Contents
What does higher AIC mean?
Since the AIC scales linearly with the number of parameters it is easily possible to get a high AIC score. The difference in the AIC scores for two different models can be interpreted as ‘extra information lost’ by using the worse model in comparison to the better model.
What does it mean to have a negative AIC?
The sign of the AIC tells you absolutely nothing about ill conditioned parameters or whether the model is suitable or not. For example, in a linear regression case, if the AIC is positive, you can make it negative (or vice versa) just by multiplying every observation on the dependent variable by the same number.
How does AIC provide a means for model selection?
Thus, AIC provides a means for model selection . AIC is founded on information theory. When a statistical model is used to represent the process that generated the data, the representation will almost never be exact; so some information will be lost by using the model to represent the process.
What’s the difference between AIC and AICC formula?
In comparison, the formula for AIC includes k but not k2. In other words, AIC is a first-order estimate (of the information loss), whereas AICc is a second-order estimate. Further discussion of the formula, with examples of other assumptions, is given by Burnham & Anderson (2002, ch.
How is the Akaike information criterion ( AIC ) used?
The Akaike information criterion (AIC) is an estimator for out-of-sample deviance 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.
How is AIC related to maximizing entropy in thermodynamics?
Indeed, minimizing AIC in a statistical model is effectively equivalent to maximizing entropy in a thermodynamic system; in other words, the information-theoretic approach in statistics is essentially applying the Second Law of Thermodynamics. As such, AIC has roots in the work of Ludwig Boltzmann on entropy.