## 3 Results
### Machine Learning Analysis
This sparse distribution of importance scores is characteristic of ensemble methods when dealing with datasets where only a subset of features holds predictive power. The dominance of _NumericImpactResponses_ underscores its centrality to the predictive mechanism of the ensemble model, likely reflecting a strong and consistent relationship with the target variable. The feature importance for the SVM model (Figure 8) was determined using the permutation method, which assesses the impact of randomly shuffling a feature on model performance. Here, _NumericImpactResponses_ emerges as the dominant feature, with an importance score of 0.1867, followed by _NumericFamilySmoking_ (0.0133), _Age_ (0.0167), and _When did you start smoking_ (0.0067). The remaining features have negligible or zero importance. This result suggests that the SVM model, which relies on maximizing the margin between classes, identifies _NumericImpactRespons_ as critical to defining the decision boundary. The relative importance of _NumericFamilySmoking_, _Age_, and _When did you start smoking_ highlights secondary relationships that contribute to the model's performance, albeit at a smaller scale. Feature importance for the k-NN model (Figure 9), also derived using the permutation method, reveals _NumericImpactResponses_ as the most significant contributor, with an importance score of 0.2433. This far exceeds the contribution of _NumericConflictResponses_ (0.008) and other features, which have zero measurable importance. The dominance of _NumericImpactResponses_ indicates that it plays a critical role in determining proximity-based classifications within the k-NN framework. Unlike tree-based models, k-NN relies on feature similarity, and the high importance score of _NumericImpactResponses_ suggests that it provides the most discriminative power in defining neighborhood relationships. Figure 7: The feature importance analysis by ensemble method. The high importance of _NumericImpactResponses_ across all models highlights its pivotal role in determining outcomes. This feature, which quantifies participants' perceptions of smoking's impact on relationships, likely reflects their personal and familial experiences. Its dominance in feature importance suggests that individuals are acutely aware of how smoking behaviors affect interpersonal dynamics, making this variable a strong predictor of relational patterns. The secondary role of features such as _NumericConflictResponses_ and _NumericAcceptanceResponses_ across models suggests that while these factors contribute to relational dynamics, they are not as consistently or strongly predictive. Their lower importance indicates that conflict or acceptance dynamics may only manifest in specific familial contexts, making them less universally applicable predictors. Among the models tested (Table 4), the ensemble model achieved the highest cross-validation accuracy of 93.33% and a minimal loss of 1.43%, effectively classifying complex relationships within the dataset. The decision tree classifier demonstrated moderate performance with an accuracy of 83.33% and a loss of 18.57%, identifying key decision points but struggling with intricate patterns. Similarly, the k-nearest neighbor (k-NN) model achieved an accuracy of 90% and a loss of 14.29%, demonstrating high sensitivity to localized data structures. The support vector machine (SVM) model underperformed, with a  
Figure 8: Feature importance analysis by SVM. Figure 9: The feature importance analysis by k-NN. cross-validation accuracy of 80% and a loss of 44.29%, reflecting challenges in handling nonlinear and high-dimensional data. To improve comparability between models, feature importance results were summarized across all four approaches--decision tree, SVM, ensemble, and k-NN--using both built-in importance metrics and permutation-based methods. As shown in Figures 6-9, one feature--_NumericImpactRespons_--consistently dominated all models in predictive strength, followed by _NumericConflictRespons_ and, in some models, _FamilySmoking_ and _Age_.