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| Beta-Regression× | Gamma-Regression (GLM)× | Methode der kleinsten Quadrate (OLS)× | |
|---|---|---|---|
| Fachgebiet≠ | Statistik | Statistik | Ökonometrie |
| Familie | Regression model | Regression model | Regression model |
| Entstehungsjahr≠ | 2004 | 1989 | 2019 |
| Urheber≠ | Ferrari & Cribari-Neto | McCullagh & Nelder (GLM framework) | Wooldridge (textbook treatment); classical least squares |
| Typ≠ | Generalized linear model (beta distribution) | Generalized linear model | Linear regression |
| Wegweisende Quelle≠ | Ferrari, S. L. P. & Cribari-Neto, F. (2004). Beta Regression for Modelling Rates and Proportions. Journal of Applied Statistics, 31(7), 799–815. DOI ↗ | McCullagh, P. & Nelder, J. A. (1989). Generalized Linear Models (2nd ed.). Chapman and Hall. DOI ↗ | Wooldridge, J. M. (2019). Introductory Econometrics: A Modern Approach (7th ed.). Cengage Learning. ISBN: 978-1337558860 |
| Aliasnamen≠ | 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 |
| Verwandt≠ | 4 | 4 | 5 |
| Zusammenfassung≠ | 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). |
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