﻿ Anchoring rating scale structures

# Anchoring rating scale structures

Anchoring (fixing) the Rasch-Andrich thresholds (step calibrations) of a rating-scale (or partial-credit scale) enables rating scales in one analysis to be equated to rating scales in another analysis.

Anchoring also enables predetermined threshold values to be imposed on an analysis.

Anchoring for equating

Obtain the Rasch-Andrich thresholds (step calibrations) from Table 8 or from the Anchorfile=.

Table 8.1  Category Statistics.

Model = ?,?,?,?,R12

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

|          DATA            |  QUALITY CONTROL  |RASCH-ANDRICH|

|Category      Counts  Cum.| Avge  Exp.  OUTFIT| THRESHOLDS  |

|   Score    Used   %    % | Meas  Meas   MnSq |Measure  S.E.|

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

|  5   0        1   0%   0%| -6.49  -6.84   .7 |             |

|  6   1        5   2%   2%| -5.89  -6.03   .5 | -7.59   1.03|

|  7   2       16   5%   7%| -3.60  -3.39   .7 | -5.82    .58|

|  8   3       33  11%  19%|  -.85   -.80   .8 | -2.63    .37|

|  9   4       72  24%  43%|  1.26   1.38   .7 |  -.47    .25|

| 10   5       93  31%  74%|  3.59   3.56   .8 |  2.20    .19|

| 11   6       59  20%  94%|  6.36   6.19  1.3 |  5.37    .22|

| 12   7       17   6% 100%|  9.08   9.08   .9 |  8.94    .36|

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

Rating scale = Myscale, R12

5 = bottom, 0, A ; the bottom category has the dummy anchor-value of 0.

6 = , -7.59, A

.....

12 = , 8.94, A

*

Pivot points

The Rating scale= specification provides the capability to choose the pivot point in a dichotomy, rating scale, partial credit or other polytomous structure.

Example: I am setting the standard for a "Competent" essay-writer. I need to anchor the mean for the essays at a particular point on the scale - "good" (6) and/or halfway between 5 and 6. How do I do this?

Here is Table 8 from an unanchored run of Essays.txt. Looking at the "Rasch-Andrich Thresholds" (step calibrations), the standard 0 logit point for the scale is the point on the latent variable at which categories 1 and 9 (the lowest and highest categories) are equally probable.

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

|      DATA            |  QUALITY CONTROL  |RASCH-ANDRICH|  EXPECTATION  |  MOST  |.5 Cumul.| Cat|Response|

| Category Counts  Cum.| Avge  Exp.  OUTFIT| THRESHOLDS  |  Measure at   |PROBABLE|Probabil.|PEAK|Category|

|Score   Used   %    % | Meas  Meas   MnSq |Measure  S.E.|Category  -0.5 |  from  |    at   |Prob|  Name  |

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

|  1        4   4%   4%|  -.86   -.74   .8 |             |( -2.70)       |   low  |   low   |100%| lowest |

|  2        4   4%   8%|  -.11   -.58  2.7 |  -.64    .53|  -1.65   -2.21|        |  -1.75  | 17%|        |

|  3       25  24%  31%|  -.36*  -.40   .9 | -2.32    .39|   -.93   -1.26|  -1.48 |  -1.39  | 48%|        |

|  4        8   8%  39%|  -.43*  -.22   .5 |   .83    .25|   -.41    -.66|        |   -.46  | 11%|        |

|  5       31  30%  69%|  -.04   -.03   .8 | -1.48    .24|    .02    -.19|   -.32 |   -.29  | 39%| middle |

|  6        6   6%  74%|  -.46*   .17  4.1 |  1.71    .25|    .44     .23|        |    .34  |  9%| six    |

|  7       21  20%  94%|   .45    .34   .6 | -1.00    .26|    .94     .68|    .35 |    .47  | 47%|        |

|  8        3   3%  97%|   .75    .50   .5 |  2.36    .44|   1.62    1.24|        |   1.37  | 16%|        |

|  9        3   3% 100%|   .77    .62   .8 |   .54    .60|(  2.69)   2.17|   1.45 |   1.70  |100%| highest|

------------------------------------------------------------(Mean)---------(Modal)--(Median)---------------

If you want the 0 logit point to be that at which categories 5 and 6 are equally probable, then

Rating scale = Creativity,R9 ;Creativity is a rating scale with possible categories 0 to 9

1 = lowest ; name of lowest observed category

5 = middle ; no need to list unnamed categories

6 = six, 0, A      ; anchor point at which 5 and  6 are equally probable at 0 logits

9 = highest ; name of highest observed category

*

If you want the 0 logit point to be that at which category 6 is most probable or at which 6 is the expected average rating (- these are the same point on the latent variable):

Rating scale = Creativity,R9 ;Creativity is a rating scale with possible categories 0 to 9

1 = lowest ; name of lowest observed category

5 = middle ; no need to list unnamed categories

6 = 1.27, 0, A      ; anchor point to make expected measure of 6 at 0 logits

;  1.27 = "Rasch-Andrich threshold for 6" (1.71) - "Expectation" for 6 (.44)

9 = highest ; name of highest observed category

*

If you want the 0 logit point to be that at which 5.5 is the expected average rating:

Rating scale = Creativity,R9 ;Creativity is a rating scale with possible categories 0 to 9

1 = lowest ; name of lowest observed category

5 = middle ; no need to list unnamed categories

6 = 1.48, 0, A      ; anchor point to make expected measure of 6 at 0 logits

;  1.27 = "Rasch-Andrich threshold for 6" (1.71) - "Expectation -0.5" for 6 (.23)

9 = highest ; name of highest observed category

*

Example 2: I want to set the person-item targeting on dichotomous items at 2 logits offset (= 88% probability of success) instead of the usual 0 logits offset (=50% chance of success). This will make all the persons appear to be 2 logits less able.

model = ?,#,MyDichotomy

rating scale = MyDichotomy, R2

0 = 0, 0, A ; place holder

1 = 1, 2, A ; anchored at 2 logits

2 = 2

*

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

|      DATA            |  QUALITY CONTROL  |RASCH-ANDRICH|  EXPECTATION  |  MOST  |  RASCH-  | Cat|Response|

| Category Counts  Cum.| Avge  Exp.  OUTFIT| Thresholds  |  Measure at   |PROBABLE| THURSTONE|PEAK|Category|

|Score   Used   %    % | Meas  Meas   MnSq |Measure  S.E.|Category  -0.5 |  from  |Thresholds|Prob|  Name  |

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

|  0       27  79%  79%|  -.79   -.67   .6 |             |(   .87)       |   low  |   low    |100%| 0      |

|  1        7  21% 100%|  2.34   1.87   .3 |  2.00A      |(  3.07)   1.99|   2.00 |   1.99   |100%| 1      |

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

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