Rasch Measurement

Course info

Course code: 
Any / unplanned
7,5 hp
Person responsible: 
Curt Hagquist, fil dr, Professor i folkhälsovetenskap
Contact email: 
Registration email: 


Course plan: 

Kursen anordnas av Centrum för forskning om barns och ungdomars psykiska hälsa och avdelningen för psykologi.

Kursen vänder sig i första hand till doktorander vid Karlstads universitet men är i mån av plats även öppen för doktorander från andra universitet och högskolor.

I. Description of the methodology – Rasch Measurement Theory
II. Description of the course
III. Course outline
IV. Tentative syllabus

I. Description of the methodology – Rasch Measurement Theory
Composite measures including multiple items are used in health and social sciences to improve the reliability and validity of the instrument. The use of such measures is psychometrically justified only if the operating characteristics of the items work in the same way for all individuals and groups. This requirement of invariant measurement was first articulated in the 1920s by Thurstone. During the 1950s the Danish mathematician Georg Rasch formalised this requirement mathematically in a probabilistic response model, the Rasch model.
The Rasch model is built upon uni-dimensional scales which are intended to measure a single concept on a latent trait represented as a linear continuum. The response format is cumulative like frequency or Likert scales, reflecting more or less of a property. Since the Rasch model facilitates disclosure of measurement problems that may not be easily detected by traditional analyses, e.g. lack of invariance, the Rasch model can be used for rigorous examinations of instruments. The Rasch model also overcomes a common cause for concern in the construction of composite measures by justifying the summation of the raw scores across items and by providing a proper method for nonlinear transformation of ordinal raw scores to linear measures.
The Rasch model is, however, an efficient tool not just for post-hoc analysis of an instrument, but also for development of new instruments.
The Rasch model was originally mainly used in educational testing but is nowadays also increasingly applied in health sciences and social science research. The increasing use of Rasch analysis is also confirmed by an increasing number of published articles based on Rasch analysis. Since the millennium shift the number of Rasch matches in Web of Science has threefold. Historically, most Rasch papers have originated from USA which still dominates representing 60 percent of all Rasch matches in Web of Science. The increasing trend of published Rasch papers applies, however, not just to USA but also to Australia and many European countries.
A distinctive feature of the Rasch-model is that it’s derived from theory which means that it is constructed a priori to the data. In Rasch analysis the data are compared with the model which is considered fixed representing required properties of the data. Therefore misfit between the data and the model should not be addressed by inclusion of additional parameters. This is opposite to traditional statistical modelling where the purpose is to describe or explain the data. Since the Rasch model has invariance as an integral property misfit between the data and the model implies that a check of fit of data to the model becomes a check of invariance. Hence, a measure that meets the requirements of the Rasch model can be used to make invariant comparisons across individuals and groups of individuals.
Although the Rasch model sometimes is described as a member of the class of Item Response Theory (IRT) models, the Rasch paradigm is contrasting the paradigm of other IRT models in a fundamental way. Instead of finding a model that best describes the data, the purpose of Rasch analysis is to disclose the anomalies in the data. In contrast, in the paradigm of other IRT-models misfit between the data and the model may lead to a model with more parameters, e.g. the 2-parameter model.
If the data fit the Rasch model the total score across items characterises a person totally. This implies that the total score is a sufficient statistic that in principle
captures the same information as a parameter estimate, enabling elimination of the person parameter in question. It follows that the item parameters can be estimated conditioning on the person total raw scores, and that there are no person parameters to be estimated simultaneously. Inversely, the sum of the item raw scores across all persons is a sufficient statistic for the item parameters. The sufficient statistic is the unique tool that enables separation of the person and item parameters in the estimation processes, which is a requirement for invariant measures.
There is no single measure to be used to examine the concordance between the data and the model, rather a variety of different tools. Also, not just formal statistical tests of fit should be used but also graphical representations e.g. Item Characteristic Curves.

II. Description of the course
The course is an introduction to Rasch measurement in social sciences and health sciences. The Rasch model is the only IRT-model that can be used to examine whether a scale or test meets the measurement requirements for invariant comparisons. If the data fit the Rasch model the total score across items characterizes a person totally enabling nonlinear transformation of ordinal raw scores to linear measures to be used with parametric statistical methods.
The course provides an overview of the theory underlying the Rasch model and its basic features. Advances in analysis of Differential Item Functioning (DIF) are covered extensively including methods to detect, quantify and resolve DIF using the Rasch model. A strong emphasis is on practical applications of Rasch analysis, including illustrative examples and hands on exercises.

III. Course outline
The target groups for the course are doctoral students in social sciences, health sciences and other fields who require knowledge about modern measurement methods.
The course starts with an introduction of the Rasch paradigm in social measurement and the theory underlying the Rasch model. The Rasch model of modern test theory is compared with traditional test theory as well as other IRT-models such as the 2-parameter model. In treating invariance, a special focus is on Differential Item Functioning (DIF) and methods to identify, quantify and resolve DIF. Other topics to be treated in the course include: targeting, tests of fit, reliability measures, multidimensionality, local dependency, categorisation of items. Each day of the course there is a mixture and integration of lectures and labs. The participants will have the opportunity to bring and analyse their own data.
The course doesn’t require prior experiences of Rasch analysis, but familiarity with statistical methods such as regression analysis and analysis of variance is desirable.
The participants are supposed to bring their own computers and work on them.

