Chi-Squared logworth, Entropy, and Gini evaluate split worth for which type of variables?

Chi-Squared logworth, Entropy, and Gini are all metrics used to evaluate split worth in decision trees and other classification models. They are specifically designed for categorical variables.

When examining the behavior of these metrics, each one helps determine the effectiveness of a categorical predictor in separating the classes of the target variable.

Chi-Squared logworth quantifies how much the observed distribution of counts differs from the expected distribution under the null hypothesis of independence, making it particularly suitable for categorical data.

Entropy measures the impurity or disorder within a set of classes, with a lower entropy value indicating a more homogeneous split, again applicable to categories of data.

Gini is another measure of impurity, specifically focusing on the likelihood of an incorrect classification of a new instance if it was randomly labeled based on the distribution of labels in the subset. This is effective in assessing splits based on categorical variables.

Thus, because all these measures reflect the presence and relationships of categories, they are ideal for evaluating split worth in datasets where the variables are categorical.