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

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

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Workshop 10.6a: Poisson regression Murray Logan 12 Sep 2016 Section 1 Poisson regression Poisson regression Probability density function Cumulative density function = 25 = 15 = 3 0 5 10 15 20 25 30 35 40 0 5 10 15 20

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SLIDE 1

Workshop 10.6a: Poisson regression

Murray Logan 12 Sep 2016

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SLIDE 2

Section 1 Poisson regression

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SLIDE 3

Poisson regression

Probability density function

λ = 25 λ = 15 λ = 3 5 10 15 20 25 30 35 40

Cumulative density function

5 10 15 20 25 30 35 40

p(Yi) = e−λλx x! log(µ) = β0 + β1xi + ... + βpxp

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SLIDE 4

Dispersion

Spread assumed to be equal to mean. (φ = 1)

Probability density function

λ = 25 λ = 15 λ = 3 5 10 15 20 25 30 35 40

Cumulative density function

5 10 15 20 25 30 35 40

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SLIDE 5

Dispersion

O v e r

  • d

i s p e r s i

  • n

Sample more varied than expected from its mean

  • variability due to other unmeasured

(latent) influences

  • quasi-poisson model
  • negative binomial
  • observation level random effect
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SLIDE 6

Dispersion

O v e r

  • d

i s p e r s i

  • n

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
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SLIDE 7

Residuals

  • difficult to interpret