# [R] Obtaining SE from the hessian matrix

Spencer Graves spencer.graves at pdf.com
Thu Feb 19 20:21:39 CET 2004

```      Minor correction:  Most likely, Prof. Lumley's statement is
correct.  However, as I'm sure he knows, it depends on what you are
maximizing or minimizing:  If you are maximizing the log(likelihood),
then the NEGATIVE of the hessian is the "observed information".  This
latter should be positive semi-definite, and if nonsingular, its inverse
will be the covariance matrix of the standard normal approximation.
Alternatively, if you MINIMIZE a "deviance" = (-2)*log(likelihood), then
the HALF of the hessian is the observed information.  In the unlikely
event that you are maximizing the likelihood itself, you need to divide
the negative of the hessian by the likelihood to get the observed
information.

hope this helps.  spencer graves

Thomas Lumley wrote:

>On Thu, 19 Feb 2004, Timur Elzhov wrote:
>
>
>>So, what is the _right_ way for obtatining SE? Why two those formulas above
>>differ?
>>
>>
>>
>
>If you are maximising a likelihood then the covariance matrix of the
>estimates is (asymptotically) the inverse of the negative of the Hessian.
>
>The standard errors are the square roots of the diagonal elements of the
>covariance.
>
>So if you have the Hessian you need to invert it, if you have the
>covariance matrix, you don't.
>
>	-thomas
>
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