The Poisson regression model should be used when the dependent (response) variable is in the form of counts or values of the response variables following a Poisson distribution. In R,
glm() function can be used to perform Poisson regression analysis.
The Poisson regression is used to analyze count data.
For the Poisson model, let us consider another built-in data set
warpbreaks. This data set describes the effect of wool type (A or B) and tension (Low, Medium, and High) on the number of warp breaks per loom, where a loom corresponds to a fixed length of yarn.
The $breaks$ variable is considered a response variable since it contains the number of breaks (count of breaks). The $tension$ and $type$ variables are taken as predictor variables.
pois_mod <- glm(breaks ~ wool + tension, data = warpbreaks, family = poisson)
The output from the
pois_mod object is
glm() provides eight choices for a family with the following default link functions:
|Family||Default Link Function|
|binomial||(link = “logit”)|
|gaussian||(link = “identity”)|
|Gamma||(link = “inverse”)|
|poisson||(link = “log”)|
|quasi||(link = “identity”, variance = “constant”)|
|quasibinomial||(link = “logit”)|
|quasipoisson||(link = “log”)|
The detailed output (estimation and testing of parameters) can be obtained as
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