Deviance (Statistics)

In statistics, deviance is a goodness-of-fit statistic for a statistical model, used often in hypothesis testing, that generalizes the idea of the residual sum of squares to maximum likelihood estimation. For a fitted model it is calculated as twice the difference between the log-likelihood of a saturated model that fits the data perfectly and the log-likelihood of the model under evaluation. Under Wilks' theorem, the difference in deviance between two nested models approximately follows a chi-squared distribution with degrees of freedom equal to the difference in the number of parameters, which is what allows deviance to be used for formal hypothesis tests comparing models. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/