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Generalized Linear Models

Generalized Linear Models. Dobson A: Generalized Linear Models. Chapman and Hall, New York, 1990. It all starts with the exponential family of distributions. The exponential family:. The normal distribution. The Binomial distribution. The Poisson Distribution. Who cares?.

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Generalized Linear Models

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  1. Generalized Linear Models

  2. Dobson A: Generalized Linear Models. Chapman and Hall, New York, 1990.

  3. It all starts with the exponential family of distributions.

  4. The exponential family:

  5. The normal distribution

  6. The Binomial distribution

  7. The Poisson Distribution

  8. Who cares?

  9. If X comes from the exponential family then lots of estimation and modeling problems can be formulated and solved within the context of the exponential family.

  10. The normal distribution

  11. Exercise, derive the mean and variance of the Poisson and Bernoulli distributions using their characterization as members of the exponential family.

  12. The generalized linear model.

  13. The linear model

  14. Logistic regression

  15. Proc Genmod

  16. %clearall odsselectparameterestimates; procgenmoddata=a.chd2018_a descending; title"Proc Genmod"; modelchd=age / dist = bin link = logit; run; odsselectparameterestimates; proclogisticdata=a.chd2018_a descending; title"Proc Logistic"; modelchd=age; run; title;

  17. Poisson Regression • data skin; • input cases city $ age $ population; • log_pop=log(population); • datalines; • 1 MSP 15-24 172675 • 16 MSP 25-34 123065 • 30 MSP 35-44 96216 • 71 MSP 45-54 92051 • 102 MSP 55-64 72159 • 130 MSP 65-74 54722 • 133 MSP 75-84 32185 • 40 MSP 85+ 8328 • 4 DFW 15-24 181343 • 38 DFW 25-34 146207 • 119 DFW 35-44 121374 • 221 DFW 45-54 111353 • 259 DFW 55-64 83004 • 310 DFW 65-74 55932 • 295 DFW 75-84 36518 • 65 DFW 85+ 7583 • ; • run;

  18. Poisson Regression %clearall procgenmoddata=skin; class city (param=ref ref=last) age (param=ref ref=last); model cases= city age / offset=log_popdist=poi link=log type3; run;

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