# why a variable is significant but not coefficients in logistic regression?

My question is, in logistic regression ,why a variable is significant with a p-value less than 0.05 but no level is significant.

In R

glm(response~var1+var2+var3, family=binomial(link='logit'),data=data)

drop1(model, test = 'Chisq')

all variable with less than ***, except var2 with * but in

summary(model)

the coefficients associated with var2 are not significant.

Thanks for any help!!!

• var1 and var3 are continuos (discrete) – CJ.Learns.Math Oct 24 '19 at 1:08
• Two reasons. First drop1 is doing likelihood ratio tests while summary is doing Wald tests. These are known to give different results for logistic regression when the fitted probabilities are close to 0 or 1, see for example stats.stackexchange.com/questions/312137 The likelihood ratio tests are more reliable. – Gordon Smyth Oct 24 '19 at 2:05
• Second, drop1 is testing for differences between all the var2 levels at once, whereas summary is testing all the levels individually. The fact that the overall test is significant does not guarantee that any individual level will be significant. That's partly we do the overall test. – Gordon Smyth Oct 24 '19 at 2:10
• @GordonSmyth Could you turn your comments into an answer? – Frans Rodenburg Oct 24 '19 at 2:40
• @FransRodenburg No, I've spent as much time as I have to give. Feel free to repeat my material if you would like to write an answer yourself. – Gordon Smyth Oct 24 '19 at 2:59

## 1 Answer

By Gordon Smyth,

Two reasons. First drop1 is doing likelihood ratio tests while summary is doing Wald tests. These are known to give different results for logistic regression when the fitted probabilities are close to 0 or 1, see for example link to the example The likelihood ratio tests are more reliable. – Gordon Smyth 2 days ago

Second, drop1 is testing for differences between all the var2 levels at once, whereas summary is testing all the levels individually. The fact that the overall test is significant does not guarantee that any individual level will be significant. That's partly we do the overall test. – Gordon Smyth 2 days ago

Thank you very much for the help Gordon Smyth.