From: HOLLADAYL@aol.com
  To  : rasmb@alpha.bbri.org
  Date: Mon, 1 May 2000 21:50:39 EDT

I've not seen this with sed eq models but... linear approximations...

Hi all:

As Mr. Spock would say, "fascinating!".  I've not seen this in any sed equil 
model I've ever done, but in other models (e.g combining acid and Gdm-Cl 
unfolding data), in which 2 parameters would be correlated not in anything 
like a straight line, but a cresent shape, VERY curved.  And in which case 
the linear approximation of the uncertainty interval was way way too small.

So my caution is to take nothing for granted.  There is no requirement that 
the correlation between two parameters in a nonlinear model take on a linear 
relationship.  The actual contours in the residual sum of squares surface can 
look like most anything you could imagine.  I've seen some real doozseys from 
unfolding models.

I favor doing bootstrap estimates for standard errors, and plotting the 
bootstrapped estimates on scatter plots to see correlations.  Generally when 
there is a large difference between the linear approximation and bootstrap 
there is a wierd (non straight line) correlation among at least two 
parameters.  In general the linear approximation will in my experience only 
underestimate by at worst 2 fold or so the interval of uncertainty.

I've come to the theological conclusion that God may or may not exist, but 
that Murphry certainly does rule in Heaven...  so beware....

Les Holladay