Difference between revisions of "Negative Binomial Regression"
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− | This is a regression [[Category::method]]. | + | This is a regression [[Category::method]] that is preferable in certain situations to Poisson Regression. |
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+ | Typically, Poisson regression is used to model counts of various kinds. However, Poisson random variables are expected to have a mean equal to its variance, which is often not the case in real-world situations. An example of this is the maximum diffusion length of Facebook fan pages in [[ Sun, E., I. Rosenn, C. A Marlow, and T. M Lento. Gesundheit! Modeling Contagion through Facebook News Feed. Proc. ICWSM 9. ]] | ||
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+ | Formally, a Poisson distribution can be characterized as: | ||
+ | :<math>f(k, \lambda)=\frac{\lambda^k e^{-\lambda}}{k!},\,\!</math> | ||
+ | |||
+ | Whereas the negative binomial distribution can be defined as: | ||
+ | : <math> | ||
+ | f(k) \equiv \Pr(X = k) = {k+r-1 \choose k} (1-p)^r p^k \quad\text{for }k = 0, 1, 2, \dots | ||
+ | </math> | ||
+ | |||
+ | Negative binomial regression is appropriate when variance >> mean. A variation of this method, called zero-inflation correction, allows one to control for excess zeros. Thus zero-inflation binomial regression allows one, in a single regression, to select variables that contribute to the true content in the response variable (“count model coefficients”) and also a (potentially | ||
+ | different) set of variables that contribute to the excess zeros in the response (“zero-inflation model coefficients”). |
Revision as of 21:07, 31 March 2011
This is a regression method that is preferable in certain situations to Poisson Regression.
Typically, Poisson regression is used to model counts of various kinds. However, Poisson random variables are expected to have a mean equal to its variance, which is often not the case in real-world situations. An example of this is the maximum diffusion length of Facebook fan pages in Sun, E., I. Rosenn, C. A Marlow, and T. M Lento. Gesundheit! Modeling Contagion through Facebook News Feed. Proc. ICWSM 9.
Formally, a Poisson distribution can be characterized as:
Whereas the negative binomial distribution can be defined as:
Negative binomial regression is appropriate when variance >> mean. A variation of this method, called zero-inflation correction, allows one to control for excess zeros. Thus zero-inflation binomial regression allows one, in a single regression, to select variables that contribute to the true content in the response variable (“count model coefficients”) and also a (potentially different) set of variables that contribute to the excess zeros in the response (“zero-inflation model coefficients”).