Solved – Large odds ratio in binary logistic regression – huge scale difference of continous variables

binary datadata transformationlogisticodds-ratiospss

I'd like to ask for some help with a binary logistic regression. In SPSS I am building a binary logistic regression with 4 independent continuous variables
(Sample size – 85).

However, with one of the variables (Bicaudatus_index) I get a huge odds ratio:

Maybe the scale of this variable is very different than other variables:

As this variable is a ratio of two measurements I try to multiply the variable 100 times and get a new variable. The odds ratio of the new variable in the same regression seems to be within normal range. However I don't know if it is appropriate to do that. If I multiply the variable not by 100, but e.g. 150 times, I get odds ratios that are different from the ones that I get with 100.

Best Answer

Nothing seems to be awry here. Coefficients in logistic regression are indeed scale-dependent; predictors with smaller SDs will in general get larger coefficients. If you want the variables to be on comparable scales, you can standardize each continuous variable by subtracting its mean and dividing by twice its SD.

Gelman, A. (2008). Scaling regression inputs by dividing by two standard deviations. Statistics in Medicine, 27, 2865–2873. doi:10.1002/sim.3107

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Solved – Relation between logistic regression coefficient and odds ratio in JMP

Ok, I drop a quick response. Your idea is correct in that the regression coefficient is the log of the OR. More precisely, if $b$ is your regression coefficient, $\exp(b)$ is the odds ratio corresponding to a one unit change in your variable. So, to get back to the adjusted odds, you need to know what are the internal coding convention for your factor levels. Usually, for a binary variable it is 0/1 or 1/2. But if it happens that your levels are represented as -1/+1 (which I suspect here), then you have to multiply the regression coefficient by 2 when exponentiating.

The same would apply if you were working with a continuous variable, like age, and want to express the odds for 5 years ($\exp(5b)$) instead of 1 year ($\exp(b)$).

Update: I just found this about JMP coding for nominal variables (version < 7).

Solved – How to estimate Relative Risks in Multivariate Binary Logistic Regression Models, instead of Odds Ratios

Here is more or less the replication of the SAS example mentioned in the comments to the question.

library("sas7bdat")
eyestudy =read.sas7bdat("eyestudy.sas7bdat")
sapply(1:ncol(eyestudy),function(z)summary(eyestudy[,z]))
for(i in c(2:3))eyestudy[,i]<-as.factor(eyestudy[,i])

tabfq=with(eyestudy, table(carrot, lenses))
(tabfqm=addmargins(tabfq))
prop.table(tabfq, 1)
#OR =  (32/17)/(21/30)  = 2.69
#RR =   (32/49)/(21/51)  = 1.59
(OR=tabfqm[1,2]/tabfqm[1,1]/(tabfqm[2,2]/tabfqm[2,1]))
(RR=tabfqm[1,2]/tabfqm[1,3]/(tabfqm[2,2]/tabfqm[2,3]))

#logit
(ml1<-glm(lenses~carrot, data=eyestudy,family =binomial(link = "logit")))
summary(ml1)
exp(-coefficients(ml1)) #OR
exp(-cbind(coef(ml1), confint(ml1)))  
(ml10 <- glm(lenses~1, data=eyestudy,family =binomial(link = "logit")))
anova(ml10, ml1, test="Chisq")

#log
(ml2<-glm(lenses~carrot, data=eyestudy,family =binomial(link = "log")))
summary(ml2)
exp(-coefficients(ml2)) #RR
exp(-cbind(coef(ml2), confint(ml2)))  

#poisson
(ml3<-glm(lenses~carrot, data=eyestudy,family =poisson(link = "log")))
summary(ml3)
exp(-coefficients(ml3)) #RR
exp(-cbind(coef(ml3), confint(ml3)))  

#poisson 2
(ml4<-glm(lenses~carrot+gender+latitude, data=eyestudy,family =poisson(link = "log")))
summary(ml4)
exp(-coefficients(ml4)) #RR
exp(-cbind(coef(ml4), confint(ml4)))

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Related Solutions

Solved – Relation between logistic regression coefficient and odds ratio in JMP

Solved – How to estimate Relative Risks in Multivariate Binary Logistic Regression Models, instead of Odds Ratios

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