The program RUMM2030, which will expire at the end of 2014, will be made available to participants. (www.rummlab.com). RUMM2030 is a user friendly software specifically designed for Rasch analysis.


Readings (preliminary)
Andrich, D. (1988). Rasch Models for Measurement. Sage University
Paper on Quantitative Applications in the social Sciences, Series
07-068. Sage Publications, Beverly Hills.
Andrich, D. (2004). Controversy and the Rasch model: a characteristic of incompatible paradigms? Medical Care, 42, 1–16.
Andrich, D. (2011). Rating scales and Rasch measurement. Expert Rev. Pharmacoeconomics Outcomes Res. 11(5), 571–585.
Andrich, D. (2013) The Legacies of R. A. Fisher and K. Pearson in the
Application of the Polytomous Rasch Model for Assessing the Empirical
Ordering of Categories. Educational and Psychological
Measurement 73(4) 553–580.
Andrich, D. & Hagquist, C. (2012). Real and artificial differential item functioning. Journal of Educational and Behavioral Statistics, 37(3), 387-416.
Andrich, D. & Hagquist, C.
Real and Artificial Differential Item Functioning in Polytomous Items
Educational and Psychological Measurement (accepted).
Hagquist, C., Andrich, D. (2004). Is the sense of coherence instrument
applicable on adolescents? A latent trait analysis using Rasch-modelling.
Personality and Individual Differences 36, 955–968.
Hagquist C, Bruce M, Gustavsson JP. (2009). Using the Rasch model in
nursing research: An introduction and illustrative example. International Journal of Nursing Studies;46:380–93.
Marais, I., Andrich, D. (2008). Formalizing dimension and response
violations of local independence in the unidimensional Rasch
model. Journal of Applied Measurement 9, 200–215.
Rasch, G. (1960/80). Probabilistic models for some intelligence and attainment tests. (Copenhagen, Danish Institute for Educational Research). Expanded edition (1980) with foreword and afterword by B. D. Wright, (1980). (Chicago: The University of Chicago Press)

Admission rules

Each syllabus states target group and eligibility, which should be based on the prerequisites necessary to understand and process the content of the course. Syllabi and scheduled course meetings are posted on the course portal web page for the doctoral level, which is also open to the public. 

Doctoral students who wish to take a course should sign up according to instructions on the course portal.  

Admitted students must meet the requirements stated in the syllabus. If there are more prospective students than the teaching capacity allows, priority is given to students as follows: 

  1. If the course is not included in the obligation stated in item 2 below, admission is primarily granted to eligible students at the department offering the course. If the course is offered jointly by several departments at Karlstad university, priority is given, as agreed, by the departments concerned. If the course is commissioned by the Faculty, all students at the Faculty belong to the prioritised group. In the case of cross-faculty courses, all students at Karlstad University belong to the prioritised group. If order of admission must be made in the prioritised group, the student who first signed up according to the requirement above, is given priority. 
  2. If the course is part of a commitment to a national or international graduate school, network or equivalent, priority is given to their participants.  
  3. If there is an agreement on exchange with a subject, department or faculty at another HEI, eligible students from such institutions have second priority 
  4. Other eligible students at Karlstad University have third priority. 
  5. Other eligible students at other HEIs have fourth priority. 

The appointed course convener decides on admission of students to a doctor level course in accordance with the order of priority stated above.  

Upon completion of the course, the course convener issues a course certificate with a proposed grade to the students.  


I kursplan anges målgrupp och behörighet. Behörighet ska utgå från de förkunskaper som behövs för att tillgodogöra sig kursens innehåll.

Kursplaner och planerade kurstillfällen görs tillgängliga på en webbsida: kurstorg för forskarnivå, som även görs tillgänglig externt.

Forskarstuderande som önskar följa en kurs ska anmäla detta enligt anvisning på kurstorget.

Studerande som ges tillträde ska uppfylla de behörighetskrav som anges i kursplanen. Om fler önskar följa kursen än vad undervisningskapaciteten tillåter görs prioritering enligt nedan.

  1. Om inte kursen ingår i ett åtagande enligt punkt 2 nedan ges tillträde i första hand till behöriga studerande vid den institution som anordnar kursen. I det fall kursen anordnas gemensamt av flera institutioner vid Karlstads universitet ges tillträde i första hand på det sätt som berörda institutioner kommit överens om. I det fall kursen är beställd av fakultet ingår alla studerande vid fakulteten i den grupp som ges tillträde i första hand. För kurser som anordnas gemensamt av fakulteterna gäller det alla studerande vid Karlstads universitet. Om prioritering behöver göras inom den grupp som ges tillträde i första hand ges den som först anmält sig enligt ovan företräde.
  2. Om anordnade av en kurs ingår i ett åtagande gentemot nationell eller internationell forskarskola, nätverk eller motsvarande ges dock deltagare därifrån tillträde i första hand.
  3. I det fall det finns överenskommelse om utbyte med ämne, institution eller fakultet vid annat lärosäte ges behöriga studerande därifrån tillträde i andra hand.
  4. I tredje hand ges tillträde till övriga behöriga studerande vid Karlstads universitet.
  5. I fjärde hand ges tillträde till övriga behöriga studerande vid andra lärosäten.

Den som institutionen utsett som kursansvarig beslutar om vilka som får delta i en kurs på forskarnivå, i enlighet med prioritetsordningen ovan. 

Efter genomförd kurs och prov lämnar kursansvarig ett intyg med förslag på betyg till kursdeltagarna.