In statistics, the focused information criterion (FIC) is a method for selecting the most appropriate model among a set of competitors for a given data set. Unlike most other model selection strategies, like the Akaike information criterion (AIC), the Bayesian information criterion (BIC) and the deviance information criterion (DIC), the FIC does not attempt to assess the overall fit of candidate models but focuses attention directly on the parameter of primary interest with the statistical analysis, say
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The concrete formulae and implementation for FIC depend firstly on the particular parameter of interest, the choice of which does not depend on mathematics but on the scientific and statistical context. Thus the FIC apparatus may be selecting one model as most appropriate for estimating a quantile of a distribution but preferring another model as best for estimating the mean value. Secondly, the FIC formulae depend on the specifics of the models used for the observed data and also on how precision is to be measured. The clearest case is where precision is taken to be mean squared error, say
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Associated with the use of the FIC for selecting a good model is the FIC plot, designed to give a clear and informative picture of all estimates, across all candidate models, and their merit. It displays estimates on the
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Generally speaking, complex models (with many parameters relative to sample size) tend to lead to estimators with small bias but high variance; more parsimonious models (with fewer parameters) typically yield estimators with larger bias but smaller variance. The FIC method balances the two desired data of having small bias and small variance in an optimal fashion. The main difficulty lies with the bias
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In situations where there is not a unique focus parameter, but rather a family of such, there are versions of average FIC (AFIC or wFIC) that find the best model in terms of suitably weighted performance measures, e.g. when searching for a regression model to perform particularly well in a portion of the covariate space.
It is also possible to keep several of the best models on board, ending the statistical analysis with a data-dicated weighted average of the estimators of the best FIC scores, typically giving highest weight to estimators associated with the best FIC scores. Such schemes of model averaging extend the direct FIC selection method.
The FIC methodology applies in particular to selection of variables in different forms of regression analysis, including the framework of generalised linear models and the semiparametric proportional hazards models (i.e. Cox regression).