library(faraway)
library(gee)
## Warning: package 'gee' was built under R version 3.5.2

ELM 9.1

The ohio data concern 536 children from Steubenville, Ohio and were taken as part of a study on the effects of air pollution. Children were in the study for four years from age seven to ten. The response was whether they wheezed or not.

data(ohio)
head(ohio)
##   resp id age smoke
## 1    0  0  -2     0
## 2    0  0  -1     0
## 3    0  0   0     0
## 4    0  0   1     0
## 5    0  1  -2     0
## 6    0  1  -1     0

We start by fitting a binomial and ignoring the effect of smokingas a group all together, similar to the example in the book.

  1. Repeat your analysis using a GLM where you assume that the observations are independent, that is, each single response value represents a different child. Indicate how the conclusions would differ and which results should be preferred.
gm1<-glm(resp~smoke,binomial,ohio)
summary(gm1)
## 
## Call:
## glm(formula = resp ~ smoke, family = binomial, data = ohio)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -0.6205  -0.6205  -0.5477  -0.5477   1.9856  
## 
## Coefficients:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept) -1.82124    0.07719 -23.595   <2e-16 ***
## smoke        0.27156    0.12334   2.202   0.0277 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 1829.1  on 2147  degrees of freedom
## Residual deviance: 1824.3  on 2146  degrees of freedom
## AIC: 1828.3
## 
## Number of Fisher Scoring iterations: 4

Probability of wheeze if smoke

testData=ohio[which((ohio$smoke==1)),]
predict(gm1,testData,type="response")[1]
##      1401 
## 0.1751337

Probability of wheeze if not smoke

testData=ohio[which((ohio$smoke==0)),]
predict(gm1,testData,type="response")[1]
##         1 
## 0.1392857
ohioF<-ohio
ohioF$age<-factor(ohioF$age)
gm2<-glm(resp~age+smoke,binomial,ohioF)
summary(gm2)
## 
## Call:
## glm(formula = resp ~ age + smoke, family = binomial, data = ohioF)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -0.6588  -0.5820  -0.5604  -0.4763   2.1132  
## 
## Coefficients:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept) -1.74395    0.12679 -13.754   <2e-16 ***
## age-1        0.05401    0.16436   0.329   0.7424    
## age0        -0.02776    0.16661  -0.167   0.8677    
## age1        -0.37553    0.17823  -2.107   0.0351 *  
## smoke        0.27246    0.12355   2.205   0.0274 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 1829.1  on 2147  degrees of freedom
## Residual deviance: 1817.1  on 2143  degrees of freedom
## AIC: 1827.1
## 
## Number of Fisher Scoring iterations: 4

Probability of wheeze if smoke

testData=ohioF[which((ohioF$smoke==1 & ohioF$age==-2)),]
predict(gm2,testData,type="response")[1]
##      1401 
## 0.1867163

