Do not use this file for anchor values. Instead use IFILE= (becomes IAFILE=) and SFILE= (becomes SAFILE=).
Communicating the functioning of a rating scale is challenging, especially if your audience think of its categories as separate and equally-spaced points on the latent variable.
If you want to communicate the categories as points, then the best points for the intermediate categories are the locations on the latent variable at which the probability of observing each category is the highest. These are also the points where the expected score on the item is the category value. In Winsteps these are the "AT CAT" measures in the ISFILE= output file. These points are at infinity for the extreme categories, so Winsteps reports the measures for expected scores of "lowest category + 0.25" ( = CAT +0.25) and "highest category - 0.25" (= CAT - 0.25).
The Rasch-Thurstone thresholds (50%PRB in ISFILE=) dichotomize the rating scale at each category boundary into 50% probability of being observed below the category and 50% probability of being observed in or above the category.
The points on the latent variable where the expected scores are 2.5, etc., are called the CAT-0.5 points in ISFILE=.
The Rasch item difficulty (in IFILE=) is the point on the latent variable at which the highest and lowest categories are equally probable.
ISFILE=? opens a Browse window
ISFILE=filename produces an output file containing the category structure measure (Andrich threshold) information for each item. All measures are added to the corresponding item's calibration and rescaled by USCALE= and UDECIMALS=. This file contains 4 heading lines (unless HLINES=N), followed by one line for each item containing:
Columns: |
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Start |
End |
Heading |
In Table |
Description |
1 |
1 |
|
Blank or ";" if no responses or deleted (status = -2, -3) |
|
2 |
6 |
ENTRY |
The item sequence number |
|
7 |
11 |
STATUS STAT |
2. The item's status 1 = Estimated calibration 2 = Anchored (fixed) calibration 3 = Anchored (fixed) calibration with extreme (minimum or maximum) observed raw score 0 = Extreme minimum (estimated using EXTRSC=) -1 = Extreme maximum (estimated using EXTRSC=) -2 = No responses available for calibration -3 = Deleted by user |
|
12 |
16 |
MAXIMUM MAX |
Number of active categories |
|
17 |
21 |
CAT BOT |
Lowest active category number, bottom category |
|
22 |
29 |
BOT+.25 |
2.2 |
Measure for an expected score of bottom category + LOWADJ= Useful as a measure for a performance in the bottom category, for which the performance range extends to -infinity. |
The following fields are repeated for the remaining active categories: |
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30 |
34 |
CAT |
Active category number |
|
35 |
39 |
ORDINAL ORD |
Ordered category number in structure = "Step counting from bottom category" |
|
40 |
47 |
THRESHOLD THRESH |
|
Rasch-Andrich threshold (step difficulty) relative to item difficulty = Rasch parameter Fj. Use this or SFILE= for anchoring in SAFILE=. |
48 |
55 |
I+THRESH I+THRSH |
2.4 |
item measure + Rasch-Andrich threshold = Structure measure = Step calibration = Rasch parameter Dij. Do not use for anchoring. Use SFILE= for SAFILE= and IFILE= for IAFILE=. |
56 |
63 |
S.E. |
|
Rasch-Andrich threshold's standard error, with the item difficulty S.E. assumed to be 0.0. |
64 |
71 |
CAT-0.5 |
2.2 |
Measure for an expected score of category - 0.5 score points. This is the Rasch-half-point threshold, the boundary between categories when conceptualized as average performances. It is not a model parameter. TOP-0.5 for the highest (top) category, |
72 |
79 |
AT CAT (TOP-0.25) |
2.2 |
Measure for an expected score of category score points (AT CAT). This is the measure corresponding to a category when predicting for an individual or sample about which nothing else is known. For items with fewer rating-scale categories, the AT CAT value shown for the highest category is the TOP-0.25 value. |
80 |
87 |
PR50% |
2.3 |
Probability 50%. Measure at Rasch-Thurstone threshold = 50% cumulative probability. |
Only for the top (highest) category |
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|
|
TOP-0.25 |
2.2 |
For the highest (top) category this value corresponds to the top category value less HIADJ= , the measure for an expected score of HIADJ= score points less than the top category value. This is useful as a measure for a performance in the top category, for which the performance range extends to infinity. For items with fewer rating-scale categories, the AT CAT value shown for the highest category is the TOP-0.25 value. |
|
|
ITEM |
|
Item label |
The "AT CAT" values in the ISFILE= are based on the Rasch-model. They are the points on the "expected score" ogive for the rating scale (also called "the model ICC") at which the expected score = the category number. This is also the point at which the probability of observing the category is highest.
For extreme categories (top and bottom of the rating scale), the model values are infinite, so an adjustment is made. The "AT CAT" values correspond to expected scores bottom+0.25 score points and top-0.25 score points. These provide reasonable estimates for performance in the extreme categories of the rating scale. The adjustment of 0.25 can be changed with LOWADJ= and HIADJ=. The "AT CAT" values are plotted on Table 2.2.
