Example 13: Paired comparisons as the basis for measurement

Paired comparisons can be modeled directly with the Facets computer program. For Winsteps a dummy facet of "occasion" or "pairing" must be introduced. On each occasion (in this example, each column), there is a winner '1', a loser '0', or a draw 'D' recorded for the two players. The data can be set up with the paired objects as rows and the pairings as columns, or the paired objects as columns or the pairings as rows. Analytically it makes no differences, so do it the way that is easier for your.

 

In this example, the paired objects are the rows, and the pairings are the columns. In column 1 of the response data in this example, Browne (1) defeated Mariotti (0). In column 2, Browne (D) drew with Tatai (D). Specifying PAIRED=YES adjusts the measures for the statistical bias introduced by this stratagem. Each player receives a measure and fit statistics. Occasion measures are the average of the two players participating. Misfitting occasions are unexpected outcomes. Point-biserial correlations have little meaning. Check the occasion summary statistics in Table 3.1 to verify that all occasions have the same raw score.

 

; This common control file is EXAM13.TXT

TITLE = 'Chess Matches at the Venice Tournament, 1971'

Name1 = 1  ; Player's name

Item1 = 11  ; First match results

PERSON = PLAYER

ITEM   = MATCH ; Example of paired comparison

CODES  = 0D1  ; 0 = loss, D = draw (non-numeric), 1 = win

 

; if you wish to just consider won-loss, and ignore the draws, omit the following line:

NEWSCORE = 012 ; 0 = loss, 1 = draw, 2 = win

 

CLFILE=*

0 Loss

D Draw

1 Win

*

NI     = 66  ; 66 matches (columns) in total

PAIRED = YES  ; specify the paired comparison adjustment

INUMBER = YES  ; number the matches in the Output

&END

Browne    1D 0  1   1    1     1      D       D        1         1          

Mariotti  0 1 D  0   1    1     1      D       1        D         1         

Tatai      D0  0  1   D    D     1      1       1        1         D        

Hort         1D1   D   D    1     D      D       D        1         0       

Kavalek         010D    D    D     1      D       1        1         D      

Damjanovic          00DDD     D     D      D       1        D         1     

Gligoric                 00D0DD      D      1       1        1         0    

Radulov                        000D0DD       D       1        D         1   

Bobotsov                              DD0DDD0D        0        0         1  

Cosulich                                      D00D00001         1         1 

Westerinen                                             0D000D0D10          1

Zichichi                                                         00D1D010000

 

Part of the output is:

 

         PLAYER STATISTICS:  MEASURE ORDER                             

+---------------------------------------------------------------------+

|ENTRY   RAW                        |   INFIT  |  OUTFIT  |           |

|NUMBR  SCORE  COUNT  MEASURE  ERROR|MNSQ  ZSTD|MNSQ  ZSTD| PLAYER    |

|-----------------------------------+----------+----------+-----------|

|    1     17    11     1.09     .35|1.10    .2|1.02    .1| Browne    |

|    2     15    11      .68     .32|1.02    .0| .96   -.1| Mariotti  |

|    3     14    11      .50     .31| .86   -.4| .83   -.5| Tatai     |

|    4     14    11      .50     .31|1.34    .9|1.54   1.3| Hort      |

|    5     13    11      .33     .31| .81   -.6| .80   -.6| Kavalek   |

|    6     11    11      .00     .30| .35  -2.8| .37  -2.6| Damjanovic|

|    7     10    11     -.17     .30| .90   -.3| .91   -.3| Gligoric  |

|    8      9    11     -.34     .31| .52  -1.8| .52  -1.7| Radulov   |

|    9      8    11     -.51     .31|1.00    .0|1.00    .0| Bobotsov  |

|   10      8    11     -.51     .31|1.18    .5|1.15    .4| Cosulich  |

|   11      7    11     -.69     .32| .95   -.1| .89   -.3| Westerinen|

|   12      6    11     -.88     .33|1.86   1.8|1.90   1.7| Zichichi  |

|-----------------------------------+----------+----------+-----------|

| MEAN     11.   11.     .00     .32| .99   -.2| .99   -.2|           |

+---------------------------------------------------------------------+


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Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar Journal of Applied Measurement Rasch models for measurement, David Andrich Constructing Measures, Mark Wilson Rasch Analysis in the Human Sciences, Boone, Stave, Yale
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