[R] se.fit in predict.glm

[Peter Dalgaard]

(Ted Harding) <Ted.Harding at nessie.mcc.ac.uk> writes:

> The documentation does not say definitely what p$se.fit is,
> only calling it "Estimated standard errors". I *believe*
> this means, at each value of X, the SE in the estimation
> of P[y=1] taking account of the joint uncertainty in the
> estimation of 'a' and 'b' in the relation
> 
>   probit(P) = a + b*X
> 
> Can someone confirm that this really is so?

Pretty accurate, I'd say. 

Basically, the fitted value is a function of the estimated parameters.
Asymptotically, the latter are approximately normally distributed with
a small dispersion so that the function is effectively linear and you
can approximate the distribution of the fitted value with a normal
distribution.

Just be aware that the fitted values can be on different scales
(P vs. logit(P)) and that the se.fit similarly.

-- 
   O__  ---- Peter Dalgaard             Blegdamsvej 3  
  c/ /'_ --- Dept. of Biostatistics     2200 Cph. N   
 (*) \(*) -- University of Copenhagen   Denmark      Ph: (+45) 35327918
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