Akaike Information Criterion

Ludden TM, Beal SL, Sheiner LB. Comparison of the Akaike Information Criterion, the Schwarz criterion and the F test as guides to model selection. /PAar-macokinet Biopharm 1994 22 431-45. 

Hurvich, C. and C. L. Tsai. A Corrected Akaike Information Criterion for Vector Autoregressive Model Selection. J Time Series Anal 14, 271-279 (1993). 

Confining their study to monofunctional molecules, Roberts et al. [38] compared seven different models for predicting human stratum corneum permeability coefficients. The performance of the models was assessed by the adjusted coefficient of determination r2dj and the Akaike Information Criterion (AIC) [39], Both r2dj and AIC allow for comparing models with different numbers of variables (degrees of freedom). Exclusion of polyfunctional molecules led to a comparatively small set of only 24 molecules. The previously reported... 

Repeat the input identification experiment with the model order MD = 2. Compare the linear regression residual errors for the two cases. Select the "best" model order on the basis of the Akaike Information Criterion (see Section 3.10.3 and ref. 27). ... 

The Akaike Information Criterion is used to select the model which minimises the AIC(0) function for a specified value of (j). In the original formulation of the above equation, Akaike used a value of (j) = 2 but an alternative selection criterion proposed by Leontaritis and Billings [Leontaritis and Billings, 1987] is based on a value of (j) = 4. 

In order to compare the performance of models containing different non-linear terms it is necessary to use a criterion which achieves a compromise between the overly simple model and the overly complex model. One such criterion is the Akaike Information Criterion, AIC(0) (see e.g. Akaike [Akaike, 1974]) given by ... 

The selection of the appropriate population pharmacokinetic base model was guided by the following criteria a significant reduction in the objective function value (p < 0.01,6.64 points) as assessed by the Likelihood Ratio Test the Akaike Information Criterion (AIC) a decrease in the residual error a decrease in the standard error of the model parameters randomness of the distribution of individual weighted residuals versus the predicted concentration and versus time post start of cetuximab administration randomness of the distribution of the observed concentration versus individual predicted concentration values around the line of identity in a respective plot. 

If the highest substrate concentration shows a linear increase in velocity, the last component of the rate equation should be V/K, i.e., vn = (V/K)n. Inclusion of additional rate components should be justified by statistical methods, such as comparing F values for the regression analyses or the minimum Akaike information criterion estimation (MAICE) (12,13). 

In order to choose the model that predicts most accurately for the test data, we need a new rule or a new information criterion. The usual criteria, the Akaike Information Criterion (AIC), the Bayesian Information Criterion (BIC), Leave One Out (LOO or Qsquared), and so on, are all insufficient for our needs. This motivated Kerry Bemis to propose a new measure which he called predictive R2 or pR2 (described below). 

Figures 11 and 12 illustrate the performance of the pR2 compared with several of the currently popular criteria on a specific data set resulting from one of the drug hunting projects at Eli Lilly. This data set has IC50 values for 1289 molecules. There were 2317 descriptors (or covariates) and a multiple linear regression model was used with forward variable selection the linear model was trained on half the data (selected at random) and evaluated on the other (hold-out) half. The root mean squared error of prediction (RMSE) for the test hold-out set is minimized when the model has 21 parameters. Figure 11 shows the model size chosen by several criteria applied to the training set in a forward selection for example, the pR2 chose 22 descriptors, the Bayesian Information Criterion chose 49, Leave One Out cross-validation chose 308, the adjusted R2 chose 435, and the Akaike Information Criterion chose 512 descriptors in the model. Although the pR2 criterion selected considerably fewer descriptors than the other methods, it had the best prediction performance. Also, only pR2 and BIC had better prediction on the test data set than the null model.

Y. Sakamoto, M. Ishiguso, and G. Kitigawa, Akaike Information Criterion Statistics (Boston, MA D. Reidel, 1986). 

Akaike Information Criterion, AICp. A model selection criterion for choosing between models with different parameters and defined as ... 

With GAM the data (covariate and individual Bayesian PM parameter estimates) would be subjected to a stepwise (single-term addition/deletion) modeling procedure. Each covariate is allowed to enter the model in any of several functional representations. The Akaike information criterion (AIC) is used as the model selection criterion (22). At each step, the model is changed by addition or deletion of a covariate that results in the largest decrease in the AIC. The search is stopped when the AIC reached a minimum value. 

The addition of a 3-compartment model dropped the Akaike Information Criterion (AIC) from 5.788 to 5.134. Although the model fit under the 3-compartment model was better than the 2-compartment model, a trend in the weighted residuals versus time plot was still apparent indicating that the model tended to underpredict (from 1 to 12 h), then overpredict (from 20 to... 

When the uncertainty in the parameter values becomes too large, the analyst should consider reducing the model. The correlation matrix between parameters can be useful in selecting the parameters that can be removed to make the model smaller. There are statistical criteria that can be used to select the better model. These include the Akaike Information Criterion (AIC) value and the F-test. The AIC value is calculated using the WSS, the number of parameters in the model, and the number of data points. The model with the lower AIC values is usually selected as the better model. The statistical F-test involves the calculation of an F value from the WSS and degrees of freedom from two analyses. The calculated F value is compared with the tabled values and a decision can be made whether the more complex model provides a significant improvement in the fit to the data. The analyst using a combination of subjective and objective criteria can make an educated decision about the best model. 

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