The effective sample size in Bayesian information criterion for level-specific fixed and random-effect selection in a two-level nested model

In this study, we derive the BIC's penalty term for level-specific fixed- and random-effect selection in a two-level nested design. In this new version of BIC, called BIC E 1 , this penalty term is decomposed into two parts if the random-effect variance-covariance matrix has full rank: (a) a term with the log of average sample size per cluster and (b) the total number of parameters times the log of the total number of clusters. Furthermore, we derive the new version of BIC, called BIC E 2 , in the presence of redundant random effects. We show that the derived formulae, BIC E 1 and BIC E 2 , adhere to empirical values via numerical demonstration and that BIC E ( E indicating either E 1 or E 2 ) is the best global selection criterion, as it performs at least as well as BIC with the total sample size and BIC with the number of clusters across various multi-level conditions through a simulation study. In addition, the use of BIC E 1 is illustrated with a textbook example dataset.PMID:38591555 | DOI:10.1111/bmsp.12327
Source: The British Journal of Mathematical and Statistical Psychology - Category: Statistics Authors: Source Type: research