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In statistics, deviance is a goodness-of-fit statistic for a statistical model; it is often used for statistical hypothesis testing. It is a generalization of the idea of using the sum of squares of residuals (SSR) in ordinary least squares to cases where model-fitting is achieved by maximum likelihood .
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The goodness of fit of a statistical model describes how well it fits a set of observations. Measures of goodness of fit typically summarize the discrepancy between observed values and the values expected under the model in question.
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Deviance (statistics), a quality of fit statistic for a model; Positive deviance, an approach to behavioral and social change; Sexual deviance (historical term) or paraphilia, recurring or intense sexual arousal to atypical things; Deviance or bid'ah, innovations and deviant acts or groups from orthodox Islamic law (Sharia)
The deviance information criterion (DIC) is a hierarchical modeling generalization of the Akaike information criterion (AIC). It is particularly useful in Bayesian model selection problems where the posterior distributions of the models have been obtained by Markov chain Monte Carlo (MCMC) simulation.
Absolute deviation in statistics is a metric that measures the overall difference between individual data points and a central value, typically the mean or median of a dataset. It is determined by taking the absolute value of the difference between each data point and the central value and then averaging these absolute differences. [ 4 ]
Deviance is analogous to the sum of squares calculations in linear regression [2] and is a measure of the lack of fit to the data in a logistic regression model. [35] When a "saturated" model is available (a model with a theoretically perfect fit), deviance is calculated by comparing a given model with the saturated model. [2]