What does the Hannan-Quinn criterion measure assess?

The Hannan-Quinn criterion is a statistical measure used primarily for model selection in the context of regression and similar analyses. It assesses the fit of a statistical model by taking into account both the goodness of fit, typically assessed through log likelihood results, and a penalty for model complexity. One of the core attributes of this criterion is that it focuses on the log likelihood of the model, which reflects how well the model explains the observed data relative to simpler models.

By incorporating log likelihood results, the Hannan-Quinn criterion provides a balance between how well the model runs (i.e., its fit to the data) and a caution against overfitting by penalizing the addition of excessive parameters. This makes it particularly useful when comparing models with different numbers of predictors. A lower Hannan-Quinn value indicates a better balance of fit and complexity, guiding analysts in selecting the most appropriate model.

The other choices do not capture the essence of what the Hannan-Quinn criterion addresses. For instance, while model fit related to sample size, parameter count, or mean absolute error are relevant concepts in statistical analysis, they do not align with the primary focus of the Hannan-Quinn criterion, which specifically integrates log likelihood into its assessment of