Average Measures, Distractors and Rating Scale Structures
The "average measure" for a category is the average ability of the people who respond in that category or to that distractor (or distracter. The term "distractor" has been in use since at least 1934). This is an empirical value. It is not a Rasch-model parameter.
The Rasch-Andrich threshold (step difficulty, step calibration, etc.) is an expression of the log-odds of being observed in one or other of the adjacent categories. This is a model-based value. It is a Rasch-model parameter.
In Table 2.5, 14.3 and similar Tables describing the items, the "observed average" measure is: sum (person abilities) / count (person abilities) for each response option or rating-scale category.
In Table 3.2 and similar Tables describing the response structures, the "observed average" measure is: sum (person abilities - item difficulties) / count (person abilities) for each response option or rating-scale category.
Our theory is that people who respond in higher categories (or to the correct MCQ option) should have higher average measures. This is verified by "average measure".
Often there is also a theory about the rating scale, such as "each category in turn should be the most probable one to be observed as one advances along the latent variable." If this is your theory, then the "step difficulties" should also advance. But alternative theories can be employed. For instance, in order to increase item discrimination one may deliberately over-categorize a rating scale - visual-analog scales are an example of this. A typical visual analog-scale has 101 categories. If these functioned operationally according to the "most probable" theory, it would take something like 100 logits to get from one end of the scale to the other.
The relationship between "average measure" and Andrich thresholds or "item difficulties" is complex. It is something like:
Andrich threshold = log ((count in lower category) / (count in higher category)) + (average of the measures across both categories) - normalizer
normalized so that: sum(Andrich thresholds) = 0
the higher the frequency of the higher category relative to the lower category, the lower (more negative) the Andrich threshold (and/or item difficulty)
and the higher the average of the person measures across both categories, the higher (more positive) the Andrich threshold (and/or item difficulty)
but the Andrich thresholds are estimated as a set, so that the numerical relationship between a pair of categories is influenced by their relationships with every other category. This has the useful consequence that even if a category is not observed, it is still possible to construct a set of Andrich thresholds for the rating scale as a whole.
Suggestions based on researcher experience:
In general, this is what we like to see:
(1) More than 10 observations per category (or the findings may be unstable, i.e., non-replicable)
(2) A smooth distribution of category frequencies. The frequency distribution is not jagged. Jaggedness can indicate categories which are very narrow, perhaps category transitions have been defined to be categories. But this is sample-distribution-dependent.
(3) Clearly advancing average measures. The average measures are not disordered.
(4) Average measures near their expected values.
(5) Observations fit with their categories: Outfit mean-squares near 1.0. Values much above 1.0 are much more problematic than values much below 1.0.
Help for Winsteps Rasch Measurement Software: www.winsteps.com. Author: John Michael Linacre
The Languages of Love: draw a map of yours!
For more information, contact firstname.lastname@example.org or use the Contact Form
|Facets Rasch measurement software.
Buy for $149. & site licenses.
Freeware student/evaluation download
Winsteps Rasch measurement software. Buy for $149. & site licenses. Freeware student/evaluation download
|State-of-the-art : single-user and site licenses : free student/evaluation versions : download immediately : instructional PDFs : user forum : assistance by email : bugs fixed fast : free update eligibility : backwards compatible : money back if not satisfied|
Rasch, Winsteps, Facets online Tutorials
|Forum||Rasch Measurement Forum to discuss any Rasch-related topic|
Click here to add your email address to the Winsteps and Facets email list for notifications.
Click here to ask a question or make a suggestion about Winsteps and Facets software.
|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|
|Winsteps Tutorials||Facets Tutorials||Rasch Discussion Groups|
|Coming Winsteps & Facets Events|
|May 22 - 24, 2018, Tues.-Thur.||EALTA 2018 pre-conference workshop (Introduction to Rasch measurement using WINSTEPS and FACETS, Thomas Eckes & Frank Weiss-Motz), https://ealta2018.testdaf.de|
|May 25 - June 22, 2018, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|June 27 - 29, 2018, Wed.-Fri.||Measurement at the Crossroads: History, philosophy and sociology of measurement, Paris, France., https://measurement2018.sciencesconf.org|
|June 29 - July 27, 2018, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com|
|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" www.promsociety.org|
|Aug. 10 - Sept. 7, 2018, Fri.-Fri.||On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com|
|Oct. 12 - Nov. 9, 2018, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
Our current URL is www.winsteps.com
Winsteps® is a registered trademark
|John "Mike" L.'s Wellness Report:
I'm 72, take no medications and, March 2018, my doctor is annoyed with me - I'm too healthy!|
According to Wikipedia, the human body requires about 30 minerals, maybe more. There are 60 naturally-occurring minerals in the liquid Mineral Supplement which I take daily.