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| Gamma-Regression (GLM)× | Logistische Regression× | Negative Binomial Regression× | |
|---|---|---|---|
| Fachgebiet≠ | Statistik | Forschungsstatistik | Ökonometrie |
| Familie≠ | Regression model | Process / pipeline | Regression model |
| Entstehungsjahr≠ | 1989 | 1958 | 2011 |
| Urheber≠ | McCullagh & Nelder (GLM framework) | David Roxbee Cox | Hilbe (textbook treatment); generalized linear model framework |
| Typ≠ | Generalized linear model | Method | Generalized linear model for count data |
| Wegweisende Quelle≠ | McCullagh, P. & Nelder, J. A. (1989). Generalized Linear Models (2nd ed.). Chapman and Hall. DOI ↗ | Cox, D. R. (1958). The regression analysis of binary sequences. Journal of the Royal Statistical Society, Series B, 20(2), 215–242. DOI ↗ | Hilbe, J. M. (2011). Negative Binomial Regression (2nd ed.). Cambridge University Press. DOI ↗ |
| Aliasnamen | gamma GLM, gamma generalized linear model, Gamma Regresyonu (GLM) | logit model, binomial logistic regression, LR | NB regression, NB2 regression, negatif binom regresyonu |
| Verwandt≠ | 4 | 3 | 4 |
| Zusammenfassung≠ | 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. | Logistic regression is a statistical method for modeling the probability of a binary outcome (disease present/absent, success/failure) as a function of continuous and categorical predictors. Developed by David Roxbee Cox (1958), it solves the problem of predicting categorical outcomes by applying a logistic transformation to constrain predictions to the [0,1] probability interval, enabling accurate risk stratification, diagnostic prediction, and causal inference in epidemiology, medicine, and social science. | 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. |
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