Which criterion is primarily used for model selection in statistical models?

The criterion used for model selection in statistical models often involves a combination of methods, and this question correctly identifies that multiple approaches are valid. AIC, BIC, and cross-validation error each provide different perspectives on model performance and complexity.

AIC focuses on the trade-off between the goodness of fit of the model and its complexity, penalizing models for having too many parameters. It is useful when trying to find an optimal model that balances fitting the data well without overfitting.

BIC is similar but imposes a stronger penalty for complexity compared to AIC, making it particularly effective in large sample settings. It tends to favor simpler models, which can help prevent overfitting in cases where the sample size is large.

Cross-validation is an empirical method that assesses how the results of a statistical analysis will generalize to an independent data set. It helps provide an estimate of a model's predictive performance and is particularly useful when the goal is to ensure the model performs well on unseen data.

Utilizing all three criteria allows practitioners to capitalize on their unique strengths, leading to more robust and reliable model selection processes. Together, they provide a more comprehensive understanding of model performance, allowing for informed decisions in the modeling process.