ProfitPress Mega CDROM2 …eeware (MSDOS)(1992)(Eng)/ProfitPress-MegaCDROM2.B6I/APPS/STATISTI/TS5ST12.ZIP/STATLADR.INF

Text File | 1990-12-23 | 11.4 KB | 245 lines

23rd December, 1990

About TS5ST in General  (Least absolute deviation multiple regression)
======================

Contents:
1. Introduction
2. Genenral description of statladr
3. Standard errors and goodness of fit statistics
4. Release notes


1. INTRODUCTION

Apply question mark ? with the program call for a brief description of a
program.

This package may be used and distributed freely for NON-COMMERCIAL,
NON-INSTITUTIONAL, PRIVATE purposes, provided it is not changed in any way.
┌────────────────────────────────────────────────────────────────────────────┐
│ For ANY other usage (such as use in a business enterprise or a university) │
│ or the full scale version contact the author for a personal or a site      │
│ license.                                                                   │
└────────────────────────────────────────────────────────────────────────────┘
Please do not distribute any part of this package separately. Uploading to
BBSes is encouraged.

The registered version is strictly for the registrant only. Identical
programs must NOT be running on more than one computer at a time. Site
licensed programs must not be run outside the licensed site.

The programs are under development. Comments and contacts are solicited. If
you have any questions, please do not hesitate to use electronic mail for
communication.
InterNet address: [e-mail]         (preferred)
Funet address:    GADO::SALMI
Bitnet address:   SALMI@FINFUN
FidoNet address:  2:515/1 (Micro Maniacs Opus, To: Timo Salmi)

The author shall not be liable to the user for any direct, indirect or
consequential loss arising from the use of, or inability to use, any program
or file howsoever caused. No warranty is given that the programs will work
under all circumstances.

Timo Salmi (in collaboration with Seppo Pynnönen)
Professor of Accounting and Business Finance
School of Business Studies, University of Vaasa
P.O. BOX 297, SF-65101 Vaasa, Finland


2. GENERAL DESCRIPTION OF STATLADR (Ver. 1.1)

   STATistics: Least Absolute Deviation multiple REGRession analysis is part
of the interactive statistical system by Timo Salmi. It is the fifth program
in the set. The first program in the set is STATistical MEASures (STATMEAS in
TS1STxx.ARC), which is intended for univariate analysis. The second program
in the set is STATistics: multiple REGRession analysis (TS2STxx.ARC). The
third program in the set is STATistics: TRANsformations (STATTRAN in
TS3STxx.ARC), which can be used for transforming the observations, and, if
necessary, also as an editor. The fourth program in the set is STATistics:
Ranks and CORrelations (STATRCOR in TS4STxx.ARC).

   STATLADR includes a handy built-in help system, which can be invoked by
typing ? at any interactive question. Because of this built-in help, and the
interactive nature of the program's user interface, no long-winding
instructions have been included. (Who reads instructions anyhow?)

   The program performs least absolute deviation (LAD) multiple regression
analysis, that is, estimates the coefficients of
        Y = a + b(1)X(1) + ... + b(M)X(M)
from a set of observations. Whereas in ordinary least squares estimation
(OLS) the sum of squared deviations between the observations and the
regression equation is minimized, in LAD estimation the sum of the absolute
deviations between the observations and the regression equation is minimized.
Least absolute deviation multiple regression is thus equivalent to the
following linear goal programming programming problem:

       n
  Min Sum (Pj + Nj)
      j=1

  subject to
                       ┌────┬─ absolute deviation
       n               │    │
  a + Sum x(i,j)b(i) + Pj + Nj  = y(j)
      j=1 │                       │
          └─ explaining variables └─ dependent variable

STATLADR finds the estimates of the intercept [a] and the regression
coefficients [b(i)] by solving this linear goal programming problem.
   If the explaining variables are very similar (multicollinearity), problems
tend to occur both in OLS and LAD regression estimation, and the estimates
become very unstable. Further problems of significance can arise if the
values of the explaining variables are of a very different scale. To test the
reliability of the solution algorithm to inaccuracy indexes are computed and
displayed. These are called the NON-OPTIMALITY OF THE LP SOLUTION and
INACCURACY OF THE LP SOLUTION. The nearer to zero these figures, the less
probability of computationally weak estimates. Although seldom reported,
these problems are inherent to most (even the top commercial) statistics
packages. For those in the know, the former index is the sum of positive
coefficients in the optimal simplex-tableau. Mathematically they all are
non-positive, but round-offs may cause some of them remain small positive
numbers. The latter is based on the recalculating the optimal simplex-tableau
on from the inverse of the basis matrix, and calculating the deviation of
each item in the recalculated optimal simplex-tableau as compared with the
original optimal simplex tableau. The inaccuracy indexes are calculated as a
so called norm, that is the square root of the sum of the squared deviations.
This measure is used because mathematically it represents the length of the
deviation vector.

