Identification of phenotypic modules, semi-autonomous sets of highly-correlated traits, can be accomplished through exploratory (e.g., cluster analysis) or confirmatory approaches (e.g., RV coefficient analysis). While 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. Empirical analysis of a dataset of 61 3-D landmarks from macaque (Macaca fuscata) skulls, representing five age categories, tested 31 models, from no modularity to 2, 3, 6, and 8 modules. Our results clearly support a complex six-module model, with separate within- and inter-module correlations, across all ages, demonstrating that this complex pattern of integration in the macaque skull is highly conserved throughout postnatal ontogeny. Subsampling analyses further demonstrate that this method is robust to relatively low sample sizes.
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