Model selection

Model selection is the process of choosing among candidate statistical or scientific models using evidence and explicit criteria. It balances explanatory fit against complexity, predictive performance, or other goals.

Akaike information criterion: A model-selection criterion that estimates relative information loss using fit and parameter count. It favors models expected to predict well while penalizing added parameters.
Statistical model: A mathematical description of how data could have been generated, including assumptions about randomness. Candidate statistical models are the objects compared during selection.
Model averaging: A method that combines predictions or inferences from multiple candidate models. It retains uncertainty across plausible models instead of selecting only one.
Stepwise regression: A regression procedure that adds or removes predictors through a sequence of local comparisons. It is a widely used, though often criticized, algorithmic approach to model selection.
Multiple comparisons problem: The increased risk of false discoveries when many statistical hypotheses are tested. Searching many candidate models can make the apparently best result overly optimistic.
Bayesian information criterion: A criterion for comparing statistical models that penalizes parameter count according to sample size. Its stronger large-sample complexity penalty can yield different choices than AIC.
Likelihood function: A function measuring how probable observed data are under different parameter values. Many selection criteria begin with a model’s likelihood of the observed data.
Hypothesis testing: A statistical framework for assessing evidence against a specified null hypothesis. Testing asks whether evidence challenges a hypothesis; selection ranks candidate models.
Generalized linear model: A model family relating a response’s expected value to predictors through a link function. Researchers select among link functions, predictors, and response distributions within this family.
Data dredging: Repeated exploration of data until an apparently notable pattern appears, without adequate adjustment. Unreported model searches undermine the evidential value of the selected result.

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