay between linguistic predictors and situation types, offering nuanced insights into their statistical associations.  
For MLR, we set the situation type of activity as the reference group while applying correlation coefficients for multicollinearity testing, which means a normal distribution test is also needed.  
The reason for applying multicollinearity testing is that multicollinearity can occur when independent variables are highly correlated with each other, which can lead to several issues in the regression model, including the following:  
* Unstable Coefficient Estimates: High multicollinearity can cause large variances in the estimated coefficients, making them unreliable and difficult to interpret
* Reduced Statistical Power: It can inflate the standard errors of the coefficients, reducing the likelihood of detecting statistically significant relationships.
* Interpretation Challenges: Multicollinearity can make it difficult to assess the individual contribution of each predictor to the model.  
The reason for the normal distribution test is that there are multiple correlation coefficient testing methods, some of which require the data to be normally distributed, such as the Pearson correlation coefficient test, while others do not, such as the Spearman correlation coefficient test. Due to the small size of our dataset, we choose Shapiro-Wilk test as the method for the distribution test.  
For correlation analysis, [PERSON]'s or [PERSON]'s tests were applied based on the data distribution, as assessed by the Shapiro-Wilk test (\(\alpha=0.05\)). Statistical analyses were performed using Python's scipy.stats module.