Probability of wheeze if not smoke

testData=ohioF[which((ohioF$smoke==0 & ohioF$age==1)),]
predict(gm2,testData,type="response")[1]
##         4 
## 0.1072178
  1. What is the predicted probability that a 7 year-old with a smoking mother, wheezes?
testData=ohioF[which((ohioF$smoke==1 & ohioF$age==-2)),]
predict(gm2,testData,type="response")[1]
##      1401 
## 0.1867163
ohioF<-ohio
ohioF$age<-factor(ohioF$age)
ohioF$id<-factor(ohioF$id)
gm2<-glm(resp~age+smoke+id,binomial,ohioF)
## Warning: glm.fit: algorithm did not converge
## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
summary(gm2)
## 
## Call:
## glm(formula = resp ~ age + smoke + id, family = binomial, data = ohioF)
## 
## Deviance Residuals: 
##    Min      1Q  Median      3Q     Max  
##  -8.49    0.00    0.00    0.00    8.49  
## 
## Coefficients: (1 not defined because of singularities)
##               Estimate Std. Error    z value Pr(>|z|)    
## (Intercept) -4.666e+15  3.365e+07 -1.387e+08   <2e-16 ***
## age-1        8.387e+13  4.096e+06  2.048e+07   <2e-16 ***
## age0        -1.677e+13  4.096e+06 -4.096e+06   <2e-16 ***
## age1         5.710e+14  4.096e+06  1.394e+08   <2e-16 ***
## smoke        9.011e+15  4.745e+07  1.899e+08   <2e-16 ***
## id1          1.181e+15  4.745e+07  2.488e+07   <2e-16 ***
## id2          3.291e+12  4.745e+07  6.935e+04   <2e-16 ***
## id3          2.226e+15  4.745e+07  4.691e+07   <2e-16 ***
## id4          1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id5          3.303e+12  4.745e+07  6.960e+04   <2e-16 ***
## id6          3.352e+15  4.745e+07  7.063e+07   <2e-16 ***
## id7          1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id8          3.302e+12  4.745e+07  6.959e+04   <2e-16 ***
## id9          3.362e+12  4.745e+07  7.084e+04   <2e-16 ***
## id10         1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id11         1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id12         1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id13         2.226e+15  4.745e+07  4.691e+07   <2e-16 ***
## id14         3.302e+12  4.745e+07  6.958e+04   <2e-16 ***
## id15         3.298e+12  4.745e+07  6.950e+04   <2e-16 ***
## id16         3.299e+12  4.745e+07  6.952e+04   <2e-16 ***
## id17         3.299e+12  4.745e+07  6.952e+04   <2e-16 ***
## id18         3.298e+12  4.745e+07  6.950e+04   <2e-16 ***
## id19         1.100e+15  4.745e+07  2.318e+07   <2e-16 ***
## id20         1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id21         3.299e+12  4.745e+07  6.951e+04   <2e-16 ***
## id22         3.300e+12  4.745e+07  6.953e+04   <2e-16 ***
## id23         3.298e+12  4.745e+07  6.950e+04   <2e-16 ***
## id24         3.300e+12  4.745e+07  6.953e+04   <2e-16 ***
## id25         3.298e+12  4.745e+07  6.950e+04   <2e-16 ***
## id26         3.298e+12  4.745e+07  6.950e+04   <2e-16 ***
## id27         3.299e+12  4.745e+07  6.953e+04   <2e-16 ***
## id28         3.352e+15  4.745e+07  7.063e+07   <2e-16 ***
## id29         3.302e+12  4.745e+07  6.959e+04   <2e-16 ***
## id30         1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id31         3.303e+12  4.745e+07  6.960e+04   <2e-16 ***
## id32         1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id33         3.229e+12  4.745e+07  6.804e+04   <2e-16 ***
## id34         2.226e+15  4.745e+07  4.691e+07   <2e-16 ***
## id35         3.218e+12  4.745e+07  6.781e+04   <2e-16 ***
## id36         1.100e+15  4.745e+07  2.318e+07   <2e-16 ***
## id37         1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id38         