deviance

A measure for judging the extent to which a model explains the variation in a set of data when the parameter estimation is carried out using the method of maximum likelihood. The deviance, D, is given by

, where L_c is the likelihood of the current model, and L_s is the likelihood of the saturated model. The deviance has an approximate chi-squared distribution; the number of degrees of freedom is given by the difference in the numbers of parameters in the two models.

A summary of how well a model fits the data is provided by McFadden's R² (which is also known as the likelihood ratio index) defined by


, where L₀ is the likelihood corresponding to the model that describes the response variable as being a constant unaffected by any explanatory variables.

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A Dictionary of Statistics. Second edition revised. Copyright © Oxford University Press, 2008. All rights reserved.

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