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StatsToDo : Negative Binomial Regression Explained

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Introduction Example R Code Example Explained
This page provides explanations and example R codes for Negative Binomial Regression, which is one of the algorithms based on the Generalized Linear Models, but the dependent variable is a discrete positive integer with a negative binomial.

Negative Binomial distribution is the reverse of the binomial distribution. Instead of stating a proportion, the statement is the number of one group is counted before a stated number of the other group is found. In Negative Binomial Regression, the algorithm is based on the number of one group found (failure, negative, 0, false) before finding each case of the other group (success, positive, 1, true), mostly counts of events or number of units. An examples is, instead of stating that the caesarean section rate is 20%, the Negative Binomial statement is having 5 vaginal deliveries for each Caesarean Section seen.

Because Negative Binomial distribution is less rigid than Poisson distribution, it is often adapted to analyse any measurements of discrete positive value where the Poisson distribution cannot be assured.

The model Negative Binomial regression in the example on this page uses the same data as that in the Poisson Regression Explained Page . The results, other than minor rounding differences, are almost identical to the analysis assuming Poisson distribution.

Negative Binomial regression, similar to other Generalized Linear Models, is conceptually and procedurally simple and easy to understand. The contraint however is that the count in the modelling data must be a positive integer, a value >0. When the expected count is low however, the count in some of the reference data may be zero, and this distorts the model. The remedy for this problem is to include a Zero Inflated Model in the algorithm, and this is explained in the panel Example Explained

References

https://en.wikipedia.org/wiki/Negative_binomial_distribution

https://ncss-wpengine.netdna-ssl.com/wp-content/themes/ncss/pdf/Procedures/NCSS/Negative_Binomial_Regression.pdf

https://stats.idre.ucla.edu/r/dae/negative-binomial-regression/

https://stats.idre.ucla.edu/r/dae/zinb/