[R-sig-eco] Confidence intervals for predicted probabilities in logistic regression

[Manuel Spínola]

Dear list members,

I am fitting a logistic regression and I want to calculate the predicted 
probabilities of a response ("positive" and "negative") for a model with 
one categorical predictor (2 levels, "yes" and "no").

oso.3 = glm(response ~ school, data=osologistic, 
family=binomial(link="logit"))

For the reference level (the intercept, level "no") the point estimate is:,

 > plogis(coef(oso.3)[1] + coef(oso.3)[2]*0)
(Intercept)
      0.13

To calculate the confidence interval (lower and upper limit) I am using 
the formula: beta0+beta1*x-1.96*se(beta0+beta1*x) and 
beta0+beta1*x+1.96*se(beta0+beta1*x), using the variance and covariance 
to calculate the standard error:

 > errore.no = sqrt(1.14 + 1.73*02 + 2*-1.14*0)

 > plogis(coef(oso.3)[1] + coef(oso.3)[2]*0-1.96*errore.no)
(Intercept)
     0.017

 > plogis(coef(oso.3)[1] + coef(oso.3)[2]*0+1.96*errore.no)
(Intercept)
      0.54

However, when I use the confint function I got:

 > plogis(confint(oso.3))
Waiting for profiling to be done...
            2.5 % 97.5 %
(Intercept) 0.0076   0.45
schoolyes   0.8025   1.00

Here, I am looking at only to the intercept that is the reference level, 
"no").
I was expecting to get the same lower and upper limit for the intercept.
Do you know why the results are different?
Do I need the covariance to calculate the se?
Thank you very much in advance.
Best,

Manuel


-- 
Manuel Spínola, Ph.D.
Instituto Internacional en Conservación y Manejo de Vida Silvestre
Universidad Nacional
Apartado 1350-3000
Heredia
COSTA RICA
mspinola at una.ac.cr
mspinola10 at gamil.com
Teléfono: (506) 2277-3598
Fax: (506) 2237-7036