Unobserved and dropped categories
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, but will make all categories of all items active in the measurement process.
2. Forced category range
3. Anchored thresholds
Using SAFILE=, reasonable threshold values can be applied to the item so that thresholds for unobserved categories are not estimated.
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:
*****************01***** Dummy data (0 for item 18, 1 for item 19)
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|Rasch Measurement Transactions (free, online)||Rasch Measurement research papers (free, online)||Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch||Applying the Rasch Model 3rd. Ed., Bond & Fox||Best Test Design, Wright & Stone|
|Rating Scale Analysis, Wright & Masters||Introduction to Rasch Measurement, E. Smith & R. Smith||Introduction to Many-Facet Rasch Measurement, Thomas Eckes||Invariant Measurement with Raters and Rating Scales: Rasch Models for Rater-Mediated Assessments, George Engelhard, Jr. & Stefanie Wind||Statistical Analyses for Language Testers, Rita Green|
|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|
|in Spanish:||Análisis de Rasch para todos, Agustín Tristán||Mediciones, Posicionamientos y Diagnósticos Competitivos, Juan Ramón Oreja Rodríguez|
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