R help - Feb 2010 - logistic regression - what is being predicted when using predict - probabilities or odds?

Dear gurus,
I've analyzed a (fake) data set ("data") using logistic regression
(glm):

logreg1 <- glm(z ~ x1 + x2 + y, data=data,
family=binomial("logit"),
na.action=na.pass)

Then, I created a data frame with 2 fixed levels (0 and 1) for each predictor:

attach(data)
x1<-c(0,1)
x2<-c(0,1)
y<-c(0,1)
newdata1<-data.frame(expand.grid(x1,x2,y))
names(newdata1)<-c("x1","x2","y")

Finally, I calculated model-predicted probabilities for each
combination of those fixed levels:

newdata1$predicted <-predict(logreg1,newdata=newdata1,
type="response")

I am pretty sure the results I get (see the table below) are actual
probabilities. But just in case - could someone please confirm that
these are probabilities rather than log odds or odds?
Thanks a lot!

x1 x2 y predicted
1  0  0 0   0.08700468
2  1  0 0   0.19262901
3  0  1 0   0.27108334
4  1  1 0   0.48216220
5  0  0 1   0.53686154
6  1  0 1   0.74373367
7  0  1 1   0.81896484
8  1  1 1   0.91887072
-- 
Dimitri Liakhovitski

Dimitri.Liakhovitski at ninah.com

On 18-Feb-10 18:58:57, Dimitri Liakhovitski wrote:
> Dear gurus,
> I've analyzed a (fake) data set ("data") using logistic
regression
> (glm):
> 
> logreg1 <- glm(z ~ x1 + x2 + y, data=data,
family=binomial("logit"),
> na.action=na.pass)
> 
> Then, I created a data frame with 2 fixed levels (0 and 1) for each
> predictor:
> 
> attach(data)
> x1<-c(0,1)
> x2<-c(0,1)
> y<-c(0,1)
> newdata1<-data.frame(expand.grid(x1,x2,y))
> names(newdata1)<-c("x1","x2","y")
> 
> Finally, I calculated model-predicted probabilities for each
> combination of those fixed levels:
> 
> newdata1$predicted <-predict(logreg1,newdata=newdata1,
type="response")
> 
> I am pretty sure the results I get (see the table below) are actual
> probabilities. But just in case - could someone please confirm that
> these are probabilities rather than log odds or odds?
> Thanks a lot!
> 
> x1 x2 y predicted
> 1  0  0 0   0.08700468
> 2  1  0 0   0.19262901
> 3  0  1 0   0.27108334
> 4  1  1 0   0.48216220
> 5  0  0 1   0.53686154
> 6  1  0 1   0.74373367
> 7  0  1 1   0.81896484
> 8  1  1 1   0.91887072
> -- 
> Dimitri Liakhovitski
Yes, they are predicted probabilities of response Z=1.
You specified this by setting 'type="response"'.

See ?predict.glm (the method for 'predict' which is used for GLMs).

Ted.

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E-Mail: (Ted Harding) <Ted.Harding at manchester.ac.uk>
Fax-to-email: +44 (0)870 094 0861
Date: 18-Feb-10                                       Time: 19:38:54
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