The Akaike Information Criterion (AIC) is the most suitable method for this task. AIC is a statistical estimator used for model selection that evaluates the relative quality of statistical models for a given set of data. It provides a means for model selection by estimating the trade-off between the goodness of fit of the model and its complexity (the number of parameters). When comparing a set of candidate models, including various nonlinear ones, the model with the lowest AIC value is preferred. This makes it an ideal tool for evaluating and comparing the performance of different model structures.

B. Chi-squared test: This test primarily assesses the goodness of fit of a single model or tests for independence between variables, not for comparing multiple, potentially non-nested models.

C. MCC: The Matthews Correlation Coefficient is a performance metric specifically for binary classification models, not a general tool for comparing various types of models as requested.

D. ANOVA: Analysis of Variance is typically used to compare the means of different groups or to compare nested linear models, making it less suitable for diverse nonlinear model comparison.

1. Hastie

T.

Tibshirani

R.

& Friedman

J. (2009). The Elements of Statistical Learning: Data Mining

Inference

and Prediction (2nd ed.). Springer. In Chapter 7

Section 7.5

"The Akaike Information Criterion

" pages 233-234

the text explains that AIC is a widely used criterion for model selection that trades off model fit with the number of parameters

making it suitable for comparing different models.

2. Burnham

K. P.

& Anderson

D. R. (2002). Model selection and multimodel inference: A practical information-theoretic approach (2nd ed.). Springer-Verlag. Chapter 2

Section 2.2

"Akaike's Information Criterion

" pages 60-66

details the application of AIC for selecting the best model from a set of candidates

emphasizing its utility in comparing models that may not be nested.

3. Pennsylvania State University. (n.d.). STAT 501: Regression Methods

Lesson 11: Model Selection & Validation. Eberly College of Science. In Section 11.2

"AIC

BIC

and Mallows' Cp

" the courseware describes AIC as an estimate of prediction error used to select the best model from a set of candidates

where the model with the lowest AIC is chosen.