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What if two models have the same AIC?
Lower AIC scores are better, and AIC penalizes models that use more parameters. So if two models explain the same amount of variation, the one with fewer parameters will have a lower AIC score and will be the better-fit model.
What are model selection techniques?
Three common resampling model selection methods include:
- Random train/test splits.
- Cross-Validation (k-fold, LOOCV, etc.).
- Bootstrap.
What does AIC value mean?
The Akaike information criterion (AIC) is an estimator of prediction error and thereby relative quality of statistical models for a given set of data. Given a collection of models for the data, AIC estimates the quality of each model, relative to each of the other models. Thus, AIC provides a means for model selection.
Which is better BIC or AIC for model selection?
Compared to the BIC method (below), the AIC statistic penalizes complex models less, meaning that it may put more emphasis on model performance on the training dataset, and, in turn, select more complex models. We see that the penalty for AIC is less than for BIC.
How does the derivation of Bic relate to AIC?
Importantly, the derivation of BIC under the Bayesian probability framework means that if a selection of candidate models includes a true model for the dataset, then the probability that BIC will select the true model increases with the size of the training dataset. This cannot be said for the AIC score.
How is the AIC statistic defined for logistic regression?
The AIC statistic is defined for logistic regression as follows (taken from “ The Elements of Statistical Learning “): Where N is the number of examples in the training dataset, LL is the log-likelihood of the model on the training dataset, and k is the number of parameters in the model.
What is the Akaike information criterion in AIC?
The Akaike Information Criterion, or AIC for short, is a method for scoring and selecting a model. It is named for the developer of the method, Hirotugu Akaike, and may be shown to have a basis in information theory and frequentist-based inference.