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| 一般化線形モデル（GLM）× | ポアソン回帰と負の二項回帰× | |
|---|---|---|
| 分野≠ | 統計学 | 計量経済学 |
| 系統 | Regression model | Regression model |
| 提唱年≠ | 1972 | 1998 |
| 提唱者≠ | John A. Nelder & Robert W. M. Wedderburn | Cameron & Trivedi (textbook treatment); Hilbe (negative binomial) |
| 種類≠ | Regression framework | Generalized linear model for count data |
| 原典≠ | Nelder, J. A., & Wedderburn, R. W. M. (1972). Generalized linear models. Journal of the Royal Statistical Society: Series A (General), 135(3), 370–384. DOI ↗ | Cameron, A. C. & Trivedi, P. K. (1998). Regression Analysis of Count Data. Cambridge University Press. DOI ↗ |
| 別名 | GLM, generalized regression, exponential family regression, link-function model | count regression, log-linear count model, negative binomial regression, Poisson / Negatif Binom Regresyon |
| 関連≠ | 6 | 4 |
| 概要≠ | The Generalized Linear Model is a unified regression framework that extends ordinary linear regression to outcomes from the exponential family — including binary, count, proportion, and continuous positive outcomes. A link function connects the linear predictor to the mean of the response, enabling principled modelling beyond the Gaussian case. | Poisson regression is a generalized linear model for count outcomes — events tallied as non-negative integers such as hospital admissions, accidents, or article counts. It models the log of the expected count as a linear function of the predictors, and is developed in the standard count-data treatment of Cameron and Trivedi (1998); when the counts are over-dispersed, the closely related negative binomial model (Hilbe, 2011) is preferred. |
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