Re: std error of parameter obtained from glm with binomial link

On Jul 30, 1:31 pm, marc.giron...@xxxxxxxxx wrote:
When parameters are estimated using mle with glm and binomial link,
all the software report the std error of the parameter, used for
example in Wald test.
I try to understand how this se is calculated.
It seems related to the rate on change of likelihood when the
parameter of interest is changed. Std error is then calculated by the
inverse of the second order derivative for the parameter of the -ln L
at the maximum likelihood (simpler to write the equation than to
describe it !)

Then I calculate the -ln likelihood at maximum likelihood and for 2
points lowering the parameter and 2 points enhancing the parameter:
parameter -LN L
11.39846408 62.64265754
11.51477494 62.01323743
mle 11.63108579 61.801192
11.74739665 62.01630013
11.86370751 62.66711422

I fit -Ln L=f(parameter) by a 4th order polynome and calculate the
second order derivative of this polynome.
The se I estimate by this procedure is much lower than the se given by
sas... so I make a strong mistake somewhere...
Any idea ?
Thanks a lot

Two ideas (I am betting on the first):
1. the inverse of the second order derivative for the parameter of the
-ln L
at the maximum likelihood is the variance and not the standard error.
Perhaps you have forgotten a square root?
2. most people would fit a quadratic polynomial to the 5 points, as
the 4th order might be overfitting (to only 5 points) - the log-
likelihood is locally quadratic at the mle (for "normal" cases).

Aniko

.

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