Nicky,
All likelihoods are approximate, it's just a question of how good.
Remember,
the Newton-Raphson iteration that is behind the scenes does not have a
convergence tolerance of 0. Even good old least squares has some round off
error. I think that you are being unnecessarily pendantic.
For some problems the Laplace computation is darned good. For example, in
mixed effects Cox models the error is on the order of 10^-14. For others,
certain glm cases for instance, it is known to be not so hot. You need to know
more about each specific case. That was exactly the type of advice that
Michael
was trying to supply -- with references.
Just because Micheal works for Insightful does not make him wrong. I'm
often
pessimistic myself (see joke below), but working outside acedemia does not
remove all honor.
Terry Therneau
Q: What's the difference between a used car salesman and a software salesman?
A. The car salesman knows when he's lying.
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