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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Poisson regression ： ウィキペディア英語版 Poisson regression In statistics, Poisson regression is a form of regression analysis used to model count data and contingency tables. Poisson regression assumes the response variable ''Y'' has a Poisson distribution, and assumes the logarithm of its expected value can be modeled by a linear combination of unknown parameters. A Poisson regression model is sometimes known as a log-linear model, especially when used to model contingency tables. Poisson regression models are generalized linear models with the logarithm as the (canonical) link function, and the Poisson distribution function as the assumed probability distribution of the response. ==Regression models== If $\backslash mathbf\; \backslash in\; \backslash mathbb^n$ is a vector of independent variables, then the model takes the form : $\backslash log\; (\backslash operatorname(Y\backslash mid\backslash mathbf))=\backslash alpha\; +\; \backslash mathbf\text{'}\; \backslash mathbf,$ where $\backslash alpha\; \backslash in\; \backslash mathbb$ and $\backslash mathbf\; \backslash in\; \backslash mathbb^n$. Sometimes this is written more compactly as :$\backslash log\; (\backslash operatorname(Y\backslash mid\backslash mathbf))=\backslash boldsymbol\text{'}\; \backslash mathbf,\backslash ,$ where x is now an (''n'' + 1)-dimensional vector consisting of ''n'' independent variables concatenated to a vector of ones. Here ''θ'' is simply ''α'' concatenated to β. Thus, when given a Poisson regression model ''θ'' and an input vector x, the predicted mean of the associated Poisson distribution is given by :$\backslash operatorname(Y\backslash mid\backslash mathbf)=e^\}.\backslash ,$ If ''Y''''i'' are independent observations with corresponding values x''i'' of the predictor variables, then ''θ'' can be estimated by maximum likelihood. The maximum-likelihood estimates lack a closed-form expression and must be found by numerical methods. The probability surface for maximum-likelihood Poisson regression is always concave, making Newton–Raphson or other gradient-based methods appropriate estimation techniques. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Poisson regression」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.