Which GLM selection consideration is valid when comparing BIC and AIC?

The correct choice highlights a key difference between Bayesian Information Criterion (BIC) and Akaike Information Criterion (AIC) in terms of how they penalize complex models as the sample size increases. BIC places a heavier penalty on the number of parameters, particularly when the sample size exceeds a threshold such as 1,000 observations. This characteristic means that as more data becomes available, BIC is more likely to favor simpler models, discouraging overfitting by placing greater importance on the number of parameters relative to the data size.

AIC, while also penalizing for the number of parameters, does so less severely in comparison, which can lead it to at times prefer more complex models. This fundamental difference in penalty scales helps investigators decide between models based on their parameters when working with larger datasets.

This understanding is crucial for model selection in statistical modeling, as using BIC can often lead to a more parsimonious model in cases with a substantial number of observations. In contrast, the other options either misstate the relationship between model fit and penalties or fail to accurately portray how AIC and BIC differ in their penalty approaches.