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http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6777506PMC
http://dx.doi.org/10.1093/af/vfz018DOI Listing

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The field of phylogenetics has burgeoned into a great diversity of statistical models, providing researchers with a vast amount of analytical tools for investigating the evolutionary theory. This abundance of theoretical work has the merit that many different aspects of evolution can be investigated using various types of data. However, empiricists may sometimes struggle to find the right model for their needs amid such variety.

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A method for comparing the fits of two non-nested models, based on a suggestion of Davidson and MacKinnon (1981), is developed in the context of linear and nonlinear regression with normal errors. Each model is regarded as a special case of an artificial "supermodel" and is obtained by restricting the value of a mixing parameter gamma to 0 or 1. To enable estimation and hypothesis testing for gamma, an approximate supermodel is used in which the fitted values from the individual models appear in place of the original parametrization.

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