Psychonomic Bulletin & Review

, Volume 11, Issue 1, pp 192–196 | Cite as

AIC model selection using Akaike weights

  • Eric-Jan WagenmakersEmail author
  • Simon FarrellEmail author
Notes and Comment


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.


Model Selection Candidate Model Akaike Weight Prior Density Leibler Discrepancy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Aitchison, J., &Dunsmore, I. R. (1975).Statistical prediction analysis. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  2. Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In B. N. Petrov & F. Caski (Eds.),Proceedings of the Second International Symposium on Information Theory (pp. 267–281). Budapest: Akademiai Kiado.Google Scholar
  3. Akaike, H. (1974). A new look at the statistical model identification.IEEE Transactions on Automatic Control,19, 716–723.CrossRefGoogle Scholar
  4. Akaike, H. (1978). On the likelihood of a time series model.The Statistician,27, 217–235.CrossRefGoogle Scholar
  5. Akaike, H. (1979). A Bayesian extension of the minimum AIC procedure of autoregressive model fitting.Biometrika,66, 237–242.CrossRefGoogle Scholar
  6. Akaike, H. (1983). Information measures and model selection.Proceedings of the 44th Session of the International Statistical Institute,1, 277–291.Google Scholar
  7. Akaike, H. (1987). Factor analysis and AIC.Psychometrika,52, 317–332.CrossRefGoogle Scholar
  8. Boltzmann, L. (1877). Über die Beziehung zwischen dem zweiten Hauptsatze der mechanischen Wärmetheorie und der Wahrscheinlichkeitsrechnung respektive den Sätzen über das Wärmegleichgewicht.Wiener Berichte,76, 373–435.Google Scholar
  9. Bozdogan, H. (1987). Model selection and Akaike’s information criterion (AIC): The general theory and its analytical extensions.Psychometrika,52, 345–370.CrossRefGoogle Scholar
  10. Buckland, S. T., Burnham, K. P., &Augustin, N. H. (1997). Model selection: An integral part of inference.Biometrics,53, 603–618.CrossRefGoogle Scholar
  11. Burnham, K. P., &Anderson, D. R. (2001). Kullback-Leibler information as a basis for strong inference in ecological studies.Wildlife Research,28, 111–119.CrossRefGoogle Scholar
  12. Burnham, K. P., &Anderson, D. R. (2002).Model selection and multimodel inference: A practical information-theoretic approach. New York: Springer-Verlag.Google Scholar
  13. Efron, B. (1986). How biased is the apparent error rate of a prediction rule?Journal of the American Statistical Association,81, 416–470.Google Scholar
  14. Eid, M., &Langeheine, R. (1999). Latent class models.Psychological Method,4, 100–116.CrossRefGoogle Scholar
  15. Eliason, S. R. (1993).Maximum likelihood estimation: Logic and practice. Newbury Park, CA: Sage.Google Scholar
  16. Golan, A. (Ed.) (2002). Information and entropy econometrics [Special issue].Journal of Econometrics,107 (1–2).Google Scholar
  17. Hastie, T., Tibshirani, R., &Friedman, J. (2001).The elements of statistical learning: Data mining, inference, and prediction. New York: Springer-Verlag.Google Scholar
  18. Hurvich, C. M., &Tsai, C.-L. (1995). Model selection for extended quasi-likelihood models in small samples.Biometrics,51, 1077–1084.PubMedCrossRefGoogle Scholar
  19. Jöreskog, K. G., &Sörbom, D. (1996).LISREL 8: User’s reference guide. Hillsdale, NJ: Erlbaum.Google Scholar
  20. Kass, R. E., &Raftery, A. E. (1995). Bayes factors.Journal of the American Statistical Association,90, 773–795.CrossRefGoogle Scholar
  21. Kullback, S., &Leibler, R. A. (1951). On information and sufficiency.Annals of Mathematical Statistics,22, 79–86.CrossRefGoogle Scholar
  22. Maddox, W. T., &Ashby, F. G. (1993). Comparing decision bound and exemplar models of categorization.Perception & Psychophysics,53, 49–70.CrossRefGoogle Scholar
  23. Maddox, W. T., &Bohil, C. J. (2001). Feedback effects on cost-benefit learning in perceptual categorization.Memory & Cognition,29, 598–615.CrossRefGoogle Scholar
  24. McQuarrie, A. D. R., &Tsai, C.-L. (1998).Regression and time series model selection. Singapore: World Scientific.CrossRefGoogle Scholar
  25. Myung, I. J., Forster, M. R., & Browne, M. W. (Eds.) (2000). Model selection [Special issue].Journal of Mathematical Psychology,44(1).Google Scholar
  26. Myung, I. J., &Pitt, M. A. (1997). Applying Occam’s razor in modeling cognition: A Bayesian approach.Psychonomic Bulletin & Review,4, 79–95.CrossRefGoogle Scholar
  27. Nosofsky, R. M. (1998). Selective attention and the formation of linear decision boundaries: Reply to Maddox and Ashby (1998).Journal of Experimental Psychology: Human Perception & Performance,24, 322–339.CrossRefGoogle Scholar
  28. Parzen, E., Tanabe, K., &Kitagawa, G. (Eds.) (1998).Selected papers of Hirotugu Akaike. New York: Springer-Verlag.Google Scholar
  29. Ploeger, A., van der Maas, H. L. J., &Hartelman, P. A. I. (2002). Stochastic catastrophe analysis of switches in the perception of apparent motion.Psychonomic Bulletin & Review,9, 26–42.CrossRefGoogle Scholar
  30. Raijmakers, M. E. J., Dolan, C. V., &Molenaar, P. C. M. (2001). Finite mixture distribution models of simple discrimination learning.Memory & Cognition,29, 659–677.CrossRefGoogle Scholar
  31. Royall, R. M. (1997).Statistical evidence: A likelihood paradigm. London: Chapman & Hall.Google Scholar
  32. Sakamoto, Y., Ishiguro, M., &Kitagawa, G. (1986).Akaike information criterion statistics. Dordrecht: Reidel.Google Scholar
  33. Schwarz, G. (1978). Estimating the dimension of a model.Annals of Statistics,6, 461–464.CrossRefGoogle Scholar
  34. Smith, P. L. (1998). Attention and luminance detection: A quantitative analysis.Journal of Experimental Psychology: Human Perception & Performance,24, 105–133.CrossRefGoogle Scholar
  35. Spiegelhalter, D. J., Best, N. G., Carlin, B. P., &van der Linde, A. (2002). Bayesian measures of model complexity and fit.Journal of the Royal Statistical Society: Series B,64, 1–34.CrossRefGoogle Scholar
  36. Sugiura, N. (1978). Further analysis of the data by Akaike’s information criterion and the finite corrections.Communications in Statistics, Theory & Methods,A7, 13–26.CrossRefGoogle Scholar
  37. Takane, Y., & Bozdogan, H. (Eds.) (1987). AIC model selection [Special issue].Psychometrika,52(3).Google Scholar
  38. Thomas, R. D. (2001). Perceptual interactions of facial dimensions in speeded classification and identification.Perception & Psychophysics,63, 625–650.CrossRefGoogle Scholar
  39. Wasserman, L. (2000). Bayesian model selection and model averaging.Journal of Mathematical Psychology,44, 92–107.PubMedCrossRefGoogle Scholar

Copyright information

© Psychonomic Society, Inc. 2004

Authors and Affiliations

  1. 1.Northwestern UniversityEvanston

Personalised recommendations