H. D. Vinod, "Review of GAUSS for Windows, Including Its Numerical
Accuracy", Journal of Applied Econometrics, Vol. 15, No. 2, 2000, 
pp. 211-220.


Dear Reader:

Thank you for your interest in using the GAUSS programs to test its
accuracy.

The programs used in this software review may be found in the file
vinod-progs.zip. Since this file was created in a Windows system, Unix users
should use "unzip -a" when unzipping it.

OUTLINE of the contents of this file:

A] PURPOSE. 
B] TARGET AUDIANCE 
C] SUPPORT. 
D] DISCLAIMER. 
E] REFERENCES. 
F] FILE NAMING CONVENTIONS.
G] RECOMMENDED STEPS. 
H] DETAILED DESCRIPTION OF RUNS WITHIN DIRECTORIES
  [H.1] Univariate, [H.2] ANOVA, [H.3] OLS, and 
  [H.3] Nonlinear Least squares.
I] BRIEF DESCRIPTION OF Procs. 
J] CONCLUSION.


A] PURPOSE: These programs are used in creating the tables appearing in
Vinod (2000, Journal of Applied Econometrics).  They show how to test GAUSS
by using NIST(1999) reference datasets and certified answers available on
the Web at the URL below in the list of references.  The directory structure
is designed for the convenience of an occasional user who may want to test
only a few test problems, not the entire set. A directory for a problem has
the problem itself, its step-by-step solution by GAUSS on my platform, the
certified values, etc.  Any updates to the published information will be
posted here.  We hope to give most up-to-date results as GUASS releases new
versions and cooperation by readers will be appreciated and your help will
be acknowledged by name.


B] TARGET AUDIANCE: Use of these programs assumes a good working knowledge
of GAUSS syntax and protocol.  It is written by a nonprofessional programmer
(namely me, H. Vinod) between Jan. to Sept. 1999. I am a professor of
economics at Fordham Univ. in New York.


C] SUPPORT: If you have any questions plese send E-mail to Vinod.  Please do
not ask questions before making a reasonable attempt to self-help. Please be
sure to follow the steps indicated below. I am only familiar with my
particular platform and will not be able to help you with any platform
related problems. I have a Pentium III speed 500MHz 128Meg RAM PC type
computer. My E-mail is vinod@fordham.edu


D] DISCLAIMER: The software is being offered "as is" with no guarantees
explicit or implicit.  The author or his employer are in no way responsible
for any losses financial or otherwise from the use of the software. It may
be copied and used for nonprofit and personal use with proper acknowledgment
to Vinod.

The software may be run on DOS or Windows version of GAUSS. You may need
separate sets of programs for the two, even though there is a lot of
similarity.


E] REFERENCES:

Vinod, H. D. (2000) 'Review of GAUSS for Windows, Including Its Numerical
Accuracy,' Journal of Applied Econometrics (in press)

McCullough, B. D. and H. D. Vinod (1999), 'The Numerical Reliability of 
Econometric Software,' Journal of Economic Literature, 37, 633-665. 

NIST (1999) National Institute of Standards and Technology, US Dept. 
of Commerce, Technology Administration, Gaithersburg, MD 20899-001, 
Statistical Reference Data Sets (StRD).  
download at: www.itl.nist.gov/div898/strd/general/dataarchive.html


F] FILE NAMING CONVENTIONS:
All files are in plain ASCII text format even though
the filename-extension is not txt.

There are five directories in the zip file:

root	mainly contains commonly needed GAUSS procedures
	Each *.g (or procedure) file explains exactly what it does.
	
univ	has nine univariate problems.

anova	has eleven analysis of variance problems.
	There are subdirectories for each NIST-StRD problem of this set.
	Let pnam="problem name" close to the name in NIST-StRD 
	(sometimes abridged) the directory name is close to pnam.
	
ols	has ordinary least squares problems..
	There are 11 subdirectories for each NIST-StRD problem of this set.
	
nls	has nonlinear least squares problems.
	There are 27 subdirectories for each NIST-StRD problem of this set.


