New g%AIC, g%AICc, g%BIC, and Power Divergence Fit Statistics Expose Mating between Modern Humans, Neanderthals and other Archaics
Peter J. Waddell, Xi Tan
The purpose of this article is to look at how information criteria, such as AIC and BIC, relate to the g%SD fit criterion derived in Waddell et al. (2007, 2010a). The g%SD criterion measures the fit of data to model based on a normalized weighted root mean square percentage deviation between the observed data and model estimates of the data, with g%SD = 0 being a perfectly fitting model. However, this criterion may not be adjusting for the number of parameters in the model comprehensively. Thus, its relationship to more traditional measures for maximizing useful information in a model, including AIC and BIC, are examined. This results in an extended set of fit criteria including g%AIC and g%BIC. Further, a broader range of asymptotically most powerful fit criteria of the power divergence family, which includes maximum likelihood (or minimum G^2) and minimum X^2 modeling as special cases, are used to replace the sum of squares fit criterion within the g%SD criterion. Results are illustrated with a set of genetic distances looking particularly at a range of Jewish populations, plus a genomic data set that looks at how Neanderthals and Denisovans are related to each other and modern humans. Evidence that Homo erectus may have left a significant fraction of its genome within the Denisovan is shown to persist with the new modeling criteria.