1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id39         3.296e+12  4.745e+07  6.947e+04   <2e-16 ***
## id40         1.100e+15  4.745e+07  2.318e+07   <2e-16 ***
## id41         1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id42         1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id43         1.108e+15  4.745e+07  2.335e+07   <2e-16 ***
## id44         1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id45         2.226e+15  4.745e+07  4.691e+07   <2e-16 ***
## id46         1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id47         1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id48         2.226e+15  4.745e+07  4.691e+07   <2e-16 ***
## id49         1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id50         1.100e+15  4.745e+07  2.318e+07   <2e-16 ***
## id51         1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id52         1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id53         3.298e+12  4.745e+07  6.950e+04   <2e-16 ***
## id54         1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id55         1.100e+15  4.745e+07  2.318e+07   <2e-16 ***
## id56         1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id57         3.297e+12  4.745e+07  6.949e+04   <2e-16 ***
## id58         1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id59         2.226e+15  4.745e+07  4.691e+07   <2e-16 ***
## id60         3.352e+15  4.745e+07  7.063e+07   <2e-16 ***
## id61         1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id62         1.100e+15  4.745e+07  2.318e+07   <2e-16 ***
## id63         1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id64         2.226e+15  4.745e+07  4.691e+07   <2e-16 ***
## id65         1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id66         1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id67         1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id68         1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id69         1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id70         2.226e+15  4.745e+07  4.691e+07   <2e-16 ***
## id71         3.298e+12  4.745e+07  6.951e+04   <2e-16 ***
## id72         2.226e+15  4.745e+07  4.691e+07   <2e-16 ***
## id73         3.298e+12  4.745e+07  6.949e+04   <2e-16 ***
## id74         1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id75         3.298e+12  4.745e+07  6.951e+04   <2e-16 ***
## id76         2.226e+15  4.745e+07  4.691e+07   <2e-16 ***
## id77         1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id78         3.352e+15  4.745e+07  7.063e+07   <2e-16 ***
## id79         1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id80         1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id81         2.226e+15  4.745e+07  4.691e+07   <2e-16 ***
## id82         1.100e+15  4.745e+07  2.318e+07   <2e-16 ***
## id83         2.226e+15  4.745e+07  4.691e+07   <2e-16 ***
## id84         2.226e+15  4.745e+07  4.691e+07   <2e-16 ***
## id85         1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id86         1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id87         2.226e+15  4.745e+07  4.691e+07   <2e-16 ***
## id88         1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id89         1.100e+15  4.745e+07  2.318e+07   <2e-16 ***
## id90         2.226e+15  4.745e+07  4.691e+07   <2e-16 ***
## id91         2.226e+15  4.745e+07  4.691e+07   <2e-16 ***
## id92         1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id93         3.310e+12  4.745e+07  6.975e+04   <2e-16 ***
## id94         3.310e+12  4.745e+07  6.974e+04   <2e-16 ***
