Hirotsugu Akaike developed a simple formula to compare statistical models. It can help to identify the model that explains the data best with the minimum number of free parameters.
Parameters:
(1) number of free parameters in the statistical model
(2) maximized value of the likelihood function (derived from the residual sum of squares, RSS)
Akaike information criterion = AIC =
= (2 * (number of free parameter)) - (2 * LN(maximized value of the likelihood function))
Interpretation:
• A model with a lower AIC is the "better" model.
• A low AIC can be seen with a small number of free parameters and high goodness of fit.
Rearranging a formula in Wikipedia the maximized value of the likelihood function can be approximated as:
maximized value of the likelihood function = L =
= (((residual sum of the squares) / (number of observations)) ^ ((-0.5) * (number of observations)))
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