   Furthermore, STATLADR draws both low-resolution and high-resolution
scatter diagrams of the data, and of the regression analysis results. The
low-resolution scatter diagrams are drawn, or rather written, using ordinary
ascii text, and they can thus be directed to a file. The high-resolution
(graphics) scatter diagrams can only be displayed on the screen.

  The data can either be given from the keyboard or taken from a file. If the
input is to be taken from a file it must first be prepared with some editor,
or some word processor which includes an option for preparing ordinary ascii
text. (Also STATTRAN can be used for this purpose.)
   The data is given to the program in the following format:

       X1 X2 X3                    !variable names (! denotes a comment)
       3.56 6.32 -1.73
       5.12 -4.21 9.18
       14.2 5.11 0.31
       END                         !END is optional in a file

A missing item in an observation is marked by a hash (#). E.g. if the first
item of the second observation were missing, the observation should be
written as  # -4.21 9.18

   The items in an observation can be separated with blanks, as in the above,
or with commas (,) e.g. 5.12,-4.21,9.18. The number of the intervening
blanks is irrelevant, and can be customized for increased readability. Thus
e.g. 5.12 -4.21 9.18 and    5.12    -4.21     9.18    are equivalent.
   A row can be continued using an ampersand (&). E.g. the variables could
be given as
       X1 X2 &
       X3
Alternatively, * or \ can be used instead of & as the continuation marker.

   Comments can be added to the input data. If ! appears on a line all text
after ! will be considered as a comment.
   A header can be entered on each page if output is directed to a file.
To accomplish this start the very first line on the input file with a
double exclamation mark (!!) and the rest of the line will be used as the
header. Thus !! indicates a header, a single ! an ordinary comment.

   The maximum number of variables is 25. The maximum number of observations
is 100 (for each variable). The public domain version, however, sets the
limits at 4 and 50 respectively.


3. STANDARD ERRORS AND GOODNESS OF FIT STATISTICS

   This chapter describes the formulas of the new features that were added
to statladr.exe in the updated version 1.1. This chapter has been written by
Seppo Pynnönen.

   The standard errors of the estimates of the regression coefficients are
calculated as

                               jj
               std(b) = s * X'X  ,


where X is the n x (M+1) data matrix of x variables with vector of ones in
                     jj
the first column, X'X   denotes the j:th diagonal element of the inverse of
the X'X-matrix and the prime (') stands for the transpose, s is an estimate
of the standard error of the residual terms of the regression model. (n
stands for the number of observations, and M for the number of explanatory
variables.) Here we have defined the standard error (s) of the residuals as

                   1
             s = ------,
                  2f(m)

where
                        2d
          f(m) = -------------------
                 n(e      - e      )
                    (m+d)     (m-d)

with d defined below, e    denote the ordered residuals, and m is the median
                       (j)
point of the ordered residuals. The parameter d depends on the sample size.
In the literature it is suggested that it should be kept small. Here we have
adopted the following convention and defined d as

             d = max[1, n'/6],

where n' = n-M-1 (i.e., the number of residuals which are not zero by
definition due to the LP-solution).

   The t-values are defined as b(j)/std(b) (j = 0, 1, ..., M, with b(0),
the intercept term), where std(b) is defined in the previous paragraphs.

   The LAD coefficient of determination is defined as

                                              Sum |e(i)|
                                               i
   LAD COEFFICIENT OF DETERMINATION = 1 - ------------------
                                          Sum |y(i) - Md(y)|
                                           i

(cf. the R-square in the OLS-regression), where Md(y) is the median of y.


4. RELEASE NOTES

   Version 1.1: The most important inprovements were descibed in the previous
chapter.
   Furthermore, I have corrected a bug, which decreased the maximum capacity
of the program by one observation.
   Some stytistic minor imporvements have also been made.

   Version 1.2: Several improvements to the nuts and bolts of the user
interface.
   The new usage of the call is
PROGNAME [/h(elp)] [/iInputFileName] [/oOutputFileName] [/cColumnsPerRow]
(the /c option, which regulates the width of the output, is for registered
versions, only). If you use the /i switch, it stuffs the InputFileName into
the appropriate recall buffer. This means that when the program asks you for
the input file name, you can invoke the input file name just by pressing the
CursorUp key. (The same goes for the /o switch, respectively.) This is very
convenient, if you use the program many times successively making small
changes in your data in between. (This assumes, of course, that you have a
command line editor like DOSEDIT or CED to recall previous MsDos commands.
These common shareware programs can be obtained from any well-stocked BBS or
FTP site.)
   The printer readiness test has been rewritten to be more general. The
earlier test failed for some printers, because the codes the printers send
when they are offline are not standardized.
   The "file exists, overwrite?" question is no more asked when the output
file is prn, in other words when the output is directed to the printer.
   The user has now a choice of a left margin from 0 to 20 blanks when output
is directed to the printer.
   The user has now a choice between formfeed and four blank lines to start
each new page of output.
   When an input file is not found, the user is given the choice of listing a
directory. The directory routine has been rewritten.
   The file ready message now also includes the file side besides the name.