## id95         3.308e+12  4.745e+07  6.972e+04   <2e-16 ***
## id96         1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id97         1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id98         3.309e+12  4.745e+07  6.973e+04   <2e-16 ***
## id99         1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id100        1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id101        3.309e+12  4.745e+07  6.974e+04   <2e-16 ***
## id102        1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id103        3.307e+12  4.745e+07  6.969e+04   <2e-16 ***
## id104        3.306e+12  4.745e+07  6.968e+04   <2e-16 ***
## id105        3.305e+12  4.745e+07  6.966e+04   <2e-16 ***
## id106        3.306e+12  4.745e+07  6.966e+04   <2e-16 ***
## id107        3.305e+12  4.745e+07  6.966e+04   <2e-16 ***
## id108        1.129e+15  4.745e+07  2.379e+07   <2e-16 ***
## id109        1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id110        2.226e+15  4.745e+07  4.691e+07   <2e-16 ***
## id111        1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id112        2.226e+15  4.745e+07  4.691e+07   <2e-16 ***
## id113        2.226e+15  4.745e+07  4.691e+07   <2e-16 ***
## id114        2.226e+15  4.745e+07  4.691e+07   <2e-16 ***
## id115        1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id116        1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id117        2.226e+15  4.745e+07  4.691e+07   <2e-16 ***
## id118        1.100e+15  4.745e+07  2.318e+07   <2e-16 ***
## id119        3.302e+12  4.745e+07  6.959e+04   <2e-16 ***
## id120        1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id121        3.303e+12  4.745e+07  6.960e+04   <2e-16 ***
## id122        3.303e+12  4.745e+07  6.960e+04   <2e-16 ***
## id123        1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id124        3.374e+12  4.745e+07  7.110e+04   <2e-16 ***
## id125        3.352e+15  4.745e+07  7.063e+07   <2e-16 ***
## id126        1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id127        1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id128        1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id129        1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id130        1.129e+15  4.745e+07  2.379e+07   <2e-16 ***
## id131        3.332e+12  4.745e+07  7.021e+04   <2e-16 ***
## id132        2.226e+15  4.745e+07  4.691e+07   <2e-16 ***
## id133        2.226e+15  4.745e+07  4.691e+07   <2e-16 ***
## id134        1.100e+15  4.745e+07  2.318e+07   <2e-16 ***
## id135        3.301e+12  4.745e+07  6.956e+04   <2e-16 ***
## id136        2.226e+15  4.745e+07  4.691e+07   <2e-16 ***
## id137        3.364e+12  4.745e+07  7.089e+04   <2e-16 ***
## id138        1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id139        2.226e+15  4.745e+07  4.691e+07   <2e-16 ***
## id140        2.226e+15  4.745e+07  4.691e+07   <2e-16 ***
## id141        1.100e+15  4.745e+07  2.318e+07   <2e-16 ***
## id142        3.303e+12  4.745e+07  6.961e+04   <2e-16 ***
## id143        2.226e+15  4.745e+07  4.691e+07   <2e-16 ***
## id144        2.226e+15  4.745e+07  4.691e+07   <2e-16 ***
## id145        2.226e+15  4.745e+07  4.691e+07   <2e-16 ***
## id146        1.100e+15  4.745e+07  2.318e+07   <2e-16 ***
## id147        2.226e+15  4.745e+07  4.691e+07   <2e-16 ***
## id148        3.305e+12  4.745e+07  6.964e+04   <2e-16 ***
## id149        1.100e+15  4.745e+07  2.318e+07   <2e-16 ***
## id150        1.100e+15  4.745e+07  2.318e+07   <2e-16 ***
## id151        1.100e+15  4.745e+07  2.318e+07   <2e-16 ***
## id152        