tag:blogger.com,1999:blog-12133335.post8701748316926597651..comments2014-03-24T17:13:56.808-04:00Comments on Walk Like a Sabermetrician: On Run Distributions, pt. 2: Negative Binomialphttp://www.blogger.com/profile/18057215403741682609noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-12133335.post-86546564878784347802012-06-17T21:56:31.947-04:002012-06-17T21:56:31.947-04:00The negative binomial distribution gets in statist...The negative binomial distribution gets in statistical in negative binomial regression. It's a type of generalized linear model for count data where you have y=exp(mx + b). In NB regression the variance is assumed to NB distributed. Originally this kind of model would have been estimated with a normal distribution. The problem with the normal distribution is that the variance is assumed constant. In count data, large predicted values are expected to have larger variances. Poisson regression was a big advance for count data because it allowed larger predicted values to have larger variances. With a Poisson distribution, the variance is equal to the mean. In many data sets the variance is greater than the mean (very rarely it's smaller). Variance that is much larger than the mean is called overdispersion and this is where NB regression comes in. NB regression allows the variance to grow quadratically. There are other variance models, including quasi-Poisson which let's the variance increase linearly with the predicted value. <br />The reason the variance is so important, is that if you get it wrong, then the standard errors of the coefficients, f values, t values, and chi-squares can all be wrong. <br /><br />AlanAnonymousnoreply@blogger.com