Disordered Rasch-Andrich thresholds

This is for 32-bit Facets 3.87. Here is Help for 64-bit Facets 4

Disordered Andrich thresholds indicate that a category occupies a narrow interval on the latent variable (usually because the category is observed relatively rarely). This is not a problem unless you need advancing abilities to probably increment smoothly up the categories of the rating scale without skipping narrow categories.

 

If this is a problem for you, then please collapse categories. This usually requires some experimenting to find the best solution:

1) Look at the average measures for each category. Combine categories with disordered average measures

2) Look at the category frequency. Combine categories with low frequencies

 

Disordered Andrich thresholds indicate that some categories on the latent variable are narrow. Disordered Andrich thresholds do not violate Rasch models, but they may impact our interpretation of how the rating scale functions.

 

Example: Imagine a location on the latent variable that is the boundary between two categories. If there are exactly 1,000 people with measures at that boundary. We would expect to observe 500 of them in categories below the boundary and 500 of them in categories above the boundary. Dichotomous items function exactly this way.

 

dichotomous item 0-1

category 0 on latent variable

category 1 on latent variable

1000 persons here →

 

500 persons observed here as 0

500 persons observed here as 1

dichotomous item difficulty →

 

 

Polytomous items (RSM, PCM) are move complex. RSM and PCM predict that some of the 1000 will be observed in categories next to the boundary, and some in categories further away, so that there will be 500 in total above the boundary and 500 below the boundary. OK so far?

 

polytomous item 0-1-2 (ordered categories, ordered Andrich thresholds)

category 0

category 1 (wide)

category 2

1000 persons here →


500 persons observed here as 0

490 persons observed here as 1

10 persons observed here as 2

|← Andrich threshold → | (ordered)

 

For 3 rating-scale categories 0,1,2 our first boundary is between 0 and 1. If category 1 is very wide, almost all the 500, say 490, will be observed in category 1 and 10 in category 2. The Andrich threshold corresponding to each boundary is basically ln(frequency of category below/frequency of category above), so the Andrich threshold for our first boundary 0-1 is something like ln(500/490) = 0.0 and for the next boundary, 1-2,  ln(490/10) = 3.9. The Andrich thresholds are in ascending order.

 

polytomous item 0-1-2 (ordered categories, disordered Andrich thresholds)

category 0

category 1 (narrow)

category 2

1000 persons here →


500 persons observed here as 0

10 persons as 1

490 persons observed here as 2

→ | Andrich threshold |← (disordered)

 

But if category 1 is very narrow, only 10 of the 500 may be observed in category 1, and 490 in category 2 above the narrow category 1. The Andrich threshold for our first boundary 0-1 is something like ln(500/10) = 3.9 and for the next boundary, 1-2,  ln(10/490) = -3.9. So the categories are disordered, even though the data fit the Rasch model perfectly!

 

Disordered Andrich thresholds indicate narrow categories on the latent variable. Statistically, these are no problem, but for practical purposes we may want all the categories to be wide enough that the Andrich thresholds are ordered.

 

The category boundaries in this example are reported as the "Rasch-Thurstone thresholds".


Help for Facets Rasch Measurement and Rasch Analysis Software: www.winsteps.com Author: John Michael Linacre.
 

Facets Rasch measurement software. Buy for $149. & site licenses. Freeware student/evaluation Minifac download
Winsteps Rasch measurement software. Buy for $149. & site licenses. Freeware student/evaluation Ministep download

Rasch Books and Publications
Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, 2nd Edn, 2024 George Engelhard, Jr. & Jue Wang Applying the Rasch Model (Winsteps, Facets) 4th Ed., Bond, Yan, Heene Advances in Rasch Analyses in the Human Sciences (Winsteps, Facets) 1st Ed., Boone, Staver Advances in Applications of Rasch Measurement in Science Education, X. Liu & W. J. Boone Rasch Analysis in the Human Sciences (Winsteps) Boone, Staver, Yale
Introduction to Many-Facet Rasch Measurement (Facets), Thomas Eckes Statistical Analyses for Language Testers (Facets), Rita Green Invariant Measurement with Raters and Rating Scales: Rasch Models for Rater-Mediated Assessments (Facets), George Engelhard, Jr. & Stefanie Wind Aplicação do Modelo de Rasch (Português), de Bond, Trevor G., Fox, Christine M Appliquer le modèle de Rasch: Défis et pistes de solution (Winsteps) E. Dionne, S. Béland
Exploring Rating Scale Functioning for Survey Research (R, Facets), Stefanie Wind Rasch Measurement: Applications, Khine Winsteps Tutorials - free
Facets Tutorials - free
Many-Facet Rasch Measurement (Facets) - free, J.M. Linacre Fairness, Justice and Language Assessment (Winsteps, Facets), McNamara, Knoch, Fan
Other Rasch-Related Resources: Rasch Measurement YouTube Channel
Rasch Measurement Transactions & Rasch Measurement research papers - free An Introduction to the Rasch Model with Examples in R (eRm, etc.), Debelak, Strobl, Zeigenfuse Rasch Measurement Theory Analysis in R, Wind, Hua Applying the Rasch Model in Social Sciences Using R, Lamprianou El modelo métrico de Rasch: Fundamentación, implementación e interpretación de la medida en ciencias sociales (Spanish Edition), Manuel González-Montesinos M.
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch Rasch Models for Measurement, David Andrich Constructing Measures, Mark Wilson Best Test Design - free, Wright & Stone
Rating Scale Analysis - free, Wright & Masters
Virtual Standard Setting: Setting Cut Scores, Charalambos Kollias Diseño de Mejores Pruebas - free, Spanish Best Test Design A Course in Rasch Measurement Theory, Andrich, Marais Rasch Models in Health, Christensen, Kreiner, Mesba Multivariate and Mixture Distribution Rasch Models, von Davier, Carstensen
As an Amazon Associate I earn from qualifying purchases. This does not change what you pay.

facebook Forum: Rasch Measurement Forum to discuss any Rasch-related topic

To receive News Emails about Winsteps and Facets by subscribing to the Winsteps.com email list,
enter your email address here:

I want to Subscribe: & click below
I want to Unsubscribe: & click below

Please set your SPAM filter to accept emails from Winsteps.com
The Winsteps.com email list is only used to email information about Winsteps, Facets and associated Rasch Measurement activities. Your email address is not shared with third-parties. Every email sent from the list includes the option to unsubscribe.

Questions, Suggestions? Want to update Winsteps or Facets? Please email Mike Linacre, author of Winsteps mike@winsteps.com


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

Our current URL is www.winsteps.com

Winsteps® is a registered trademark