手法を比較

	ベータ回帰	ガンマ回帰 (GLM)	最小二乗法 (OLS) 回帰	分位点回帰
分野	統計学	統計学	計量経済学	計量経済学
系統	Regression model	Regression model	Regression model	Regression model
提唱年	2004	1989	2019	1978
提唱者	Ferrari & Cribari-Neto	McCullagh & Nelder (GLM framework)	Wooldridge (textbook treatment); classical least squares	Koenker & Bassett
種類	Generalized linear model (beta distribution)	Generalized linear model	Linear regression	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.	Wooldridge, J. M. (2019). Introductory Econometrics: A Modern Approach (7th ed.). Cengage Learning. ISBN: 978-1337558860	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)	ordinary least squares, classical linear regression, linear regression, en küçük kareler regresyonu	conditional quantile regression, regression quantiles, Kantil Regresyon
関連	4	4	5	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.	Ordinary Least Squares is the classical linear regression method that explains a continuous outcome as a linear combination of predictors. It estimates the coefficients by minimising the sum of squared residuals, and under the Gauss-Markov assumptions these estimates are the best linear unbiased estimator (BLUE).	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.