AIC model selection using Akaike weights

The Akaike information criterion (AIC; Akaike, 1973) is a popular method for comparing the adequacy of multiple, possibly nonnested models. Current practice in cognitive psychology is to accept a single model on the basis of only the “raw” AIC values, making it difficult to unambiguously interpret the observed AIC differences in terms of a continuous measure such as probability. Here we demonstrate that AIC values can be easily transformed to so-called Akaike weights (e.g., Akaike, 1978, 1979; Bozdogan, 1987; Burnham & Anderson, 2002), which can be directly interpreted as conditional probabilities for each model. We show by example how these Akaike weights can greatly facilitate the interpretation of the results of AIC model comparison procedures.

[1]  R. A. Leibler,et al.  On Information and Sufficiency , 1951 .

[2]  H. Akaike,et al.  Information Theory and an Extension of the Maximum Likelihood Principle , 1973 .

[3]  H. Akaike.  A new look at the statistical model identification , 1974 .

[4]  N. Sugiura.  Further analysts of the data by akaike' s information criterion and the finite corrections , 1978 .

[5]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[6]  Hirotugu Akaike,et al.  On the Likelihood of a Time Series Model , 1978 .

[7]  H. Akaike.  A Bayesian extension of the minimum AIC procedure of autoregressive model fitting , 1979 .

[8]  J. Aitchison,et al.  Statistical Prediction Analysis , 1975 .

[9]  B. Efron.  How Biased is the Apparent Error Rate of a Prediction Rule , 1986 .

[10]  H. Bozdogan.  Model selection and Akaike's Information Criterion (AIC): The general theory and its analytical extensions , 1987 .

[11]  H. Akaike.  Factor analysis and AIC , 1987 .

[12]  G. Kitagawa,et al.  Akaike Information Criterion Statistics , 1988 .

[13]  G. Kitagawa,et al.  Akaike Information Criterion Statistics , 1988 .

[14]  Karl G. Jöreskog,et al.  Lisrel 8: User's Reference Guide , 1997 .

[15]  W T Maddox,et al.  Comparing decision bound and exemplar models of categorization , 1993, Perception & psychophysics.

[16]  Scott R. Eliason.  Maximum likelihood estimation: Logic and practice. , 1994 .

[17]  C. Clogg.  Latent Class Models , 1995 .

[18]  Clifford M. Hurvich,et al.  Model selection for extended quasi-likelihood models in small samples. , 1995, Biometrics.

[19]  R. Nosofsky,et al.  Selective attention and the formation of linear decision boundaries. , 1996, Journal of experimental psychology. Human perception and performance.

[20]  L. Wasserman,et al.  Computing Bayes Factors by Combining Simulation and Asymptotic Approximations , 1997 .

[21]  K. Burnham,et al.  Model selection: An integral part of inference , 1997 .

[22]  I. J. Myung,et al.  Applying Occam’s razor in modeling cognition: A Bayesian approach , 1997 .

[23]  R. Royall.  Statistical Evidence: A Likelihood Paradigm , 1997 .

[24]  Robert M. Nosofsky,et al.  Selective attention and the formation of linear decision boundaries: Reply to Maddox and Ashby (1998). , 1998 .

[25]  Philip L. Smith.  Attention and luminance detection : A quantitative analysis , 1998 .

[26]  A. McQuarrie,et al.  Regression and Time Series Model Selection , 1998 .

[27]  Genshiro Kitagawa,et al.  Selected papers of Hirotugu Akaike , 1998 .

[28]  M. Eid,et al.  The measurement of consistency and occasion specificity with latent class models: A new model and its application to the measurement of affect , 1999 .

[29]  Wasserman,et al.  Bayesian Model Selection and Model Averaging. , 2000, Journal of mathematical psychology.

[30]  I. J. Myung,et al.  GUEST EDITORS' INTRODUCTION: Special Issue on Model Selection , 2000 .

[31]  R D Thomas,et al.  Perceptual interactions of facial dimensions in speeded classification and identification , 2001, Perception & psychophysics.

[32]  David R. Anderson,et al.  Kullback-Leibler information as a basis for strong inference in ecological studies , 2001 .

[33]  P C Molenaar,et al.  Finite mixture distribution models of simple discrimination learning , 2001, Memory & cognition.

[34]  Corey J. Bohil,et al.  Feedback effects on cost-benefit learning in perceptual categorization , 2001, Memory & cognition.

[35]  Aki Vehtari.  Discussion to "Bayesian measures of model complexity and fit" by Spiegelhalter, D.J., Best, N.G., Carlin, B.P., and van der Linde, A. , 2002 .

[36]  Amos Golan,et al.  Information and Entropy Econometrics—Editor's View , 2002 .

[37]  Annemie Ploeger,et al.  Stochastic catastrophe analysis of switches in the perception of apparent motion , 2002, Psychonomic bulletin & review.

[38]  A. Davison,et al.  Report of the Editors—2001 , 2002 .

[39]  Bradley P. Carlin,et al.  Bayesian measures of model complexity and fit , 2002 .

[40]  David R. Anderson,et al.  Model selection and multimodel inference : a practical information-theoretic approach , 2003 .

[41]  D. Ruppert.  The Elements of Statistical Learning: Data Mining, Inference, and Prediction , 2004 .