手法を比較

	ベータ回帰	ガンマ回帰 (GLM)	分位点回帰
分野	統計学	統計学	計量経済学
系統	Regression model	Regression model	Regression model
提唱年	2004	1989	1978
提唱者	Ferrari & Cribari-Neto	McCullagh & Nelder (GLM framework)	Koenker & Bassett
種類	Generalized linear model (beta distribution)	Generalized linear model	Conditional quantile regression
原典	Ferrari, S. L. P. & Cribari-Neto, F. (2004). Beta Regression for Modelling Rates and Proportions. Journal of Applied Statistics, 31(7), 799–815.	McCullagh, P. & Nelder, J. A. (1989). Generalized Linear Models (2nd ed.). Chapman and Hall.	Koenker, R. & Bassett, G., Jr. (1978). Regression Quantiles. Econometrica, 46(1), 33-50.
別名	beta regression model, proportion regression, Beta Regresyonu	gamma GLM, gamma generalized linear model, Gamma Regresyonu (GLM)	conditional quantile regression, regression quantiles, Kantil Regresyon
関連	4	4	5
概要	Beta regression is a generalized linear model introduced by Ferrari and Cribari-Neto (2004) for outcomes that are rates or proportions confined to the open interval (0,1). It models the mean of a beta-distributed response through a link function, making it the natural choice for fractions, probability scores, and proportion indices.	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.	Quantile regression models conditional quantiles of an outcome - the median, the 25th or 75th percentile, and so on - rather than the conditional mean that OLS targets. Introduced by Koenker and Bassett in 1978, it reveals how predictors act across the whole distribution, including its tails.