The output below presents part of the S-Plus output listing the
estimates of the regressions coefficients and their standard errors.
We see that the
coefficients for gender, length-of-stay, and the WAB score at
discharge are all significantly related to the probability of
spontaneous language recovery at the 0.05 level. The coefficient for
length-of-stay is negative indicating that the longer patients are in
the hospital the smaller the chance of spontaneous language recovery
relative to patients who have shorter lengths-of-stay even after
controlling for the effect of the WAB1 score. The coefficient for
WAB1 is positive as we would expect. Males, after controlling for the
other variables in the model, are 
times as likely to
recover spontaneous language function as females. A 95% confidence
interval for 
, the adjusted log odds ratio of recovery for
males relative to females, however, is large and ranges from 0.47 to
5.29. We also note that side of stroke and subject's age do not have
a statistically significant association with spontaneous language
recovery after controlling for the effects of the other variables.
Details about these tests can be found in Hosmer and
Lemeshow (1989, Chapter 5).
402 > stroke <- read.table("stroke.dat", head=T)
402 > stroke[1:10,]
Side Gender Age LOSD WAB1 Status
1 0 0 79 27 18.2 0
2 0 0 82 17 86.0 0
3 1 0 72 42 46.3 0
4 0 0 59 23 35.6 0
5 0 0 60 28 0.0 0
6 1 1 75 12 81.9 1
7 0 0 75 53 56.0 0
8 0 0 85 46 17.3 0
9 0 0 79 58 74.9 0
10 0 1 82 34 18.2 0
402 > mymod <- glm(Status ~ Side + Gender + Age + LOSD +WAB1, family=binomial,
+ data=stroke)
402 > summary(mymod)
Call: glm(formula = Status ~ Side + Gender + Age + LOSD + WAB1, family = binomial,
data = stroke)
Deviance Residuals:
Min 1Q Median 3Q Max
-1.317524 -0.2999725 -0.003778562 -0.0002212266 2.862154
Coefficients:
Value Std. Error t value
(Intercept) -11.072759221 6.28633143 -1.7614024
Side -1.369026127 1.10318267 -1.2409786
Gender 2.876569185 1.25325078 2.2952862
Age -0.006938071 0.03062231 -0.2265691
LOSD -0.196137069 0.09595028 -2.0441532
WAB1 0.164467235 0.07172681 2.2929674
(Dispersion Parameter for Binomial family taken to be 1 )
Null Deviance: 65.71913 on 60 degrees of freedom
Residual Deviance: 28.9878 on 55 degrees of freedom
Number of Fisher Scoring Iterations: 7
Correlation of Coefficients:
(Intercept) Side Gender Age LOSD
Side 0.2553975
Gender -0.5007016 -0.2793548
Age -0.3373404 -0.1265137 0.2006563
LOSD 0.1199385 0.2046374 -0.5309336 -0.1894954
WAB1 -0.9292116 -0.3055970 0.5278826 0.0616042 -0.2969773
402 > anova(mymod)
Analysis of Deviance Table
Binomial model
Response: Status
Terms added sequentially (first to last)
Df Deviance Resid. Df Resid. Dev
NULL 60 65.71913
Side 1 0.10011 59 65.61902
Gender 1 3.36010 58 62.25892
Age 1 1.45449 57 60.80444
LOSD 1 12.25425 56 48.55018
WAB1 1 19.56238 55 28.98780
402 >