Poisson regression is a type of Generalized Linear Model.

Question

BlackTom AI · Accepted Answer

The question asks whether Poisson regression is a type of Generalized Linear Model (GLM).
Option 1: True. Poisson regression is indeed categorized as a Generalized Linear Model. In GLMs, one specifies three components: a random component from an exponential family distribution, a linear predictor, and a link function that relates the mean of the distribution to the linear predictor. For Poisson regression, the outcome variable is count data assumed to follow a Poisson distribution (an exponential family member), the linear predictor is formed from covariates, and the canonical link function is the log link, which ties the expected log-count to the linear predictor. This structure matches the GLM framework, so it is correct to classify Poisson regression as a GLM.
Option 2: False. This statement would be incorrect because it claims Poisson regression is not a GLM. However, Poisson regression explicitly fits within the GLM family by using the Poisson distribution for the response and a log link, aligning with the GLM three-part formulation. Recognizing Poisson regression as a GLM follows standard generalized linear model theory, and omitting this would overlook the established connection between Poisson models and GLMs.
To summarize the conceptual alignment: a GLM requires a distribution from the exponential family (Poisson qualifies), a linear predictor constructed from covariates (present in Poisson regression), and a link function connecting the mean to the linear predictor (log link in Poisson regression). Each of these elements is satisfied in Poisson regression, reinforcing its classification as a GLM.

2025WI_MSDS_410-DL_SEC56 Quiz #5: Poisson and ZIP Regression

Poisson regression is a type of Generalized Linear Model.

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