How to calculate AIC in glmfit?

load hospital
modelspec = 'Smoker ~ Age*Weight*Sex - Age:Weight:Sex';
mdl = fitglm(hospital,modelspec,'Distribution','binomial')
mdl.ModelCriterion
ans = 
     AIC: 137.141380948166
    AICc: 138.358772252513
     BIC: 155.377572250082
    CAIC: 162.377572250082

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MURAT OKATAN 2021-4-26

Note, however, that fitglm computes the model criteria using mdl.NumCoefficients as the number of parameters estimated, and mdl.NumCoefficients does not account for the dispersion parameter of the Normal, Gamma and Inverse Gaussian distributions [1]. But, according to some studies [e.g. 2,3 and 4], the dispersion parameter needs to be counted among estimated parameters in computing the model criteria in GLMs that use those distributions.

[1] MATLAB Version: 9.7.0.1261785 (R2019b) Update 3.

[2] Clifford M. Hurvich, Chih-Ling Tsai, Regression and time series model selection in small samples, Biometrika, Volume 76, Issue 2, June 1989, Pages 297–307, https://doi.org/10.1093/biomet/76.2.297.

[3] Joseph E. Cavanaugh, Unifying the derivations for the Akaike and corrected Akaike information criteria, Statistics & Probability Letters, Volume 33, Issue 2, 1997, Pages 201-208, ISSN 0167-7152, https://doi.org/10.1016/S0167-7152(96)00128-9.

[4] Burnham, K.P. and Anderson, D.R. (2002) Model Selection and Inference: A Practical Information-Theoretic Approach. 2nd Edition, Springer-Verlag, New York. (e.g. p.95 Table 2.1)

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