Calculating and Interpreting Information Criteria

This technical report discusses the calculation and interpretation of various information criteria, specifically the Bayesian Information Criterion (BIC), consistent Akaike’s Information Criterion (CAIC), and corrected Akaike’s Information Criterion (AICc). It outlines the methods used in Stata for calculating these criteria, emphasizing the importance of the number of observations (N) in model comparisons. The report explains that Stata defaults to using e(N) for N unless specified otherwise, and it provides examples illustrating the implications of using different definitions of N in model fitting. The document also addresses common pitfalls in comparing models using these criteria, particularly when likelihood functions are not conformable. It concludes with a discussion on the correct application of these information criteria in statistical modeling, referencing foundational literature on the subject.