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Deviance (statistics)
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. It plays an important role in exponential dispersion models and generalized linear models. Definition The unit deviance d(y,\mu) is a bivariate function that satisfies the following conditions: * d(y,y) = 0 * d(y,\mu) > 0 \quad\forall y \neq \mu The total deviance D(\mathbf,\hat) of a model with predictions \hat of the observation \mathbf is the sum of its unit deviances: D(\mathbf,\hat) = \sum_i d(y_i, \hat_i). The (total) deviance for a model ''M''0 with estimates \hat = E \hat_0/math>, based on a dataset ''y'', may be constructed by its likelihood as:McCullagh and Nelder (1989): page 17 D(y,\hat) = 2 \left(\log \left (y\mid\hat \theta_s)\right- \log \left p(y\mid\hat \theta_0) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistics
Statistics (from German: '' Statistik'', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of surveys and experiments.Dodge, Y. (2006) ''The Oxford Dictionary of Statistical Terms'', Oxford University Press. When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample to the population as a whole. An ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
