## 3 Methodology
### Applied Tools and Techniques
#### 3.2.3 Quick, Unbiased, Efficient, Statistical Tree--QUEST  
The QUEST algorithm, short for quick, unbiased, efficient, statistical tree, is a classification tree induction method designed to provide more reliable and statistically sound decision trees. It addresses some limitations found in earlier tree algorithms, particularly the tendency of certain methods to favor variables with many potential split points. QUEST aims to produce smaller, more interpretable trees while maintaining efficiency and accuracy. The algorithm uses binary splits and a two-step procedure for selecting the best splitting variable and the best split point. First, it chooses the variable to split on by using significance tests that help avoid bias toward variables with multiple categories or a wide range of values. It evaluates candidate variables based on statistical tests of association (for categorical predictors) or correlation (for continuous predictors) with the target variable. Variables that show stronger evidence of a relationship with the outcome are considered for the next phase, while those that do not are excluded. After identifying a candidate variable, QUEST determines the exact split point differently for categorical and continuous predictors. For a categorical variable, it uses statistical procedures to find the grouping of categories that best separates classes. For a continuous variable, it often uses a linear discriminant analysis-based approach to identify a split that effectively divides the data into two groups that differ in their class distributions. This approach helps reduce selection bias and leads to splits that reflect the true underlying structure in the data, rather than being driven by the sheer number of possible cut points. The QUEST algorithm implements several additional features to support reliable and interpretable trees and includes methods to handle missing values, often by using surrogate splits or imputation-like strategies. Pruning procedures are applied to avoid overfitting and to produce trees that do not grow unnecessarily large. Furthermore, QUEST's computational efficiency makes it possible to handle moderate to large datasets without excessive computational cost. The QUEST (quick, unbiased, efficient statistical tree) algorithm was chosen due to several key advantages [132]:  
* Speed and accuracy: Its accuracy remains stable even at higher processing speeds, making it efficient without sacrificing precision. * Handling missing values: Unlike the CART (classification and regression tree) algorithm, which uses surrogate splits for missing data, QUEST applies imputations, offering a more robust approach. * Categorical predictors: It effectively handles categorical predictor variables with multiple categories, providing flexibility across different data types. * Lack of bias in variable selection: The algorithm avoids bias in variable selection prior to splitting, ensuring fairer and more accurate decision-making processes. * Data types: QUEST is applicable to nominal, ordinal, and continuous values. It uses ANOVA for ordinal and continuous values, and Pearson's \(\chi^{2}\) for categorical values, making it adaptable across various datasets. * Pruning via cross-validation: The use of cross-validation in pruning ensures that the resulting model is both generalizable and efficient. * Flexibility with split types: QUEST supports variate splits as well as combinations of linear splits, improving its versatility in different scenarios. * These features make QUEST a suitable algorithm for the given data structure and classification objectives. The QUEST algorithm begins by selecting the primary variable and subsequently determines the optimal split point. This approach helps the algorithm avoid any bias toward categorical variables. Additionally, quadratic discriminant analysis (QDA) is applied to consolidate multiple variable classes into two larger super-classes, followed by a binary split process.