Markon Kristian E, Krueger Robert F
Department of Psychology, University of Minnesota, Elliot Hall, 75 East River Road, Minneapolis, MN 55455, USA.
Behav Genet. 2004 Nov;34(6):593-610. doi: 10.1007/s10519-004-5587-0.
Information theory provides an attractive basis for statistical inference and model selection. However, little is known about the relative performance of different information-theoretic criteria in covariance structure modeling, especially in behavioral genetic contexts. To explore these issues, information-theoretic fit criteria were compared with regard to their ability to discriminate between multivariate behavioral genetic models under various model, distribution, and sample size conditions. Results indicate that performance depends on sample size, model complexity, and distributional specification. The Bayesian Information Criterion (BIC) is more robust to distributional misspecification than Akaike's Information Criterion (AIC) under certain conditions, and outperforms AIC in larger samples and when comparing more complex models. An approximation to the Minimum Description Length (MDL; Rissanen, J. (1996). IEEE Transactions on Information Theory 42:40-47, Rissanen, J. (2001). IEEE Transactions on Information Theory 47:1712-1717) criterion, involving the empirical Fisher information matrix, exhibits variable patterns of performance due to the complexity of estimating Fisher information matrices. Results indicate that a relatively new information-theoretic criterion, Draper's Information Criterion (DIC; Draper, 1995), which shares features of the Bayesian and MDL criteria, performs similarly to or better than BIC. Results emphasize the importance of further research into theory and computation of information-theoretic criteria.
信息论为统计推断和模型选择提供了一个有吸引力的基础。然而，对于不同信息论标准在协方差结构建模中的相对性能，尤其是在行为遗传学背景下，人们了解甚少。为了探讨这些问题，我们比较了信息论拟合标准在各种模型、分布和样本量条件下区分多元行为遗传模型的能力。结果表明，性能取决于样本量、模型复杂性和分布规范。在某些条件下，贝叶斯信息准则（BIC）比赤池信息准则（AIC）对分布错误指定更具鲁棒性，并且在较大样本中以及比较更复杂模型时优于AIC。一种涉及经验Fisher信息矩阵的最小描述长度（MDL；Rissanen，J.（1996）。《IEEE信息论汇刊》42：40 - 47，Rissanen，J.（2001）。《IEEE信息论汇刊》47：1712 - 1717）准则的近似，由于估计Fisher信息矩阵的复杂性，表现出可变的性能模式。结果表明，一种相对较新的信息论标准，即德雷珀信息准则（DIC；Draper，1995），它兼具贝叶斯和MDL准则的特征，其性能与BIC相当或优于BIC。结果强调了进一步研究信息论标准的理论和计算的重要性。
