# Confidence interval for the intercept in logistic regression

Some major commercial statistical packages (e.g., SPSS) do not report a CI for the intercept term in logistic regression. [Based on answer below R does provide CI for intercept]

Why might confidence intervals for the intercept term not be included by default?

UPDATE:

Based on feedback, Confidence Intervals for odds associated with intercept term are reported in some stat. packages. And, obviously, they can be easily computed manually, knowing the standard error. Therefore, reformulated question:

What is the interpretation of intercept's CIs (for odds) in logistic regression?

• Although I can find plenty of annotated outputs of SPSS binary logistic regression on the Web, none of them directly provide confidence intervals, but they all report standard errors (from which CIs are easily computed), including for the constant term. Do you think you could document the behavior you are asking about by means of a reproducible example? – whuber May 14 '14 at 19:01
• SPSS is good for behavioral sciences, where they normally don't care about those C.I that much ;) – Stat May 14 '14 at 19:06
• I agree with both above comments. But still I found it a bit suspicious - please see my comments to gung's answer below – Oleg Shirokikh May 14 '14 at 19:07
• Use Generalized Linear Model, you'll get 95% CI that way. But I agree with another answer that 95%CI in terms of Odds Ratio for the intercept is pretty hard to interpret. – Penguin_Knight May 14 '14 at 19:24
• Is there an option to run the model without the intercept in SPSS? (I know there is for linear regression, not sure about logistic). If so, create a variable in SPSS which is equal to 1 for everyone, put that in as a predictor, and ask to remove the intercept. The new variable will be the intercept and will have CIs. – Jeremy Miles May 14 '14 at 20:09

Well, that's not correct. You can use confint funtion in both S-plus and R to obtain C.I. for the estimated parameters. I will give an example for logistic regression in R since I don't have the S-plus:

> mydata <- read.csv("http://www.ats.ucla.edu/stat/data/binary.csv")
> mylogit <- glm(admit ~ gre + gpa + rank, data = mydata, family = "binomial")
> confint(mylogit)
Waiting for profiling to be done...
2.5 %       97.5 %
(Intercept) -5.7109591680 -1.260314066
gre          0.0001715446  0.004461385
gpa          0.1415710585  1.428341503
rank        -0.8149612229 -0.315479733
>

• Interesting. I haven't checked R.. E.g. SPSS doesn't provide CIs for intercept. Please see updated question – Oleg Shirokikh May 14 '14 at 18:48

I don't have access to SPSS, but I strongly suspect that it can output a confidence interval for the intercept in logistic regression. You probably have to know how to use the underlying syntax (e.g., PASTE) to call for it.

As to why it isn't output by default, you'd really have to contact the company. But I would guess that they believe people aren't very interested in seeing the CI for the intercept and want to minimize the volume of statistical output.

• Thanks. I've checked documentation and all UI options and I'm pretty sure that there is no option to display CI for intercepts. They provide a table with coefficients and statistics including CIs for predictors - but leave space for CI for intercept empty. For instance, ats.ucla.edu/stat/spss/output/logistic.htm - last table. – Oleg Shirokikh May 14 '14 at 19:05
• Therefore I became curious - maybe this can be justified by some reasoning (though I don't see any) – Oleg Shirokikh May 14 '14 at 19:06
• I don't know SPSS's syntax, but I believe it can be done the UCLA page notwithstanding. You can also compute it yourself (remember that the SEs will be on the scale of the linear predictor) fairly easily. – gung May 14 '14 at 19:11
• At the related page ats.ucla.edu/stat/stata/faq/oratio.htm (about 2/3 the way down) the SPSS output includes a CI for the constant by default. This is because no odds ratio calculations were requested. I'm not surprised that CIs are not provided for an odds ratio for a constant: after all, what would that even mean? Thus it would behoove us all to distinguish carefully between output in terms of the raw parameter estimates and output in terms of odds ratios. – whuber May 14 '14 at 19:23