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Investigating the performance of AIC in selecting phylogenetic models

Author

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  • Jhwueng Dwueng-Chwuan

    (Department of Statistics, Feng-Chia University, Taichung, Taiwan 40724, R.O.C.)

  • Huzurbazar Snehalata

    (Statistical and Applied Mathematical Sciences Institute, Research Triangle Park, NC 27709, USA Department of Statistics, University of Wyoming, Laramie, WY 82071, USA Department of Statistics, North Carolina State University, Raleigh, NC 27695, USA)

  • O’Meara Brian C.

    (Department of Ecology and Evolutionary Biology, University of Tennessee, Knoxville, TN 37996, USA)

  • Liu Liang

    (Department of Statistics and Institute of Bioinformatics, University of Georgia, 101 Cedar Street, Athens, GA 30606 USA)

Abstract

The popular likelihood-based model selection criterion, Akaike’s Information Criterion (AIC), is a breakthrough mathematical result derived from information theory. AIC is an approximation to Kullback-Leibler (KL) divergence with the derivation relying on the assumption that the likelihood function has finite second derivatives. However, for phylogenetic estimation, given that tree space is discrete with respect to tree topology, the assumption of a continuous likelihood function with finite second derivatives is violated. In this paper, we investigate the relationship between the expected log likelihood of a candidate model, and the expected KL divergence in the context of phylogenetic tree estimation. We find that given the tree topology, AIC is an unbiased estimator of the expected KL divergence. However, when the tree topology is unknown, AIC tends to underestimate the expected KL divergence for phylogenetic models. Simulation results suggest that the degree of underestimation varies across phylogenetic models so that even for large sample sizes, the bias of AIC can result in selecting a wrong model. As the choice of phylogenetic models is essential for statistical phylogenetic inference, it is important to improve the accuracy of model selection criteria in the context of phylogenetics.

Suggested Citation

  • Jhwueng Dwueng-Chwuan & Huzurbazar Snehalata & O’Meara Brian C. & Liu Liang, 2014. "Investigating the performance of AIC in selecting phylogenetic models," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 13(4), pages 459-475, August.
    • Handle: RePEc:bpj:sagmbi:v:13:y:2014:i:4:p:17:n:5
    DOI: 10.1515/sagmb-2013-0048
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    References listed on IDEAS

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    1. Makio Ishiguro & Yosiyuki Sakamoto & Genshiro Kitagawa, 1997. "Bootstrapping Log Likelihood and EIC, an Extension of AIC," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(3), pages 411-434, September.
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