If the nonlinear models are (for example) tree-based, neural networks, SVMs, or other machine-learning approaches, AIC generally is not the go-to metric—these models do not always provide a straightforward likelihood function to plug into AIC.
A Chi-squared test or ANOVA are generally geared toward hypothesis testing in more classical statistics contexts and are not typically used as a single performance metric across various kinds of models.
MCC (Matthews Correlation Coefficient) is a performance metric specifically for classification problems. It can be used to compare any classification model (linear or nonlinear) on how well it predicts binary labels, handling imbalanced data gracefully.
Hence, if you are comparing multiple classification models (and you want a single, robust performance measure), MCC is an excellent choice among the four listed.
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SuntzuLegacy
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