In many places, the GLM documentation says that the canonical link for the negative binomial is the negative binomial link.
Even if we run a negative binomial regression without a link function like the following:
gm19 = fit(GeneralizedLinearModel, @formula(Days ~ Eth + Sex + Age + Lrn), quine, NegativeBinomial(2.0))
The output says the same.
StatsModels.TableRegressionModel{GeneralizedLinearModel{GLM.GlmResp{Vector{Float64}, NegativeBinomial{Float64}, **NegativeBinomialLink**}, GLM.DensePredChol{Float64, LinearAlgebra.Cholesky{Float64, Matrix{Float64}}}}, Matrix{Float64}}
But in the list distributions with their canonical link, it is mentioned LogLink is the canonical link of negative binomial distribution.
NegativeBinomial (LogLink)
This may confuse the users.
In many places, the GLM documentation says that the canonical link for the negative binomial is the negative binomial link. Even if we run a negative binomial regression without a link function like the following:
gm19 = fit(GeneralizedLinearModel, @formula(Days ~ Eth + Sex + Age + Lrn), quine, NegativeBinomial(2.0))The output says the same.StatsModels.TableRegressionModel{GeneralizedLinearModel{GLM.GlmResp{Vector{Float64}, NegativeBinomial{Float64}, **NegativeBinomialLink**}, GLM.DensePredChol{Float64, LinearAlgebra.Cholesky{Float64, Matrix{Float64}}}}, Matrix{Float64}}But in the list distributions with their canonical link, it is mentionedLogLinkis the canonical link of negative binomial distribution.NegativeBinomial (LogLink)This may confuse the users.