Workshop 10.6a: Poisson regression Murray Logan 12 Sep 2016 - PowerPoint PPT Presentation

Workshop 10.6a: Poisson regression Murray Logan 12 Sep 2016

Section 1 Poisson regression

Poisson regression Probability density function Cumulative density function λ = 25 λ = 15 λ = 3 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 e − λ λ x p ( Y i ) = x ! log ( µ ) = β 0 + β 1 x i + ... + β p x p

Dispersion Spread assumed to be equal to mean. ( φ = 1 ) Probability density function Cumulative density function λ = 25 λ = 15 λ = 3 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40

Dispersion o n r s i s p e d i e r - O v Sample more varied than expected from its mean • variability due to other unmeasured (latent) influences ◦ quasi-poisson model ◦ negative binomial ◦ observation level random effect

Dispersion n s i o p e r d i s e r - O v Sample more varied than expected from its mean • variability due to other unmeasured (latent) influences • clumpiness ◦ negative binomial model • due to more zeros than expected ◦ zero-inflated model

Residuals • difficult to interpret