[Rasch] Reversed Thresholds in Partial Credit Models: A Reason for Collapsing Categories?

stefanjcano at gmail.com stefanjcano at gmail.com
Sat Nov 8 03:47:00 EST 2014

Thanks for posting this Scott


For those interested in this area, I think it’s probably important to flag that David Andrich responded to (and further expanded upon his views about) the Adams, Wu, and Wilson article referred to in the Wetzel & Cartensen abstract in the below papers:



An Expanded Derivation of the Threshold Structure of the Polytomous Rasch Model That Dispels Any “Threshold Disorder Controversy” 


David Andrich




Responses to items with formats in more than two ordered categories are ubiquitous in education and the social sciences. Because the putative ordering of the categories reflects an understanding of what it means to have more of the variable, it seems mandatory that the ordering of the categories is an empirical property of the assessments and not merely a property of the model used to analyze them. To provide an unequivocal interpretation of category ordering in rating formats, this article expands the original derivation of the polytomous Rasch model for ordered categories. To do so, it integrates a complex of mathematical relationships among response spaces from which a space of experimentally independent Bernoulli variables, characterized by Rasch’s simple logistic model, can be inferred. From this inference, the article establishes the necessary and sufficient evidence to test the hypothesis that the required ordering of the categories is an empirical property of the assessments. This expanded derivation, which exposes how Adams, Wu, and Wilson (2012) misconstrue the model and its implications, is intended to dispel the so-called disordered threshold controversy they claim exists. 


Educational and Psychological Measurement February 2013   vol. 73  no. 1  78-124 


 <http://epm.sagepub.com/content/73/1/78.abstract> http://epm.sagepub.com/content/73/1/78.abstract




The Legacies of R. A. Fisher and K. Pearson in the Application of the Polytomous Rasch Model for Assessing the Empirical Ordering of Categories 


David Andrich 




Assessments in response formats with ordered categories are ubiquitous in the social and health sciences. Although the assumption that the ordering of the categories is working as intended is central to any interpretation that arises from such assessments, testing that this assumption is valid is not standard in psychometrics. This is surprising given that it has been known for some 35 years that this assumption can be checked routinely using the psychometric Rasch model for more than two ordered categories. The purpose of this article is twofold. First, to demonstrate three distinct but related legacies of R. A. Fisher that have contributed to the use of the Rasch model to assess the empirical ordering of categories: (a) his construction of sufficient statistics, (b) his recognition that the ordering of categories should be an empirical property of the data, and (c) his integration of the design of empirical studies with statistical analyses of data. Second, to suggest two reasons behind both the indifference, and even the rejection, of both the need and possibility of testing the assumption of the empirical ordering of categories: (a) the lack of recognition of the problem before it was understood that it could be solved using the Rasch model and (b) the legacy of K. Pearson that legitimized the atheoretical modeling of data with parameters that have no substantive meaning. 


Educational and Psychological Measurement August 2013   vol. 73  no. 4  553-580


 <http://epm.sagepub.com/content/73/4/553.abstract?rss=1> http://epm.sagepub.com/content/73/4/553.abstract?rss=1



Stefan Cano, PhD, CPsychol, AFBPsS │ Co-Founder and Chief Science Officer 

 <http://www.modusoutcomes.com/> www.modusoutcomes.com


measure the right things well






From: rasch-bounces at acer.edu.au [mailto:rasch-bounces at acer.edu.au] On Behalf Of SR Millis
Sent: 07 November 2014 14:55
To: Rasch List
Subject: [Rasch] Reversed Thresholds in Partial Credit Models: A Reason for Collapsing Categories?
Importance: High


Interesting study:


Assessment. 2014 Apr 30. [Epub ahead of print]


Reversed Thresholds in Partial Credit Models: A Reason for Collapsing Categories?


Wetzel E(1), Carstensen CH.


Author information: 

(1)Otto-Friedrich-University Bamberg, Germany.


When questionnaire data with an ordered polytomous response format are analyzed

in the framework of item response theory using the partial credit model or the

generalized partial credit model, reversed thresholds may occur. This led to the 

discussion of whether reversed thresholds violate model assumptions and indicate 

disordering of the response categories. Adams, Wu, and Wilson showed that

reversed thresholds are merely a consequence of low frequencies in the categories

concerned and that they do not affect the order of the rating scale. This article

applies an empirical approach to elucidate the topic of reversed thresholds using

data from the Revised NEO Personality Inventory as well as a simulation study. It

is shown that categories differentiate between participants with different trait 

levels despite reversed thresholds and that category disordering can be analyzed 

independently of the ordering of the thresholds. Furthermore, we show that

reversed thresholds often only occur in subgroups of participants. Thus,

researchers should think more carefully about collapsing categories due to

reversed thresholds.


PMID: 24789857  [PubMed - as supplied by publisher]



Scott R Millis, PhD, ABPP, CStat, PStat®
Wayne State University School of Medicine
Email: aa3379 at wayne.edu <mailto:aa3379 at wayne.edu> 
Email: srmillis at yahoo.com <mailto:srmillis at yahoo.com> 
Tel: 313-993-8085

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