Definition
Rasch polytomous models are statistical models for test and questionnaire data suitable for the analysis of data collected using rating scales, Likert-type response scales, or other response data with ordered categories, while preserving the main defining characteristics of Rasch analysis for binary responses.
Description
The Rasch model is often initially introduced as a model for binary data. In that case, we consider 0 (zero) as an indicator of a negative or incorrect response, while we consider 1 (one) as indicating a positive or correct response. In questionnaires used to assess quality of life, patient reported outcomes, or personality traits, however, we often find a response format that is more fine-grained.
The Likert scale (Likert 1932) is maybe the most commonly used of these ordinal response formats: The responses in this rating scale are ordered, ranging from a low end that typically...
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Adams, R. J., Wilson, M. R., & Wang, W. (1997). The multidimensional random coefficients multinomial logit model. Applied Psychological Measurement, 21, 1–23.
Adams, R. J., Wu, M. L., & Carstensen, C. H. (2007). Application of multivariate Rasch models in international large scale educational assessment. In M. von Davier & C. H. Carstensen (Eds.), Multivariate and mixture distribution Rasch models: Extensions and applications (pp. 271–280). New York: Springer.
Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika, 43, 561–573.
Andrich, D. (1982). An extension of the Rasch model for ratings providing both location and dispersion parameters. Psychometrika, 47, 105–113.
Fischer, G. H., & Molenaar, I. W. (1995). Rasch models – Foundations, recent developments and applications. New York: Springer.
Jansen, M. G. H. (1995). The Rasch poisson counts model for incomplete data: An application of the EM algorithm. Applied Psychological Measurement, 19(3), 291–302.
Likert, R. (1932). A technique for the measurement of attitudes. Archives of Psychology, 140, 1–55.
Masters, G. (1982). A Rasch model for partial credit scoring. Psychometrika, 47, 147–174.
Müller, H. (1987). A Rasch model for continuous ratings. Psychometrika, 52, 165–181.
Muraki, E. (1992). A generalized partial credit model: Application of an EM algorithm. Applied Psychological Measurement, 16, 159–176.
Rost, J. (1988). Measuring attitudes with a threshold model drawing on a traditional scaling concept. Applied Psychological Measurement, 12, 397–409.
Rost, J. (1991). A logistic mixture distribution model for polytomous item responses. British Journal of Mathematical and Statistical Psychology, 44, 75–92.
von Davier, M. (2000). WINMIRA 2001 – Software manual. IPN: Institute for Science Education. Student Version available at: http://www.von-davier.com
von Davier, M. (2005). A general diagnostic model applied to language testing data (ETS Research Report RR-05-16). Princeton: Educational Testing Service.
von Davier, M. (2010). Hierarchical mixtures of diagnostic models. Psychological Test and Assessment Modeling, 52(1), 8–28. Retrieved May 10, 2010, from http://www.psychologie-aktuell.com/fileadmin/download/ptam/1-2010/02_vonDavier.pdf
von Davier, M., & Carstensen, C. H. (Eds.). (2007). Multivariate and mixture distribution Rasch models: Extensions and applications. New York: Springer.
von Davier, M., & Rost, J. (1995). Polytomous mixed Rasch models. In G. H. Fischer & I. W. Molenaar (Eds.), Rasch models – Foundations, recent developments and applications (pp. 371–379). New York: Springer.
Xu, X. (2007). Monotone properties of a general diagnostic model (ETS Research Rep. No. RR-07-25). Princeton: Educational Testing Service.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Section Editor information
Rights and permissions
Copyright information
© 2023 Springer Nature Switzerland AG
About this entry
Cite this entry
von Davier, M. (2023). Rasch Polytomous Models. In: Maggino, F. (eds) Encyclopedia of Quality of Life and Well-Being Research. Springer, Cham. https://doi.org/10.1007/978-3-031-17299-1_2412
Download citation
DOI: https://doi.org/10.1007/978-3-031-17299-1_2412
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-17298-4
Online ISBN: 978-3-031-17299-1
eBook Packages: Social SciencesReference Module Humanities and Social SciencesReference Module Business, Economics and Social Sciences