I have avoided getting into this hassle.
The argument is basically which screw is better, a slotted head or a
Phillips head, a metric screw or an American standard one.........
The various stat packages are all tools to get a job done. Obviously one
tool will not do everything.
EXCEL is built using VisualBasic subroutines, functions and other modules.
The number crunching is standard IEEE 64 bit double precision, 2 and 4 byte
integers and the 8 byte money variable. All the packages end using the basic
Intel instruction set. Microsoft has a lot of years of experience in getting
the bugs out of the basic numerical functions that Visual Basic depends on.
So the basic nuts and bolts are pretty much the same for all the stat
packages that use the windows operating system.
The issue then is what you describe as "algorithms", or the structure. This
is where the numerical analysts come in. Much has been done over the recent
years to improve the structure. Such algorithms found in the LABPACK and
LINPACK collections and the "Numerical Recipes" collection are not
necessarily the best for a particular job, and many are obsolete. I suspect
a lot of stat software developers also plop in textbook and paper equations.
This is where the problem starts.
For example I have been grinding thru Mardia's 1970 paper. His equation 2.21
is a bad computer algorithm, and gives errors of up to 20%, compared to
programming the direct equation 2.23.
The other problem is that the current fads (i.e... annealing for solution of
optimization problems) are usually not robust to the enormous variations of
input of real world problems.
Another problem I have encountered is the issue of biased or unbiased
estimates. The numerical values are different for the same equations
depending of what is generated by a "textbook or paper" equation. Most of
the math development in papers is so compressed, one really can't determine
what all the underlying assumptions were that the author used to go from A
to B. One developer may interpret it one way, and another a different way.
Some developers standardize/normalize input data to reduce computational
errors. Others do not. They don't tell you what they do.
Just like I have been saying, stat software packages are all black boxes
being sold by a salesman whose objective is to get his box on the market as
soon as possible to maximize his profit. Let the buyer beware.
DAH
