Generalized linear models | Poisson distribution | Categorical regression models

Poisson regression

In statistics, Poisson regression is a generalized linear model form of regression analysis used to model count data and contingency tables. Poisson regression assumes the response variable Y has a Poisson distribution, and assumes the logarithm of its expected value can be modeled by a linear combination of unknown parameters. A Poisson regression model is sometimes known as a log-linear model, especially when used to model contingency tables. Negative binomial regression is a popular generalization of Poisson regression because it loosens the highly restrictive assumption that the variance is equal to the mean made by the Poisson model. The traditional negative binomial regression model is based on the Poisson-gamma mixture distribution. This model is popular because it models the Poisson heterogeneity with a gamma distribution. Poisson regression models are generalized linear models with the logarithm as the (canonical) link function, and the Poisson distribution function as the assumed probability distribution of the response. (Wikipedia).

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Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Short Introduction to the Poisson Distribution

From playlist Statistics

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From playlist Statistics: Distributions

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Related pages

Survival analysis | Iteratively reweighted least squares | Regression analysis | Zero-inflated model | Contingency table | Statistics | Logarithm | Parameter | Log-linear model | Generalized linear model | Link function | Overdispersion | Count data | Poisson distribution | Sides of an equation | Quasi-likelihood | Variance | Convex optimization | Closed-form expression | Likelihood function | R (programming language) | Overfitting | Gradient descent | Fixed-effect Poisson model | Negative binomial distribution | Ridge regression | Expected value | Probability mass function