The Akaike’s Information Criteria Value Calculation

Dear Support,

In calculating the AIC value for measuring the goodness of fit of a distribution,

the formula is AIC = -2log(ML value) + 2(No. of parameters estimated), where log is natural log.

Now the clarifications I would like to seek are, 1. the value of Maximum Likelihood (ML) used in the calculation, is it the absolute value or not. Because Log of negative number does not exist. 2. also, the value of AIC calculated, is the absolute that is used for making inference?

Much thanks is advance. Silas

[Silas Adiko]

sorry, 2. should read like this:

 2. also, the value of AIC calculated, is it the absolute value that is used for making inference?

Thanks

[Chen Xing]

Hi, I had exactly the same question, then after thinking it through, I realised that the term 'log(ML value)' refers to the log-likelihood value itself, i.e. once you calculate the maximum likelihood value (which is frequently in logarithmic units for ease of calculation), you have already obtained the 'log(ML value)' and do not need to take the log of it again. Thus, you plug your negative 'log(ML value)' directly into the equation, multiplying it by -2 and adding 2DF.

Your original interpretation (which is also what I thought initially) was that the maximised value (which is usually already in log coordinates) was the 'ML value' and one had to calculate its log (again)- this is where the misunderstanding resides.

As for the second part of your question, from what I've read, AIC values can be negative or positive; there is no need to take the absolute of the AIC values- rather, just find the lowest value within the group of AIC values that are to be compared. According to Anderson's textbook, 'Model-Based Inference in the Life Sciences' (2008):

"As defined, AIC is strictly positive. However, during an analysis, it is common to omit mathematical terms that are constant across models and such shortcuts can result in negative values of AIC. Computing AIC from regression statistics often results in negative AIC values. This creates no problem, one just identifies the model with the smallest value of AIC and declares it is the model estimated to be the best. This fitted model is estimated to be “closest” to full reality and is a good approximation for the information in the data, relative to the other models considered."

Answer 1

[Youssef Khmou]

hi,

from what i know , the values calculated using the Aic or the Minimum Descriptive Length MDL are >0 , and the number of parameters corresponds to the minimum of the values, but without using the abs operator , for example to estimate the number of signals from the Cross correlation matrix we compute the sum and product of the eigenvalues and all the AIC values are >0, the Min corresponds to the value estimated. the AIC technique is sensitive to the noise contained in the data. try to verify the formula in your case ( real or complex numbers, forward backward averaged, real matrices, .... )