G] RECOMMENDED STEPS:

1) Choose your root directory and copy the programs and subdirectories you
   may be interested in. If you are using DOS version check the file called
   gogauss.bat

2) Run all procedures *.g files on your platform and make sure they are
   accessible.  This is a very important step. It is platform dependent, and
   I can help only if your platform resembles mine.

   To run the procedures in the Windows version you will simply edit and run
   vinodjae.src and vinodols.src files. vinodols.src files is from the
   directory OLS needed there when one uses the QR algorithm to do the OLS
   estimation. The QR algorithm is known to have better numerical accuracy.
   These files collect the *.g files of DOS version together You must run
   them first to make sure everything is ok.

   My windows version is in C:\gausswin. I have c:\gausswin\lib\user.lcg. A
   copy of this file is named user-lcg.txt is included here for your
   convenience.  You may want your current user.lcg to have these statements
   included. be sure to check the path of the location of files

3) Run the specific problem files in proper sequence.
   Recall that pnam="problem name" is close to the name 
   in NIST-StRD (sometimes abridged) and is also the subdirectory name.


H] DETAILED DESCRIPTION OF RUNS WITHIN DIRECTORIES

H.1] UNIV: UNIARIATE set of NIST has 9 problems.
  Let "problem name"=pnam for the purpose of following description.
  c:\jae\univ
      subdirectory is UNIV.  There are no further subdirectories here.
      pnam without any extension has GAUSS program.
      pnam.out with "out" as its extension has the output files.
      pnam.dat has data files downloaded from NIST-StRD.
      *.g  are procedure files.
      A new kind of improved mean and standard deviation is implemented
      which does improve the NAD (no of accurate digits) score.
      See McCullough-Vinod (1999) for theory of improved mean algorithms.

H.2] ANOVA:  Analysis of Variance set has 11 problems and as many 
  subdirectories.
  c:\jae\anova
      subdirectory is ANOVA
      see files named anov.g and anov2.g in the root directory c:\jae
      Each proc file does explain exactly what it does.

problem name=pnam
there are 11 subdirectories for each problem

pnam.dat  has data
panm.txt  has gauss program
pnam.out  has output file (text format)
pnam.ori  has original information downloaded form NIST-StRD

      A new kind of improved mean and standard deviation is implemented
      which does improve the NAD (no of accurate digits) score.
      anov2.g  does this work

H.3] OLS:  ordinary least squares
c:\jae\ols is the subdirectory within which there are 11 subdirectories.

For my own procedures used here, see files named *.g in the root directory
c:\jae. Each proc file does try to explain exactly what it does.

Let us denote "problem name"=pnam
there are 11 subdirectories for each OLS problem

pnam.dat  has data
panm.txt  has gauss program
pnam.out has output file
pnam.ori  has original information downloaded form NIST-StRD
In some cases pnam.ori file is absent but all the information
as downloaded is included in the pnam.txt file itself with
generous use of comment symbols.

H.4] NLS
Nonlinear least squares
c:\jae\nls is the subdirectory within which there are 27 subdirectories.

We test GAUSS program called CO (constrained optimum)
using NIST-STRD data sets

The CO manual (p. 48) suggests 'Newton' algorithm (among 5 choices),
'Brent' line search (4 choices),
and central differences for numerical gradients (2 choices).

Among the 5x4x2=40 ways of solving each nonlinear regression problem,
we expect a typical researcher to use the choice in the manual. Since
different choices yield different NADs, one may compare the final values
of the minimands. Accordingly, for some examples, we also consider the
'bfgs' algorithm with the 'stepbt' line search and pick the solution with
the smallest minimand. Future CO versions should automate ranking
and selection among the many choices.

Recall that we denote a problem name by "pnam".
There are 27 problems in NLS set
each problem has its own sub directory

files named  pnam.ori have original data

files named pnam.1 have 1st stage run which genreates
   bh.fmt
   a vector of estimates.

