[Rasch] Person Dimensionality

Stoeckel, Tim tstoecke at sky.miyazaki-mic.ac.jp
Fri Dec 12 11:02:05 EST 2014


Dear all,

I would appreciate your thoughts on output from Winsteps showing person
dimensionality for a simulated data. My apologies for the lengthy post; I
highlighted my questions so that they are easy to see.



For the simulation, I created a normally distributed sample of 1,000
persons and distributed 140 multiple-choice items equally across a range of
difficulties. Five hundred persons never guessed on unknown test items
(instead, they responded with an “I don’t know” option), and the other 500
persons always guessed. For the latter, unknown items had a 25% chance of
being answered correctly. The resulting dataset was Rasch analyzed, with
persons labeled as either “IDK” or “guesser”.



My thoughts/questions on the output below:

By conventional criteria, the unexplained variance in the first contrast is
too small to be considered a secondary dimension. This seems to be
supported by the low values for residual loadings. However, there is an
obvious and extreme pattern of person loadings according to whether they
were guessers or not (this pattern continues with remarkable consistency
throughout).



*In your opinions, would it be appropriate to refer to this as a dimension?
If not, how might it be referred to?  *I am considering describing this as
something like “The pattern of residual loadings in the data suggests
[quite clearly?] that test scores reflect not only the primary latent
construct but also willingness to skip unknown test items. *Would you agree
with that interpretation of the data?*



It should also be noted that person numbers are ordered according to
ability; 1 = lowest ability, 1000 = highest ability. From this it also
seems evident to me that the persons most affected by this are those of
lowest ability (the guessers in the right hand column are ordered more or
less from low to high throughout). This makes sense to me as low-ability
guessers would have to most to gain. *Does this interpretation make sense
to you?*


Best,


Tim Stoeckel



*Output from Table 24 of Winsteps:*

Table of STANDARDIZED RESIDUAL variance (in Eigenvalue units)

                                                 -- Empirical --    Modeled

Total raw variance in observations     =       1629.2 100.0%         100.0%

  Raw variance explained by measures   =        629.2  38.6%          38.7%

    Raw variance explained by persons  =        184.7  11.3%          11.4%

    Raw Variance explained by items    =        444.6  27.3%          27.3%

  Raw unexplained variance (total)     =       1000.0  61.4% 100.0%   61.3%

    Unexplned variance in 1st contrast =         23.2   1.4%   2.3%

    Unexplned variance in 2nd contrast =         13.1    .8%   1.3%

    Unexplned variance in 3rd contrast =         12.6    .8%   1.3%

    Unexplned variance in 4th contrast =         12.4    .8%   1.2%



STANDARDIZED RESIDUAL LOADINGS FOR PERSON (SORTED BY LOADING)



---------------------------------------------------------
--------------------------------------------------

|CON-  |       |       INFIT OUTFIT| ENTRY              | |       |       INFIT
OUTFIT| ENTRY              |

| TRAST|LOADING|MEASURE  MNSQ MNSQ |NUMBER PERSON       |
|LOADING|MEASURE  MNSQ
MNSQ |NUMBER PERSON       |

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

|  1   |   .47 |    1.11  .63  .47 |A  901 IDK      901 | |  -.43 |     .07
1.51 1.61 |a   98 guesser   98 |

|  1   |   .42 |    1.30  .67  .47 |B  911 IDK      911 | |  -.42 |     .29
1.53 1.74 |b  108 guesser  108 |

|  1   |   .42 |    1.54  .72  .47 |C  959 IDK      959 | |  -.41 |    -.16
1.67 1.90 |c    4 guesser    4 |

|  1   |   .39 |     .34  .68  .55 |D  755 IDK      755 | |  -.41 |    -.16
1.57 1.79 |d   78 guesser   78 |

|  1   |   .38 |    1.02  .69  .51 |E  929 IDK      929 | |  -.36 |    -.07
1.54 1.84 |e   36 guesser   36 |

|  1   |   .36 |    1.11  .70  .55 |F  823 IDK      823 | |  -.36 |    -.07
1.54 1.74 |f   90 guesser   90 |

|  1   |   .36 |     .70  .71  .55 |G  837 IDK      837 | |  -.35 |    -.35
1.60 1.98 |g    8 guesser    8 |

|  1   |   .35 |    1.07  .68  .49 |H  831 IDK      831 | |  -.34 |    -.68
1.60 2.16 |h    2 guesser    2 |

|  1   |   .35 |     .88  .70  .52 |I  919 IDK      919 | |  -.34 |    -.07
1.65 2.00 |i   50 guesser   50 |

|  1   |   .34 |    1.16  .73  .52 |J  909 IDK      909 | |  -.34 |    -.07
1.48 1.78 |j   38 guesser   38 |

|  1   |   .33 |     .57  .71  .64 |K  735 IDK      735 | |  -.34 |     .48
1.41 1.49 |k  182 guesser  182 |

|  1   |   .32 |     .34  .70  .60 |L  613 IDK      613 | |  -.33 |     .07
1.39 1.51 |l  140 guesser  140 |

|  1   |   .31 |     .52  .67  .73 |M  825 IDK      825 | |  -.33 |     .52
1.34 1.29 |m  474 guesser  474 |

|  1   |   .31 |    1.45  .76  .52 |N  953 IDK      953 | |  -.33 |    -.49
1.37 1.75 |n   40 guesser   40 |

|  1   |   .31 |    -.25  .68  .62 |O  347 IDK      347 | |  -.32 |     .61
1.39 1.48 |o  240 guesser  240 |

|  1   |   .30 |     .79  .72  .57 |P  791 IDK      791 | |  -.31 |    -.30
1.72 2.12 |p   22 guesser   22 |

|  1   |   .30 |     .39  .66  .57 |Q  641 IDK      641 | |  -.30 |     .16
1.29 1.39 |q  104 guesser  104 |

|  1   |   .30 |    1.49  .77  .53 |R  906 guesser  906 | |  -.29 |     .16
1.33 1.50 |r   94 guesser   94 |

|  1   |   .29 |     .48  .71  .57 |S  617 IDK      617 | |  -.29 |    -.11
1.49 1.66 |s   46 guesser   46 |

|  1   |   .29 |    1.64  .80  .56 |T  969 IDK      969 | |  -.29 |     .25
1.42 1.69 |t  106 guesser  106 |

|  1   |   .29 |    1.69  .79  .52 |U  983 IDK      983 | |  -.28 |     .57
1.47 1.63 |u  184 guesser  184 |

|  1   |   .29 |     .34  .72  .59 |V  701 IDK      701 | |  -.28 |     .02
1.49 1.63 |v   34 guesser   34 |

|  1   |   .29 |     .25  .74  .63 |W  569 IDK      569 | |  -.28 |     .70
1.30 1.16 |w  368 guesser  368 |

|  1   |   .29 |     .02  .75  .60 |X  413 IDK      413 | |  -.28 |    -.68
1.41 1.83 |x   12 guesser   12 |

|  1   |   .28 |    -.30  .73  .62 |Y  195 IDK      195 | |  -.27 |     .34
1.49 1.63 |y  128 guesser  128 |

|  1   |   .28 |     .11  .69  .57 |Z  497 IDK      497 | |  -.27 |    -.63
1.53 2.09 |z   32 guesser   32 |
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