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In statistics, Poisson regression is a generalized linear model form of regression analysis used to model count data and contingency tables. [1] 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.
Hilbe [3] notes that "Poisson regression is traditionally conceived of as the basic count model upon which a variety of other count models are based." In a Poisson model, "… the random variable y {\displaystyle y} is the count response and parameter λ {\displaystyle \lambda } (lambda) is the mean.
Poisson regression and negative binomial regression Poisson regression and negative binomial regression are useful for analyses where the dependent (response) variable is the count (0, 1, 2, ... ) of the number of events or occurrences in an interval.
Generalized linear models were formulated by John Nelder and Robert Wedderburn as a way of unifying various other statistical models, including linear regression, logistic regression and Poisson regression. [1] They proposed an iteratively reweighted least squares method for maximum likelihood estimation (MLE) of the model parameters. MLE ...
In statistics, a fixed-effect Poisson model is a Poisson regression model used for static panel data when the outcome variable is count data.Hausman, Hall, and Griliches pioneered the method in the mid 1980s.
The earliest regression form was seen in Isaac Newton's work in 1700 while studying equinoxes, being credited with introducing "an embryonic linear aggression analysis" as "Not only did he perform the averaging of a set of data, 50 years before Tobias Mayer, but summing the residuals to zero he forced the regression line to pass through the ...
Poisson regression for contingency tables, a type of generalized linear model. The specific applications of log-linear models are where the output quantity lies in the range 0 to ∞, for values of the independent variables X, or more immediately, the transformed quantities f i (X) in the range −∞ to +∞.
The Poisson model is a popular model for recurrent event data, which models the number of recurrences that have occurred. Poisson regression assumes that the number of recurrences has a Poisson distribution with a fixed rate of recurrence over time.