HOW TO USE DISTRAN

Let

represent the data matrix for the ith subject of r observations on n stimuli. We assume there are M such matrices.

Let D⁽ⁱ⁾ = (d⁽ⁱ⁾_jk)represent the matrix of interpoint distances

between the pair of points j and k for the ith subject. Let

_    _

D = (djk)

average subject.

If the data are standardized, let

represent the data matrix for the ith subject. This is computed simply by the formula

(z_ijt) = ((x_ijt) - (x_it) ) / s_it

where x_it and s_it are respectively, the mean and standard deviation for the tth variable of the ith subject. With no standardization the distance d_ijk is given by the formula:

In the case of standardization, the z values take the place of x values. The distance, d_jk, for the average subject is computed by the formula:

LINE 1: PARAMETER LINE: N,M,STNDD,ITRAN,NUMGEN,IW,ITM (FREE FORMAT)

Number of rows or number of points: N

Number of columns = Number of dimensions of configuration: M

Standardize Input Data:

STNDD = 1 STANDARDIZE INPUT DATA
STNDD = 0 DO NOT STANDARDIZE DATA

Standardization is generally desirable. However, if the option for transposing input data is also used (if ITRAN = 1 and STNDD = 1), then the program will first transpose input data and then standardize the transposed data.

Transpose Input Data:

ITRAN=0 USE INPUT DATA
ITRAN=1 USE TRANSPOSE OF INPUT DATA
NOTE: PROGRAM COMPUTES INTER-ROW DISTANCES

Weighting Parameter

IW=1 Indicates that you are going to provide weights
IW=0 Indicates you will not provide weights.
IF IW=0 WEIGHTS ARE ASSUMED TO BE EQUAL TO 1.0
If you provide weights, line 3 should provide a format to read in weights. The format should completely specify the variable set: that is, if number of columns for example is 12 the following format could be used (12F3.1). The format should be followed by weights.

Number of Distance Matrices

ITM = The number of distance matrices to be calculated under this one control line.
At the end of reading in (ITM) matrices, an average distance matrix is calculated.

LINE 2: INPUT DATA FORMAT (UP TO 80 COLUMNS IN F FORMAT)

If numgen is supplied for generation of random configuration, then additional title information may be entered on LINE 3 (80 CHARACTERS MAX), or you may leave it blank. In any case, an input format statement must appear in the data stream.

LINE 3:FORMAT FOR WEIGHTS, OR IF WEIGHTS ARE NOT USED, LINE 3 ONWARDS IS THE DATA LIST.

1. The raw data including the means and standard deviations.

2. Standardized data coordinates. (When appropriate).

3. Transpose of input data matrix when requested.

4. The standardized (or non-standardized) interpoint distances in half matrix form.

5. The mean interpoint distance of the standardized configuration.

6. Matrix of average distances when ITM greater than 1.

1. This discussion of Distran is taken from P. E. Green and V. R. Rao Applied Multidimensional Scaling, Dryden Press (1972), pp. 187.

    8  2  1  0  0  2
  (3X, 2F2.0)  
  001 2 3    
  002 4 2    
  003 2 1    
  004 7 2    
  005 1 3    
  006 3 1    
  007 1 5    
  008 2 5    
  001 1 2    
  002 4 5    
  003 4 1    
  004 1 3    
  005 2 3    
  006 2 1    
  007 1 6    
  008 1 2 

                                      DISTRAN
                        DISTANCE TRANSPOSE STANDARDIZATION
                           WRITTEN BY F. J. CARMONE  JR.
                                  PC-MDS VERSION

     ANALYSIS TITLE: DISTRAN TEST DATA
     DATA IS READ FROM FILE:  DISTRAN.DAT
     OUTPUT PRINT FILE IS: TEST.PRN                                    
     FINAL OUTPUT DATA FILE IS: TEST.DAT                               
     NUMBER OF ROWS(POINTS) =     8
     NUMBER OF COLUMNS(DIMENSIONS) =     2
      (3X, 2F2.0)                                                      
	  WEIGHTS
        1.00   1.00

     RAW DATA--MEANS--STD DEVIATIONS
             1        2
    1 .200E+01 .300E+01
    2 .400E+01 .200E+01
    3 .200E+01 .100E+01
    4 .700E+01 .200E+01
    5 .100E+01 .300E+01
    6 .300E+01 .100E+01
    7 .100E+01 .500E+01
    8 .200E+01 .500E+01

     MEANS
      .275E+01 .275E+01

     STD DEVIATIONS
      .185E+01 .148E+01

     STANDARDIZED DATA POINTS
          1        2
    1-.405E+00 .169E+00
    2 .674E+00-.507E+00
    3-.405E+00-.118E+01
    4 .229E+01-.507E+00
    5-.944E+00 .169E+00
    6 .135E+00-.118E+01
    7-.944E+00 .152E+01
    8-.405E+00 .152E+01

     STANDARDIZED INTERPOINT DISTANCES
           1       2       3       4       5       6       7   8 
    2   .13E+01
    3   .14E+01 .13E+01
    4   .28E+01 .16E+01 .28E+01
    5   .54E+00 .18E+01 .15E+01 .33E+01
    6   .15E+01 .86E+00 .54E+00 .23E+01 .17E+01
    7   .15E+01 .26E+01 .28E+01 .38E+01 .14E+01 .29E+01
    8   .14E+01 .23E+01 .27E+01 .34E+01 .15E+01 .28E+01 .54E+00
      MEAN INTERPOINT DISTANCE =    1.941

     RAW DATA--MEANS--STD DEVIATIONS
     RAW DATA
             1        2
    1 .100E+01 .200E+01
    2 .400E+01 .500E+01
    3 .400E+01 .100E+01
    4 .100E+01 .300E+01
    5 .200E+01 .300E+01
    6 .200E+01 .100E+01
    7 .100E+01 .600E+01
    8 .100E+01 .200E+01

     MEANS
      .200E+01 .288E+01

     STD DEVIATIONS
      .122E+01 .169E+01

     STANDARDIZED DATA POINTS
          1        2
    1-.816E+00-.517E+00
    2 .163E+01 .126E+01
    3 .163E+01-.111E+01
    4-.816E+00 .739E-01
    5 .000E+00 .739E-01
    6 .000E+00-.111E+01
    7-.816E+00 .185E+01
    8-.816E+00-.517E+00

     STANDARDIZED INTERPOINT DISTANCES
           1       2       3       4       5       6       7    8
    2   .30E+01
    3   .25E+01 .24E+01
    4   .59E+00 .27E+01 .27E+01
    5   .10E+01 .20E+01 .20E+01 .82E+00
    6   .10E+01 .29E+01 .16E+01 .14E+01 .12E+01
    7   .24E+01 .25E+01 .38E+01 .18E+01 .20E+01 .31E+01
    8   .00E+00 .30E+01 .25E+01 .59E+00 .10E+01 .10E+01 .24E+01

     MEAN INTERPOINT DISTANCE =    1.928

DISTRAN TEST DATA                                                     
AVERAGE DISTANCES MATRIX
           1       2       3       4       5       6       7    8
    2   .21E+01
    3   .19E+01 .18E+01
    4   .17E+01 .22E+01 .28E+01
    5   .77E+00 .19E+01 .17E+01 .21E+01
    6   .12E+01 .19E+01 .11E+01 .18E+01 .15E+01
    7   .19E+01 .26E+01 .33E+01 .28E+01 .17E+01 .30E+01
    8   .68E+00 .27E+01 .26E+01 .20E+01 .12E+01 .19E+01 .15E+01