[R] SE of difference in fitted probabilities from logistic model.

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