From: Rolf Turner <r.turner_at_auckland.ac.nz>

Date: Fri, 16 May 2008 12:03:03 +1200

R-help_at_r-project.org mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. Received on Fri 16 May 2008 - 08:13:52 GMT

Date: Fri, 16 May 2008 12:03:03 +1200

I am fitting a logistic binomial model of the form

glm(y ~ a*x,family=binomial)

where a is a factor (with 5 levels) and x is a continuous predictor.

To assess how much ``impact'' x has, I want to compare the fitted
success probability

when x = its maximum value with the fitted probability when x = its
mean value.

(The mean and the max are to be taken by level of the factor ``a'',

but that's

not really an issue.)

I can of course easily calculate p.hat(x.max) - p.hat(x.mean) using
predict()

(with type="response"). And I can get the standard error for p.hat

*(x.max) and
*

p.hat(x.mean) by specifiying se.fit=TRUE. No problem there.

But how can I get a handle on the standard error of the difference?

In a linear model this would just be SE(beta_1.hat)*(x.max-x.mean)

(where

beta_1.hat is specific to the particular level of `a' being considered).
If I am not mistaken. (Please correct me if I am!)

But in the logistic model, everything is entangled in the inverse link function (the ``expit'' function as it is called by some), and I can see no way of disentangling.

Is there any way of getting at this? I figure that simulation/Monte
Carlo inference/

parametric bootstrapping would provide a workaround, but before I go
that route,

can anyone point me to a simpler method? There wouldn't be anything
built into R

or an R package, would there? (I did a fairly basic RSiteSearch()
and came up

empty handed.)

Thanks for any tips.

cheers,

Rolf Turner

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