Statistics 175 Applied Statistics Generalized Linear Models Jianqing Fan
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1 Statistics 175 Applied Statistics Generalized Linear Models Jianqing Fan Example 1 (Kyhposis data): (The data set kyphosis consists of measurements on 81 children following corrective spinal surgery. Variable collected include Y = kyphosis, X 1 = age in month, X 2 = Number = number of vertebrae in the operation, X 3 = start = begining of the range of vertebrae involved. > attach(kyphosis) > kyphosis[1:13,] Kyphosis Age Number Start 1 absent absent present absent absent absent absent absent absent present present absent absent > kyph.glm1 <- glm(kyphosis ~ Age + Start + Number, family = binomial, + data = kyphosis) > kyph.glm1 Call: glm(formula = Kyphosis ~ Age + Start + Number, family = binomial, data = kyphosis) (Intercept) Age Start Number Degrees of Freedom: 81 Total; 77 Residual Residual Deviance: > summary(kyph.glm1) Call: glm(formula = Kyphosis ~ Age + Start + Number, family = binomial, data = kyphosis) (Intercept) Age Start Number (Dispersion Parameter for Binomial family taken to be 1 ) 1
2 Null Deviance: on 80 degrees of freedom Residual Deviance: on 77 degrees of freedom Number of Fisher Scoring Iterations: 5 Correlation of (Intercept) Age Start Age Start Number > anova(kyph.glm1, test="chi") Binomial model Response: Kyphosis Df Deviance Resid. Df Resid. Dev Pr(Chi) NULL Age Start Number > resid <- residuals(kyph.glm1, type="deviance") > resid[1:5] > kyph.glm2 Call: glm(formula = Kyphosis ~ Start + Number + Age, family = binomial) (Intercept) Start Number Age Degrees of Freedom: 81 Total; 77 Residual Residual Deviance: > anova(kyph.glm2, test = "Chi") Binomial model Response: Kyphosis Df Deviance Resid. Df Resid. Dev Pr(Chi) NULL Start Number Age
3 Example 2: (Wave-soldering data) In 1988, an experiment was designed and implemented at one of AT & T s factories to investigate alternatives in the wave-soldering procedure for mounting electronic components on printed circuits boards. The response, measured by eye, is a count of the number of visible solder skips for a board soldered under a particular choice of levels for the experimental factors. > attach(solder.balance) > summary(solder.balance) Opening Solder Mask PadType Panel skips S:240 Thin :360 A1.5:180 L9 : 72 1:240 Min. : M:240 Thick:360 A3 :180 W9 : 72 2:240 1st Qu.: L:240 B3 :180 L8 : 72 3:240 Median : B6 :180 L7 : 72 Mean : D7 : 72 3rd Qu.: L6 : 72 Max. : (Other):288 > paov <- glm(skips~., family=poisson, data=solder.balance) > summary(paov) Call: glm(formula = skips ~ Opening + Solder + Mask + PadType + Panel, family = poisson, data = solder.balance) (Intercept) Opening.L Opening.Q Solder Mask Mask Mask PadType PadType PadType PadType PadType PadType PadType PadType PadType Panel Panel Number of Fisher Scoring Iterations: 4 Correlation of (Intercept) Opening.L Opening.Q Solder Mask1 Mask2 Opening.L > options(contrasts=c("contr.treatment", "contr.treatment","contr.treatment", 3
4 + "contr.treatment","contr.treatment")) # The effect remains for duration of the session. You could also change # part of them to be "contr.sum", "contr.poly", and your own contrasts. > paov1 <- glm(skips~., family=poisson, data=solder.balance) > summary(paov1) Call: glm(formula = skips ~ Opening + Solder + Mask + PadType + Panel, family = poisson, data = solder.balance) (Intercept) OpeningM OpeningL Solder MaskA MaskB MaskB PadTypeD PadTypeL PadTypeD PadTypeL PadTypeD PadTypeL PadTypeL PadTypeW PadTypeL Panel Panel (Dispersion Parameter for Poisson family taken to be 1 ) Null Deviance: on 719 degrees of freedom Residual Deviance: on 702 degrees of freedom Number of Fisher Scoring Iterations: 4 Correlation of... > anova(paov1, test = "Chi") Poisson model Response: skips 4
5 Df Deviance Resid. Df Resid. Dev Pr(Chi) NULL Opening e+00 Solder e+00 Mask e+00 PadType e+00 Panel e-15 Example 3 (Ship damage data): Try the following commands: ship.dat <- read.table("ship.dat",header=t) attach(ship.dat) options(contrasts=c("contr.treatment", "contr.treatment","contr.treatment")) ship.glm <- glm(damage ~log(survice + 1) + Type+Year+Period, family=poisson) summary(ship.glm) 5
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