Re:
From: harrold@sage.che.pitt.edu
Subject: Re:
Date: Thu, 16 Aug 2001 13:26:11 -0400 (EDT)
Sometime in August Alan Xiao assaulted keyboard and produced...
|Hello, Dear Dr. Beal,
|
|Thanks for your comments. About the saddle point, how could it be formed and
if memory serves.
in one dimenstion a saddle point occurs at a point when your first
derivative is zero and your second derivative is also zero. think back to
calculus and points of inflection. in multiple dimensions this occurs
when the gradient is zero and the determinant of the hessian is
singular. these are of course referring to the derivatives of the
function you are trying to minimize/maximize.
in minimization terms the first order necessary condition requires that
the gradient be zero and the second order necessary condition requires
that the hessian be positive definate at this point.
|Can (linear) addition of some extra covariates into the model change the surface
|around a point from a cone shape or whatever into a saddle shape surface? Or
|is this just from the structure of the model and not related to covariates at all
|(as you mentioned "fundamental" problems in the last email)? If yes, then how to
|explain that it's no problem for the structural model and all models with up to
|23 covariates to go through $COV step by default? - You won't suggest that we can
|still get the right R on a saddle shape surface, right?
|
|On the other hand, if a saddle shape surface is so big that it covers the whole
|range of you data (wild?), what could you do?
then i believe that your minimum would lie somewhere along the boundary of
your search space.