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StatsToDo : Poisson Regression Explained

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Introduction Example R Code Example Explained
This page provides explanations and example R codes for Poisson Regression, which is one of the algorithms based on the Generalized Linear Models, but the dependent variable is a discrete positive integer with Poisson distribution, mostly counts of events or number of units. Examples are the number of cells seen in a field under the microscope, the number of asthma attacks per 100 child year, the number of pregnancies per 100 women year using a particular form of contraception.

The Poisson Regression is a powerful analytical tool, providing that the data conforms to the Poisson distribution. When there is doubt about the distribution, the less powerful methods with less rigorous assumptions should be used. These are the Ordinal Regression as explained in the Ordinal Logistic Regression Explained Page , or the Negative Binomial Regression, as explained in the Negative Binomial Regression Explained Page

Poisson 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/Poisson_regression

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

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

https://en.wikipedia.org/wiki/Zero-inflated_model

https://en.wikipedia.org/wiki/Vuong%27s_closeness_test

https://www.rdocumentation.org/packages/mpath/versions/0.1-20/topics/vuong.test


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