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This question already has an answer here:

This is from the book The statistical sleuth--A course in methods of Data analysis Chapter 20, Exercise 12(c)-(e). I am using logistic regression to predict carrier with possible predictors CK and H. Here is my solution:

Carrier <- c(0,0,0,0,0,1,1,1,1,1)  
CK      <- c(52,20,28,30,40,167,104,30,65,440)  
H       <- c(83.5,77,86.5,104,83,89,81,108,87,107)  
logCK   <- log(CK)  
fit4    <- glm(Carrier~logCK+H, family="binomial", control=list(maxit=100))  
Warning message:  
glm.fit: fitted probabilities numerically 0 or 1 occurred   
summary(fit4)
## 
## Call:
## glm(formula = Carrier ~ logCK + H, family = "binomial", control = list(maxit = 100))
## 
## Deviance Residuals: 
##        Min          1Q      Median          3Q         Max  
## -1.480e-05  -2.110e-08   0.000e+00   2.110e-08   1.376e-05  
##
## Coefficients:  
##              Estimate Std. Error z value Pr(>|z|)  
## (Intercept)   -2292.8  4130902.8  -0.001        1  
## logCK           315.6   589675.2   0.001        1  
## H                11.5    21279.6   0.001        1

This results appear to be weird, because it seems that all coefficients are not significant. Also the next question is to do a drop-in-deviance test for this full model and the reduced model that neither of logCK and H is useful predictor. I get:

fit5 <- glm(Carrier~1, family="binomial")  
1-pchisq(deviance(fit5)-deviance(fit4), df.residual(fit5)-df.residual(fit4))  
## [1] 0.0009765625

So the p-value indicates that at least one of logCK and H is useful. Then I'm stuck at the next question, it asks me to calculate odds ratio for a woman with (CK, H)=(300,100) over one with (CK, H)=(80, 85).

But how can I get a meaningful result with all coefficients in this model ranging so wildly? Is there anything wrong with the way I did this logistic regression? Are there any remedial measures?

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marked as duplicate by gung, Scortchi, Nick Cox, Momo, chl Nov 4 '13 at 20:31

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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    $\begingroup$ Look up the idea of "separation"; the UCLA web site is pretty good. $\endgroup$ – Aaron Nov 4 '13 at 15:42
  • $\begingroup$ And the CV question here. $\endgroup$ – Scortchi Nov 4 '13 at 15:51