In GLM selection, which statement is accurate?

In generalized linear model (GLM) selection, the statement that BIC generally applies higher penalties for more parameters than AIC is accurate. The Bayesian Information Criterion (BIC) and the Akaike Information Criterion (AIC) are both used to compare models, but they differ in how they penalize complexity (the number of parameters).

BIC includes a penalty term that is proportional to the logarithm of the sample size, which tends to be larger than the linear penalty incorporated in AIC as the sample size increases. This means that as models become more complex (adding additional parameters), BIC imposes a stronger penalty than AIC, making it more conservative in terms of selecting models with many parameters. This characteristic of BIC makes it more suitable for scenarios where the aim is to avoid overfitting.

In contrast, while AIC also penalizes model complexity, its penalty is not as severe as that of BIC, which may lead to selecting more complex models when the sample size is large. Therefore, BIC is generally preferred when a strong preference for simpler models is desired, especially in larger datasets.

This understanding is crucial in model selection as it allows practitioners to make informed decisions based on the trade-offs between model fit and complexity