use chisq density to measure confidence interval fudge factor

[jpritikin]

See around ComputeGD.cpp line 744 if (fabs(diff) > 1e-1). Maybe leave the bounded Wu Neale (2012) stuff as is?

[jpritikin]

Here is more background:

Date: Thu, 22 Jul 2021 21:08:23 +0000
From: Robert Kirkpatrick <robert.kirkpatrick@vcuhealth.org>
To: Team OpenMx <openmx-developers@virginia.edu>
Subject: thread 4737

   See here:  [1]https://openmx.ssri.psu.edu/node/4737 .  The user's
   questions have been satisfactorily addressed.  However, there are still
   2 things from this thread worth discussing amongst us developers.
   First, the user reports getting slightly different results for
   confidence intervals when changing the start values, even though
   changing the start values doesn't appreciably change the MLE (i.e., the
   result of the primary optmization).  I don't really understand how that
   can be, unless the confidence-limit searches are sensitive to precision
   in point estimates beyond the 6th decimal place.  Second, can't we do
   something to improve user experience when summary() (with
   verbose=FALSE ) reports a confidence limit as NaN?  As it is, the
   user then has to re-run summary() with a non-default argument, look at
   the 'CI details' table, subtract the fit at the MLE from the fit at
   the  dubious confidence limit, maybe call pchisq(), and decide whether
   the dubious confidence limit is "close enough".

   One possibility is to add columns to 'CI details' that show the change
   in fit, and the corresponding cumulative probability from a chi-square
   distribution on 1df.  Another possibility is to let the user set the
   threshold for how "off" a confidence limit can be before it gets
   reported as NaN in summary() output.

[tbates]

#78 is relevant for this issue to (in terms of the confidence limit = NaN and user work required with summary(), 'CI details' table, possible subtraction of fit at the MLE from the fit at the dubious confidence limit etc.