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 Lc is the likelihood of the current model, and Ls 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.
Subjects: Public Health and Epidemiology — Probability and Statistics.