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Denote the AIC values of those models by AIC 1, AIC 2, AIC 3, ..., AIC R. Let AIC min be the minimum of those values. Then the quantity exp((AIC min − AIC i)/2) can be interpreted as being proportional to the probability that the ith model minimizes the (estimated) information loss. [6]
Both BIC and AIC attempt to resolve this problem by introducing a penalty term for the number of parameters in the model; the penalty term is larger in BIC than in AIC for sample sizes greater than 7. [1] The BIC was developed by Gideon E. Schwarz and published in a 1978 paper, [2] as a large-sample approximation to the Bayes factor.
In statistics, the Widely Applicable Information Criterion (WAIC), also known as Watanabe–Akaike information criterion, is the generalized version of the Akaike information criterion (AIC) onto singular statistical models. [1] It is used as measure how well will model predict data it wasn't trained on.
They also note that HQC, like BIC, but unlike AIC, is not an estimator of Kullback–Leibler divergence. Claeskens & Hjort (2008, ch. 4) note that HQC, like BIC, but unlike AIC, is not asymptotically efficient ; however, it misses the optimal estimation rate by a very small ln ( ln ( n ) ) {\displaystyle \ln(\ln(n))} factor.
R^2 values range from 0-1. If the AIC is better than the null model, it should be smaller. If the numerator is larger than the denominator, the R^2_{AIC} will be less than 1. This is saying that better models will generate a negative R^2_{AIC}. It would make sense if the model were: R^2_{AIC}= 1 - \frac{AIC_i}{AIC_0}
The version of BIC as described here is not compatible with the definition of AIC in wikipedia. There is a divisor n stated with BIC, but not AIC in the Wikipedia entries. It would save confusion if they were consistently defined! I would favour not dividing by n: i.e. BIC = -2log L + k ln(n) AIC = -2log L + 2k
RIT vs. American International matchup The Tigers and Yellow Jackets split their season series during a two-game stand at AIC in December. The hosts won the opener 3-2 in overtime, while RIT ...
The likelihood ratio test is not valid in this setting because the estimating equations are not necessarily likelihood equations. Model selection can be performed with the GEE equivalent of the Akaike Information Criterion (AIC), the quasi-likelihood under the independence model criterion (QIC). [8]