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.


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


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 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 Publications
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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Coming Rasch-related Events
April 10-12, 2018, Tues.-Thurs. Rasch Conference: IOMW, New York, NY,
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May 22 - 24, 2018, Tues.-Thur. EALTA 2018 pre-conference workshop (Introduction to Rasch measurement using WINSTEPS and FACETS, Thomas Eckes & Frank Weiss-Motz),
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July 25 - July 27, 2018, Wed.-Fri. Pacific-Rim Objective Measurement Symposium (PROMS), (Preconference workshops July 23-24, 2018) Fudan University, Shanghai, China "Applying Rasch Measurement in Language Assessment and across the Human Sciences"
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