An indice used as an aid in choosingbetween competing statistical models. Formula-wise it is given as: -2Ln +2k or conversely 2k – 2Ln(L), where L isthe maximized log-likelihood and k the number of parameters or predictors inthe model (the likelihood function giving the probability of observing the data given aparticular set of model parameters, something that has not to be confused withthe probability of the model being true). Itis one of a number of fit indices, or more precisely information criteria indices, that can beused in structural equation modeling. The indice accounts for both the statistical goodness-of-fit and thenumber of parameters that have to be estimated in order to achieve a particulardegree of fit. It does so by imposing apenalty for increasing the number of parameters (in keeping with Ockham’srazor). Thus, 2k amounts to a ‘penalty’ for including extra predictors in themodel, while -2Ln ‘rewards’ the fit between the model and thedata. Lower values indicate the preferred model(i.e., the one with the fewest parameters and which at the same time providesan adequate fit to the data). As withmany such models, AIC requires a sample size of 200 in order for itto be considered reliable. At the core ofthe AIC is the Kullback-Leibler divergence, which can be considered as ameasure of the informational distance between two probabilitydistributions. Thus, the K-L distancebetween a real-world distribution and a model distribution indicates how muchinformation is lost by summarizing the data with that model. In recent years, there has been a debateabout the relative merits of AIC and Bayesian Information Criterion. The indice was originally devised by the Japanesestatistician Hirotugu Akaike(1927-2009) who based it on information theory and information entropy inparticular. He published it as a bookchapter. In essence, Akaike usedinformation theory as means of deriving a numerical equivalent of Ockham’srazor or canon of parsimony.
See Canon of parsimony, Ockham’s (or Occam’s) razor, Structural equation modeling