Area under the ROC Curve has the Most Consistent Evaluation for Binary Classification
This addresses the problem of reliable model evaluation and selection in binary classification for researchers and practitioners, though it is incremental as it builds on existing metric analysis.
The study investigated the consistency of 18 model evaluation metrics across 156 data scenarios with varying prevalence, finding that metrics less influenced by prevalence, such as Area Under the ROC Curve (AUC), offered more consistent evaluation and ranking of models, with AUC showing the smallest variance.
The proper use of model evaluation metrics is important for model evaluation and model selection in binary classification tasks. This study investigates how consistent different metrics are at evaluating models across data of different prevalence while the relationships between different variables and the sample size are kept constant. Analyzing 156 data scenarios, 18 model evaluation metrics and five commonly used machine learning models as well as a naive random guess model, I find that evaluation metrics that are less influenced by prevalence offer more consistent evaluation of individual models and more consistent ranking of a set of models. In particular, Area Under the ROC Curve (AUC) which takes all decision thresholds into account when evaluating models has the smallest variance in evaluating individual models and smallest variance in ranking of a set of models. A close threshold analysis using all possible thresholds for all metrics further supports the hypothesis that considering all decision thresholds helps reduce the variance in model evaluation with respect to prevalence change in data. The results have significant implications for model evaluation and model selection in binary classification tasks.