Two stages are necessary to cover the possibility of
non convergence of the first stage algorithm.

Files named pnam.2 are to be run only after the files named
pnam.1 are run.
Their outputs are called  pnam.ou1 and pnam.ou2 respectively.

The run times in output files are on a Pentium III  speed 500MHz
128Meg RAM PC type computer.


I] BRIEF DESCRIPTION OF Procs
anov.g proc Computes analysis of variance ratio
  F statistic=(mean square between group means)/(mean sq within groups)
  ssd is called output is within, between, and F.

anov2.g proc is similar to anov.g except that it calls ssd2

autocor.g proc computes specified autocorrelations for each column 
   of a matrix. The data are assumed to have 0 mean. 
   Use x = x-meanc(x)'  if necessary.

gogauss.bat file this is a batch file useful for getting GAUSS
   to find the needed files, proc files etc. The way I use it
   is to type gogauss before anything, then type gauss and then edit

meanc2.g proc Computes numerically more accurate column means
  author H. D. Vinod,  March 9, 1999
  Reference: R. F. Ling,  JASA, vol 69, p.859

nistols.g proc to compute the ols tests using NIST -STRD datasets
  DO NOT include col of ones for the intercept, it is automatic.
    cb=certified values of b the regr coefficients
    cstdb= certified standard errors for b
    cr2=certified R-square
  Output:  printout of NAD results
  needs a proc for NAD calculation of scalars called numacc.g and
  another proc for NADs as the minimum from a vector of NADs numaccv2.g

nistolsf.g   f => regr. line is forced  through the origin otherwise 
  similar to nistols.g  

nistuni2.g proc is a 2nd version using numerically superior meanc2.g 
   and stdc3.g procs to compute the mean std.dev and autocorrelation
   coefficient
   as done by NIST-StRD to find the no of accurate digits or NADs
   Input: y=data col.vector
      cybar=certified mean
      csig=certified standard deviation
      crho1=certified 1st order autocorrelatin coeff using NIST formula
   Output:  printing of NADs for mean, std.dev and autocorr. coeff
   needs a proc for NAD calculation of scalars called numacc.g
   
nistuniv.g proc is similar to nistuni2.g described above.  This is
    the first version using GAUSS's meanc(x) to compute means.

numacc.g proc to compute the Number of accurate digits NADs 
     As described in the text Vinod (2000)
    Also, See McCullough, Amer Statistician
      eq.(2) page 360, Nov. 1998 for definition of NAD 
    input q=observed value (or estimated value)
        c=certified value
    output: NAD number of accurate digits 

numaccv.g is vector version of Numacc.g described above. It returns
    the smallest NAD after computing the NAD for each vector element.

numaccv2.g is vector version of Numacc.g described above. It returns
    the smallest NAD after computing the NAD for each vector element.
    The 2 in its name refers to 2nd version for detailed printing of
    Estimated value,  Certified value,  Absolute difference |q-c|, etc.

reshape2.g is an improved version of GAUSS's reshape where one does 
      not have to input the number of rows in the data

ssd.g proc computes sum of squared deviations(ssd) from the 
      column means  using GAUSS's meanc

ssd2.g proc is similar to ssd.g above, except that it uses meanc2.g
      to compute column means.


J] CONCLUSION:

Again, thanks for your interest. Please help me in updating this.
Hope this is useful and eventually leads to better software and
more reproducible econometrics.

 These routines and the associated files may be used freely for
 non-commercial purposes, provided that proper attribution is made.
 Please cite the paper

Vinod, H. D. (2000) "Review of GAUSS for Windows, Including Its Numerical
Accuracy", Journal of Applied Econometrics (in press)

 The routines and files may not be incorporated into any book
 or computer program without the express, written consent of the author.

H. D. Vinod
vinod@fordham.edu
Updated on: March 27, 2000
Modified by JGM: April 7, 2000