Since the ISFILE= has the same number of category entries for every item, the repeated fields are filled out with "0" for any further categories up to the maximum categories for any item.
When CSV=Y, commas separate the values with quotation marks around the "Item name". When CSV=T, the commas are replaced by tab characters.
When STKEEP=YES and there are intermediate null categories, i.e., with no observations, then the Rasch-Andrich threshold into the category is set about 40 logits above the previous threshold. The threshold out of the category, and into the next category, is set about 40 logits above. The exact values depend on the category frequencies of the observed categories. Thus:
Rasch-Andrich Thresholds for Unobserved Categories |
||
Category |
in Table 3.2 |
in SFILE= |
0 (observed) 1 (observed) 2 (unobserved) 3 (observed) |
NULL -1.00 NULL 1.00 |
0.00 -1.00 39.00 -38.00 |
Total: |
0.00 |
0.00 |
Meanings of the columns
There are several ways of conceptualizing the category boundaries or thresholds of a rating (or partial credit) scale item. Imagine a rating (or partial credit) scale with categories, 1, 2, 3:
From the "expected score ogive", also called the "model item characteristic curve"
Average rating: |
Measure (must be ordered) |
1.25 |
Measure for an expected score of 0.25 (BOT+.25) when LOWADJ=0.25 |
1.5 |
Measure for an expected score of category - 0.5 score points (CAT-0.5) |
2.0 |
Measure for an expected score of category score points (AT CAT) |
2.5 |
Measure for an expected score of category - 0.5 score points (CAT-0.5) |
2.75 |
Measure for an expected score of category score points (AT CAT) |
From the "category probability curves" relative to the origin of the measurement framework (need not be ordered)
1-2 equal probability |
Structure measure = Rasch-Andrich threshold + item measure = Dij (MEASURE) |
standard error |
Rasch-Andrich threshold's standard error (ERROR) |
2 maximum probability |
Measure for an expected score of category score points (AT CAT) - (yes, same as for the ogive) |
2-3 equal probability |
Structure measure = Rasch-Andrich threshold + item measure = Dij (MEASURE) |
standard error |
Rasch-Andrich threshold's standard error (ERROR) |
From the "cumulative probability curves" (preferred by Thurstone) (must be ordered)
Category 1 at .5 probability |
Measure at the Rasch-Thurstone threshold = 50% cumulative probability (50%PRB) |
Category 1+2 at .5 probability |
Measure at the Rasch-Thurstone threshold = 50% cumulative probability (50%PRB) |
Example 1: You wish to write a file on disk called "ITEMST.FIL" containing the item statistics reported in Table 2.2, for use in constructing your own tables:
ISFILE = ITEMST.FIL
ISGROUPS = 0 ; each item has its own "partial credit" scale
LOWADJ = 0.25 ; the standard for the low end of the rating scale
HIADJ = 0.25 ; the standard for the high end of the rating scale
For column definitions, see above.
; ACT ITEM-STRUCTURE FILE (not for anchoring: use SFILE=) FOR LIKING FOR SCIENCE (Wright & Masters p.18) Mar 24 20:55 2015
;ENTRY STAT MAX CAT BOT+.25 CAT ORD THRESH I+THRSH S.E. CAT-0.5 AT CAT PR50% CAT ORD THRESH I+THRSH S.E. CAT-0.5 TOP-.25 PR50% ACT
1 1 2 0 -2.68 1 1 -1.03 -1.50 .14 -1.76 -.47 -1.61 2 2 1.03 .55 .13 .81 1.74 .66 Watch birds
2 1 2 0 -3.01 1 1 -1.03 -1.83 .14 -2.09 -.80 -1.94 2 2 1.03 .23 .13 .49 1.41 .33 Read books on animals
Example 2: To produce a Table of expected measures per item-category similar to Pesudovs, K., E. Garamendi, et al. (2004). "The quality of life impact of refractive correction (QIRC) questionnaire: Development and validation." Optometry and Vision Science 81(10): 769-777, write the ISFILE= to Excel. Then delete or hide unwanted columns.
Example 3: To plot the operating range of each item using Excel.
"Output Files", "ISFILE=", output to Excel.
"Output Files", "IFILE=", output to Excel.
Paste the "MEASURE" column from the Excel IFILE= into the Excel ISFILE=
Arrange the columns: TOP-.25, BOT+.25, MEASURE
If some items have fewer categories, then paste their highest values into the TOP-.25 column
Draw a "hi-lo-close" plot with TOP-.25, BOT+.25, MEASURE for each item
If some items have fewer categories, then use their highest values in ISFILE=
This is one I have drawn from Exam12.txt with Exam12lo.txt+Exam12hi.txt
