# [R-sig-ME] Logistic regression with spatial autocorrelation structure

Rolf Turner r.turner at auckland.ac.nz
Mon Feb 7 22:09:46 CET 2011

```On 8/02/2011, at 8:55 AM, Douglas Bates wrote:

> On Mon, Feb 7, 2011 at 1:26 PM,  <Dale.W.Steele at gmail.com> wrote:
>> Suspect I'm not asking the question well. I'm clear on how to get
>> a point
>> estimate for
>> the predicted probability in both cases. How much uncertainty
>> is inherent in these prediction(s)? Not yet clear to me how to obtain
>> something like a 95% confidence
>> interval. Best. --Dale
>
> That is considerably more complex and I'm not quite sure how to answer
> it in the general case.  In fact, I don't really know how the standard
> error of a predicted probability would be calculated even for a
> fixed-effects GLM.

I am very likely just displaying my ignorance and/or stupidity, but
isn't
it trivial in the case of a fixed effects GLM?

The asymptotic theory (and the glm() function in R) give you a standard
error for the linear predictor.  You get a confidence interval (based on
asymptotic Gaussianity) for the linear predictor LP = X beta, of the
form

[A = LP.hat - (table value)*SE, B = LP.hat + (table value)*SE]

Then [expit(A),expit(B)] is the corresponding confidence interval for
expit(LP), the latter being the probability that you are trying to
estimate.
Nicht wahr?

By ``expit'' I mean the function expit(y) = exp(y)/(1+exp(y)), the
inverse
of the logit function.  (Properly called the logistic function?  But
this
always confuses me.)

Of course all of this is of at best academic interest because it all
goes
to hell in a handcart when there are random effects in the model.

cheers,

Rolf Turner

```

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