A Coefficient of Determination for Generalized Linear Models.
The coefficient of determination, a.k.a. R, iswell-defined in linear regression models, and measures the proportion of variation in the dependent variable explained by the predictors included in themodel. To extend it for generalized linearmodels, we use the variance function to define the total var...
| Publicado en: | American Statistician Vol. 71; no. 4; pp. 310 - 317 |
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| Formato: | Artículo |
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Taylor & Francis Ltd
2017
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| Acceso en línea: | Ver este registro en EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=ssf&AN=127412315&site=ehost-live header: @attributes: shortDbName: ssf uiTerm: 127412315 longDbName: Social Sciences Full Text (H.W. Wilson) uiTag: AN controlInfo: bkinfo: jinfo: jid: 00031305 STT jtl: American Statistician issn: 00031305 maglogo: Y pubinfo: dt: 2017 vid: 71 iid: 4 pid: 377 pub: Taylor & Francis Ltd artinfo: ui: 127412315 10.1080/00031305.2016.1256839 ppf: 310 ppct: 7 formats: tig: atl: A Coefficient of Determination for Generalized Linear Models. aug: au: Zhang, Dabao affil: Department of Statistics, Purdue University, West Lafayette, IN su: Analysis of variance Linear statistical models Regression analysis Exponential families (Statistics) Distribution (Probability theory) Mathematical variables sug: subj: Analysis of variance Linear statistical models Regression analysis Exponential families (Statistics) Distribution (Probability theory) Mathematical variables keyword: Exponential family distribution Quasi-model R2 R2 Variance function Exponential family distribution Quasi-model R2 R2 Variance function ab: The coefficient of determination, a.k.a. R, iswell-defined in linear regression models, and measures the proportion of variation in the dependent variable explained by the predictors included in themodel. To extend it for generalized linearmodels, we use the variance function to define the total variation of the dependent variable, as well as the remaining variation of the dependent variable after modeling the predictive effects of the independent variables. Unlike other definitions that demand complete specification of the likelihood function, our definition of R only needs to know the mean and variance functions, so applicable to more general quasi-models. It is consistent with the classicalmeasure of uncertainty using variance, and reduces to the classical definition of the coefficient of determination when linear regression models are considered. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: N holdings: @attributes: islocal: N |
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