Zeroes: Structural and Incidental: Ordinal or Keep

Unobserved categories can be dropped from rating scales (or partial credit items) and the remaining category recounted during estimation. For intermediate categories only, recounting can be prevented and unobserved categories retained in the analysis. This is useful when the unobserved categories are important to the rating scale (or partial credit) logic or are usually observed, even though they happen to have been unused this time. Category transitions for which anchor Rasch-Andrich threshold-values (step calibrations) are supplied are always maintained wherever computationally possible, even when there are no observations of a category in the current data set.


Use "Rating Scale= .... Keep" when there may be intermediate categories in your rating scale (or partial credit) that aren't observed in this data set, i.e., incidental zeroes.


Use "Rating Scale= .... Ordinal" when your category numbering deliberately skips over intermediate categories, i.e., structural zeroes.


"Rating Scale= .... Ordinal" Eliminate unused categories and close up the observed categories.


"Rating Scale= .... Keep" Retain unused non-extreme categories in the ordinal categorization.


When "Rating Scale= .... Keep", missing categories are retained in the rating scale (or partial credit), so maintaining the raw score ordering. But missing categories require arbitrarily extreme Rasch-Andrich thresholds. If these threshold values are to be used for anchoring later runs, compare these thresholds with the thresholds obtained by an unanchored analysis of the new data. This will assist you in determining what adjustments need to be made to the original threshold-values in order to establish a set of anchor threshold-values that maintain the same rating scale (or partial credit) structure.


Example 1: Incidental unobserved categories. Keep the developmentally important rating scale (or partial credit) categories, observed or not. Your small Piaget scale goes from 1 to 6. But some levels may not have been observed in this data set.

 Models = ?,?,?, Piagetscale

 Rating Scale = Piagetscale, R6, Keep


Example 2: Structural unobserved categories. Responses have been coded as "10", "20", "30", "40", but they really mean 1,2,3,4

 Models = ?, ?, ?, Tensscale

 Rating Scale = Tensscale, R40, Ordinal

 ; if "Rating Scale= .... Keep", then data are analyzed as though categories 11, 12, 13, 14, etc. could exist, which would distort the measures.

 ; for reporting purposes, multiply Facets reported raw scores by 10 to return to the original 10, 20, 30 categorization.


Example 3: Some unobserved categories are structural and some incidental. Rescore the data and use "Rating Scale= .... Keep". Possible categories are 2,4,6,8 but only 2,6,8 are observed this time.

 (a) Rescore 2,4,6,8 to 1,2,3,4

 (b) Set "Rating Scale= .... Keep", so that the observed 1,3,4 and unobserved 2 are treated as 1,2,3,4

 (c) For reporting purposes, multiply the reported Facets scores by 2 using Excel or similar software.

 Models = ?,?,?,Evenscale

 Rating Scale = Evenscale, R8, Keep

 1 = original 2, , , 2

 2 = original 4, , , 4

 3 = original 6, , , 6

 4 = original 8, , , 8




Incidental and Structural Zeroes: Extreme and Intermediate


For missing intermediate categories, there are two options.


If the categories are missing because they cannot be observed, then they are "structural zeroes". Specify "Rating Scale= .... Ordinal". This effectively recounts the observed categories starting from the bottom category, so that 1,3,5,7 becomes 1,2,3,4.


If they are missing because they just do not happen to have been observed this time, then they are "incidental or sampling zeros". Specify "Rating Scale= .... Keep". Then 1,3,5,7 is treated as 1,2,3,4,5,6,7.


Categories outside the observed range are always treated as structural zeroes.


When "Rating Scale= .... Keep", unobserved intermediate categories are imputed using a mathematical device noticed by Mark Wilson. This device can be extended to runs of unobserved categories.

Help for Facets Rasch Measurement Software: Author: John Michael Linacre.

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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,
April 13-17, 2018, Fri.-Tues. AERA, New York, NY,
May 22 - 24, 2018, Tues.-Thur. EALTA 2018 pre-conference workshop (Introduction to Rasch measurement using WINSTEPS and FACETS, Thomas Eckes & Frank Weiss-Motz),
May 25 - June 22, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps),
June 27 - 29, 2018, Wed.-Fri. Measurement at the Crossroads: History, philosophy and sociology of measurement, Paris, France.,
June 29 - July 27, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps),
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"
Aug. 10 - Sept. 7, 2018, Fri.-Fri. On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets),
Sept. 3 - 6, 2018, Mon.-Thurs. IMEKO World Congress, Belfast, Northern Ireland
Oct. 12 - Nov. 9, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps),


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