1.100e+15  4.745e+07  2.318e+07   <2e-16 ***
## id153        2.226e+15  4.745e+07  4.691e+07   <2e-16 ***
## id154        3.309e+12  4.745e+07  6.974e+04   <2e-16 ***
## id155        1.100e+15  4.745e+07  2.318e+07   <2e-16 ***
## id156        3.324e+12  4.745e+07  7.005e+04   <2e-16 ***
## id157        2.226e+15  4.745e+07  4.691e+07   <2e-16 ***
## id158        1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id159        3.325e+12  4.745e+07  7.007e+04   <2e-16 ***
## id160        1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id161        1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id162        1.100e+15  4.745e+07  2.318e+07   <2e-16 ***
## id163        1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id164        1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id165        2.226e+15  4.745e+07  4.691e+07   <2e-16 ***
## id166        1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id167        1.100e+15  4.745e+07  2.318e+07   <2e-16 ***
## id168        3.325e+12  4.745e+07  7.007e+04   <2e-16 ***
## id169        3.325e+12  4.745e+07  7.006e+04   <2e-16 ***
## id170        3.323e+12  4.745e+07  7.003e+04   <2e-16 ***
## id171        3.327e+12  4.745e+07  7.010e+04   <2e-16 ***
## id172        1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id173        1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id174        1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id175        2.226e+15  4.745e+07  4.691e+07   <2e-16 ***
## id176        1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id177        2.226e+15  4.745e+07  4.691e+07   <2e-16 ***
## id178        3.326e+12  4.745e+07  7.010e+04   <2e-16 ***
## id179        1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id180        3.324e+12  4.745e+07  7.005e+04   <2e-16 ***
## id181        1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id182        3.325e+12  4.745e+07  7.007e+04   <2e-16 ***
## id183        1.100e+15  4.745e+07  2.318e+07   <2e-16 ***
## id184        1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id185        3.325e+12  4.745e+07  7.007e+04   <2e-16 ***
## id186        1.100e+15  4.745e+07  2.319e+07   <2e-16 ***
## id187        1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
## id188        3.221e+12  4.745e+07  6.787e+04   <2e-16 ***
## id189        1.128e+15  4.745e+07  2.377e+07   <2e-16 ***
## id190        1.100e+15  4.745e+07  2.318e+07   <2e-16 ***
## id191        3.326e+12  4.745e+07  7.009e+04   <2e-16 ***
## id192        3.328e+12  4.745e+07  7.014e+04   <2e-16 ***
## id193        1.129e+15  4.745e+07  2.380e+07   <2e-16 ***
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## id437       -5.659e+15  4.745e+07 -1.192e+08   <2e-16 ***
## id438       -7.881e+15  4.745e+07 -1.661e+08   <2e-16 ***
## id439       -7.881e+15  4.745e+07 -1.661e+08   <2e-16 ***
## id440       -5.659e+15  4.745e+07 -1.192e+08   <2e-16 ***
## id441       -7.881e+15  4.745e+07 -1.661e+08   <2e-16 ***
## id442       -5.659e+15  4.745e+07 -1.192e+08   <2e-16 ***
## id443       -7.881e+15  4.745e+07 -1.661e+08   <2e-16 ***
## id444       -5.659e+15  4.745e+07 -1.192e+08   <2e-16 ***
## id445       -7.881e+15  4.745e+07 -1.661e+08   <2e-16 ***
## id446       -5.659e+15  4.745e+07 -1.192e+08   <2e-16 ***
## id447       -5.659e+15  4.745e+07 -1.192e+08   <2e-16 ***
## id448       -7.881e+15  4.745e+07 -1.661e+08   <2e-16 ***
## id449       -5.659e+15  4.745e+07 -1.192e+08   <2e-16 ***
## id450       -5.659e+15  4.745e+07 -1.192e+08   <2e-16 ***
## id451       -5.659e+15  4.745e+07 -1.192e+08   <2e-16 ***
## id452       -7.881e+15  4.745e+07 -1.661e+08   <2e-16 ***
## id453       -5.659e+15  4.745e+07 -1.192e+08   <2e-16 ***
## id454       -7.881e+15  4.745e+07 -1.661e+08   <2e-16 ***
## id455       -5.659e+15  4.745e+07 -1.192e+08   <2e-16 ***
## id456       -7.881e+15  4.745e+07 -1.661e+08   <2e-16 ***
## id457       -5.659e+15  4.745e+07 -1.192e+08   <2e-16 ***
## id458       -5.659e+15  4.745e+07 -1.192e+08   <2e-16 ***
## id459       -7.881e+15  4.745e+07 -1.661e+08   <2e-16 ***
## id460       -5.659e+15  4.745e+07 -1.192e+08   <2e-16 ***
## id461       -7.881e+15  4.745e+07 -1.661e+08   <2e-16 ***
## id462       -7.881e+15  4.745e+07 -1.661e+08   <2e-16 ***
## id463       -7.881e+15  4.745e+07 -1.661e+08   <2e-16 ***
## id464       -5.659e+15  4.745e+07 -1.192e+08   <2e-16 ***
## id465       -5.659e+15  4.745e+07 -1.192e+08   <2e-16 ***
## id466       -5.659e+15  4.745e+07 -1.192e+08   <2e-16 ***
## id467       -5.659e+15  4.745e+07 -1.192e+08   <2e-16 ***
## id468       -6.755e+15  4.745e+07 -1.424e+08   <2e-16 ***
## id469       -6.755e+15  4.745e+07 -1.424e+08   <2e-16 ***
## id470       -6.755e+15  4.745e+07 -1.424e+08   <2e-16 ***
## id471       -6.755e+15  4.745e+07 -1.424e+08   <2e-16 ***
## id472       -6.755e+15  4.745e+07 -1.424e+08   <2e-16 ***
## id473       -6.755e+15  4.745e+07 -1.424e+08   <2e-16 ***
## id474       -6.755e+15  4.745e+07 -1.424e+08   <2e-16 ***
## id475       -6.755e+15  4.745e+07 -1.424e+08   <2e-16 ***
## id476       -4.506e+15  4.745e+07 -9.495e+07   <2e-16 ***
## id477       -6.755e+15  4.745e+07 -1.424e+08   <2e-16 ***
## id478       -4.551e+15  4.745e+07 -9.591e+07   <2e-16 ***
## id479       -6.755e+15  4.745e+07 -1.424e+08   <2e-16 ***
## id480       -6.755e+15  4.745e+07 -1.424e+08   <2e-16 ***
## id481       -6.755e+15  4.745e+07 -1.424e+08   <2e-16 ***
## id482       -3.378e+15  4.745e+07 -7.118e+07   <2e-16 ***
## id483       -3.378e+15  4.745e+07 -7.118e+07   <2e-16 ***
## id484       -6.755e+15  4.745e+07 -1.424e+08   <2e-16 ***
## id485       -6.755e+15  4.745e+07 -1.424e+08   <2e-16 ***
## id486       -6.755e+15  4.745e+07 -1.424e+08   <2e-16 ***
## id487       -6.755e+15  4.745e+07 -1.424e+08   <2e-16 ***
## id488       -6.755e+15  4.745e+07 -1.424e+08   <2e-16 ***
## id489       -6.755e+15  4.745e+07 -1.424e+08   <2e-16 ***
## id490       -6.755e+15  4.745e+07 -1.424e+08   <2e-16 ***
## id491       -6.755e+15  4.745e+07 -1.424e+08   <2e-16 ***
## id492       -6.755e+15  4.745e+07 -1.424e+08   <2e-16 ***
## id493       -6.755e+15  4.745e+07 -1.424e+08   <2e-16 ***
## id494       -6.755e+15  4.745e+07 -1.424e+08   <2e-16 ***
## id495       -5.659e+15  4.745e+07 -1.192e+08   <2e-16 ***
## id496       -3.378e+15  4.745e+07 -7.118e+07   <2e-16 ***
## id497       -3.378e+15  4.745e+07 -7.118e+07   <2e-16 ***
## id498       -5.659e+15  4.745e+07 -1.192e+08   <2e-16 ***
## id499       -3.378e+15  4.745e+07 -7.118e+07   <2e-16 ***
## id500       -3.378e+15  4.745e+07 -7.118e+07   <2e-16 ***
## id501       -3.378e+15  4.745e+07 -7.118e+07   <2e-16 ***
## id502       -4.504e+15  4.745e+07 -9.491e+07   <2e-16 ***
## id503       -4.504e+15  4.745e+07 -9.491e+07   <2e-16 ***
## id504       -4.504e+15  4.745e+07 -9.491e+07   <2e-16 ***
## id505       -4.504e+15  4.745e+07 -9.491e+07   <2e-16 ***
## id506       -6.756e+15  4.745e+07 -1.424e+08   <2e-16 ***
## id507       -6.755e+15  4.745e+07 -1.424e+08   <2e-16 ***
## id508       -6.756e+15  4.745e+07 -1.424e+08   <2e-16 ***
## id509       -6.755e+15  4.745e+07 -1.424e+08   <2e-16 ***
## id510       -4.533e+15  4.745e+07 -9.552e+07   <2e-16 ***
## id511       -6.755e+15  4.745e+07 -1.424e+08   <2e-16 ***
## id512       -4.533e+15  4.745e+07 -9.552e+07   <2e-16 ***
## id513       -5.629e+15  4.745e+07 -1.186e+08   <2e-16 ***
## id514       -3.378e+15  4.745e+07 -7.118e+07   <2e-16 ***
## id515       -3.378e+15  4.745e+07 -7.118e+07   <2e-16 ***
## id516       -3.378e+15  4.745e+07 -7.118e+07   <2e-16 ***
## id517       -3.378e+15  4.745e+07 -7.118e+07   <2e-16 ***
## id518       -3.407e+15  4.745e+07 -7.180e+07   <2e-16 ***
## id519       -4.504e+15  4.745e+07 -9.491e+07   <2e-16 ***
## id520       -3.378e+15  4.745e+07 -7.118e+07   <2e-16 ***
## id521       -3.378e+15  4.745e+07 -7.118e+07   <2e-16 ***
## id522       -3.378e+15  4.745e+07 -7.118e+07   <2e-16 ***
## id523       -3.378e+15  4.745e+07 -7.118e+07   <2e-16 ***
## id524       -4.504e+15  4.745e+07 -9.491e+07   <2e-16 ***
## id525       -4.504e+15  4.745e+07 -9.491e+07   <2e-16 ***
## id526       -4.504e+15  4.745e+07 -9.491e+07   <2e-16 ***
## id527       -4.504e+15  4.745e+07 -9.491e+07   <2e-16 ***
## id528       -4.504e+15  4.745e+07 -9.491e+07   <2e-16 ***
## id529       -4.504e+15  4.745e+07 -9.491e+07   <2e-16 ***
## id530       -4.932e+04  4.745e+07 -1.000e-03    0.999    
## id531       -1.149e+05  4.745e+07 -2.000e-03    0.998    
## id532       -3.294e+04  4.745e+07 -1.000e-03    0.999    
## id533        6.536e+04  4.745e+07  1.000e-03    0.999    
## id534        1.621e+04  4.745e+07  0.000e+00    1.000    
## id535        3.259e+04  4.745e+07  1.000e-03    0.999    
## id536               NA         NA         NA       NA    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance:  1829.1  on 2147  degrees of freedom
## Residual deviance: 17156.8  on 1608  degrees of freedom
## AIC: 18237
## 
## Number of Fisher Scoring iterations: 25
  1. Fit an appropriate GEE model and determine the effects of age and maternal smoking on wheezing.
gg<-gee(resp~smoke,id=id,data=ohioF,family=binomial,corstr="exchangeable",scale.fix=TRUE)
## Beginning Cgee S-function, @(#) geeformula.q 4.13 98/01/27
## running glm to get initial regression estimate
## (Intercept)       smoke 
##  -1.8212353   0.2715636
summary(gg)
## 
##  GEE:  GENERALIZED LINEAR MODELS FOR DEPENDENT DATA
##  gee S-function, version 4.13 modified 98/01/27 (1998) 
## 
## Model:
##  Link:                      Logit 
##  Variance to Mean Relation: Binomial 
##  Correlation Structure:     Exchangeable 
## 
## Call:
## gee(formula = resp ~ smoke, id = id, data = ohioF, family = binomial, 
##     corstr = "exchangeable", scale.fix = TRUE)
## 
## Summary of Residuals:
##        Min         1Q     Median         3Q        Max 
## -0.1751337 -0.1751337 -0.1392857 -0.1392857  0.8607143 
## 
## 
## Coefficients:
##               Estimate Naive S.E.    Naive z Robust S.E.   Robust z
## (Intercept) -1.8212353  0.1106159 -16.464500   0.1099193 -16.568845
## smoke        0.2715636  0.1767516   1.536414   0.1776030   1.529048
## 
## Estimated Scale Parameter:  1
## Number of Iterations:  1
## 
## Working Correlation
##           [,1]      [,2]      [,3]      [,4]
## [1,] 1.0000000 0.3512202 0.3512202 0.3512202
## [2,] 0.3512202 1.0000000 0.3512202 0.3512202
## [3,] 0.3512202 0.3512202 1.0000000 0.3512202
## [4,] 0.3512202 0.3512202 0.3512202 1.0000000
  1. In your model, what indicates that a child who already wheezes is likely to continue to wheeze?

We have a positive estimate for smoke

  1. Sum the number of times wheezing is recorded for a child over the four measurements and model this as a function of the smoking status of the mother.