EMMLi: a maximum likelihood approach to the analysis of modularity

Identification of phenotypic modules, semiautonomous sets of highly correlated traits, can be accomplished through exploratory (e.g., cluster analysis) or confirmatory approaches (e.g., RV coefficient analysis). Although statistically more robust, confirmatory approaches are generally unable to compare across different model structures. For example, RV coefficient analysis finds support for both two- and six-module models for the therian mammalian skull. Here, we present a maximum likelihood approach that takes into account model parameterization. We compare model log-likelihoods of trait correlation matrices using the finite-sample corrected Akaike Information Criterion, allowing for comparison of hypotheses across different model structures. Simulations varying model complexity and within- and between-module contrast demonstrate that this method correctly identifies model structure and parameters across a wide range of conditions. We further analyzed a dataset of 3-D data, consisting ...