手法を比較

	ガンマ回帰 (GLM)	負の二項回帰	ポアソン回帰と負の二項回帰
分野	統計学	計量経済学	計量経済学
系統	Regression model	Regression model	Regression model
提唱年	1989	2011	1998
提唱者	McCullagh & Nelder (GLM framework)	Hilbe (textbook treatment); generalized linear model framework	Cameron & Trivedi (textbook treatment); Hilbe (negative binomial)
種類	Generalized linear model	Generalized linear model for count data	Generalized linear model for count data
原典	McCullagh, P. & Nelder, J. A. (1989). Generalized Linear Models (2nd ed.). Chapman and Hall.	Hilbe, J. M. (2011). Negative Binomial Regression (2nd ed.). Cambridge University Press.	Cameron, A. C. & Trivedi, P. K. (1998). Regression Analysis of Count Data. Cambridge University Press.
別名	gamma GLM, gamma generalized linear model, Gamma Regresyonu (GLM)	NB regression, NB2 regression, negatif binom regresyonu	count regression, log-linear count model, negative binomial regression, Poisson / Negatif Binom Regresyon
関連	4	4	4
概要	Gamma regression is a generalized linear model that uses the gamma distribution to model a positive, right-skewed continuous outcome. Developed within the GLM framework of McCullagh and Nelder (1989), it is an alternative to ordinary linear regression for variables such as health-care costs, durations, and income.	Negative Binomial Regression is a generalized linear model for count outcomes that extends Poisson regression to handle overdispersion, where the variance of the counts exceeds their mean. Developed in the GLM tradition and treated in depth by Hilbe (2011), it adds a dispersion parameter so that inference stays valid when Poisson would understate the spread of the data.	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.