Poisson Regression STA 2101/442 Fall 2017

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Poisson Regression STA 2101/442 Fall 2017 See last slide for copyright information

Regression: Outcomes are Counts Poisson process model roughly applies Examples: Relationship of explanatory variables to Number of children Number of typos in a short document Number of workplace accidents in a short time period Number of marriages For large λ, CLT says a normality assumption is okay, but not constant variance

Linear Model for log λ log λ = β0 + β1x1 + … + βp-1xp-1 Implicitly for i = 1, …n Everybody in the sample has a different λ=λi Take exponential function of both sides Substitute into Poisson likelihood Maximum likelihood as usual Likelihood ratio tests, etc.

log λ = β0 + β1x1 + … + βp-1xp-1 Increase xk with everything else held constant, and Log λ increases by βk λ is multiplied by eβk

Copyright Information This slide show was prepared by Jerry Brunner, Department of Statistics, University of Toronto. It is licensed under a Creative Commons Attribution - ShareAlike 3.0 Unported License. Use any part of it as you like and share the result freely. These Powerpoint slides are available from the course website: http://www.utstat.toronto.edu/brunner/oldclass/appliedf17