If you have data in which a category is not observed, then you must make an assertion about the unobserved category. There are several options:
For intermediate categories: either
(a) this category will never be observed (this is called a "structural zero"). Generally, these categories are collapsed or recoded out of the rating scale hierarchy. This happens automatically with STKEEP=No.
or (b) this category didn't happen to be observed this time (an "incidental" or "sampling" zero). These categories can be maintained in the rating scale hierarchy (using STKEEP=Yes), but are estimated to be observed with a probability of zero.
1. Dummy data
For extreme categories:
(a) if this category will never be observed, the rating scale is analyzed as a shorter scale. This is the Winsteps standard.
(b) if this category may be observed, then introduce a dummy record into the data set which includes the unobserved extreme category, and also extreme categories for all other items except the easiest (or hardest) item. This forces the rare category into the category hierarchy.
(c) If an extreme (top or bottom) category is only observed for persons with extreme scores, then that category will be dropped from the rating (or partial credit) scales. This can lead to apparently paradoxical or incomplete results. This is particularly noticeable with ISGROUPS=0. Again, dummy data solves this.
In order to account for unobserved extreme categories, a dummy data record needs to be introduced. If there is a dropped bottom category, then append to the data file a person data record which has bottom categories for all items except the easiest, or if the easiest item is in question, except for the second easiest.
If there is a dropped top category, then append to the data file a person data record which has top categories for all items except the most difficult, or if the most difficult item is in question, except for the second most difficult.
This extra person record will have very little impact on the relative measures of the non-extreme persons, , especially if you give it a very small weight with PWEIGHT=, but will make all categories of all items active in the measurement process.
If it is required to produce person statistics omitting the dummy record, then at the Specification Menu use PDELETE= or PSELECT= to omit it, and regenerate Table 3.
See also Null or unobserved categories: structural and incidental zeroes
Example: when the "Liking for Science" data, example0.txt, are analyzed with the Partial Credit Model, ISGROUPS=0, item 18, "Go on a Picnic", does not have the bottom 0 category of the 3-category 0-1-2 rating scale. The next easiest item is item 19, "Go to the zoo", so add a dummy data record looking like, to which you can give a very small influence by using PWEIGHT= with a small value.
*****************01***** Dummy data (0 for item 18, 1 for item 19)
Example 2: Item 1 has no category 0 in this dataset, but the category should exist.
Title="test"
Codes=012
Isgroups=0 ; each item has its own rating-scale
NI=3
Item1=1
Name1=1
Pweight=*
4 0.01 ; small weight for dummy person 4 - adjust this weight if 0 for item 4 is too far away
*
&END
END LABELS
211 Person 1
122 Person 2
100 Person 3
011 Dummy person 4 because there was no 0 for item 1
2. Forced category range
Another approach is to specify the unobserved categories with ISRANGE=, and then model all the categories with a polynomial function: SFUNCTION=.
3. Anchored thresholds
Using SAFILE=, reasonable threshold values can be applied to the item so that thresholds for unobserved categories do not need to be estimated.
