Final answer:
AIC and BIC will favor the simpler model because it is less likely to overfit, easier to interpret, and more robust to data variations. AIC is preferred for prediction, while BIC is better for identifying key variables in large datasets.
Step-by-step explanation:
When two models are approximately equally good in predicting or explaining a dataset, measures like the Aikaike's Information Criterion (AIC) and the Bayesian Information Criterion (BIC) will favor the simpler model. This preference is grounded in the principle of parsimony, which holds that the simplest model providing the strongest explanatory power is favored. Simpler models are often better for several reasons:
- Simpler models pose less risk of overfitting, meaning they are better at generalizing from the sample to the larger population.
- They are more easily interpreted, which is crucial in scientific understanding and communication.
- Simpler models are also more robust to small changes in the data, making them more reliable.
Both AIC and BIC include bias correction terms which inherently promote parsimony; AIC is typically preferred for prediction purposes, while BIC is recommended when it is important to identify the most important variables, especially with large datasets.