[en] Warm (1989) established the equivalence between the so-called Jeffreys modal and the weighted likelihood estimators of proficiency level with some dichotomous item response models. The purpose of this note is to extend this result to polytomous item response models. First, a general condition is derived to ensure the perfect equivalence between these two estimators. Second, it is shown that this condition is fulfilled by two broad classes of polytomous models including, among others, the partial credit, rating scale, graded response and nominal response models.
Disciplines :
Education & instruction
Author, co-author :
Magis, David ; Université de Liège - ULiège > Département d'éducation et formation > Psychométrie et édumétrie
Language :
English
Title :
A note on weighted likelihood and Jeffreys modal estimation of proficiency levels in polytomous item response models
Publication date :
2015
Journal title :
Psychometrika
ISSN :
0033-3123
eISSN :
1860-0980
Publisher :
Psychonomic Society, Research Triangle Park, United States - Virginia
scite shows how a scientific paper has been cited by providing the context of the citation, a classification describing whether it supports, mentions, or contrasts the cited claim, and a label indicating in which section the citation was made.
Bibliography
Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika, 43, 561–573. doi:10.1007/BF02293814.
Bock, R.D. (1972). Estimating item parameters and latent ability when responses are scored in two or more nominal categories. Psychometrika, 37, 29–51. doi:10.1007/BF02291411.
Embretson, S.E., & Reise, S.P. (2000). Item response theory for psychologists. Mahwah: Lawrence Erlbaum Associates.
Jeffreys, H. (1946). An invariant form for the prior probability in estimation problems. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 186, 453–461.
Magis, D., & Raîche, G. (2012). On the relationships between Jeffreys modal and weighted likelihood estimation of ability under logistic IRT models. Psychometrika, 77, 163–169. doi:10.1007/s11336-011-9233-5.
Masters, G.N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47, 149–174. doi:10.1007/BF02296272.
Muraki, E. (1990). Fitting a polytomous item response model to Likert-type data. Applied Psychological Measurement, 14, 59–71. doi:10.1177/014662169001400106.
Muraki, E. (1992). A generalized partial credit model: application of an EM algorithm. Applied Psychological Measurement, 16, 159–176. doi:10.1177/014662169201600206.
Samejima, F. (1969). Estimation of latent ability using a response pattern of graded scores. Psychometrika monograph (Vol. 17).
Samejima, F. (1998, April). Expansion of Warm’s weighted likelihood estimator of ability for the three-parameter logistic model to general discrete responses. Paper presented at the annual meeting of the National Council on Measurement in Education, San Diego, CA.
Thissen, D., & Steinberg, L. (1986). A taxonomy of item response models. Psychometrika, 51, 567–577. doi:10.1007/BF02295596.
Warm, T.A. (1989). Weighted likelihood estimation of ability in item response models. Psychometrika, 54, 427–450. doi:10.1007/BF02294627.
This website uses cookies to improve user experience. Read more
Save & Close
Accept all
Decline all
Show detailsHide details
Cookie declaration
About cookies
Strictly necessary
Performance
Strictly necessary cookies allow core website functionality such as user login and account management. The website cannot be used properly without strictly necessary cookies.
This cookie is used by Cookie-Script.com service to remember visitor cookie consent preferences. It is necessary for Cookie-Script.com cookie banner to work properly.
Performance cookies are used to see how visitors use the website, eg. analytics cookies. Those cookies cannot be used to directly identify a certain visitor.
Used to store the attribution information, the referrer initially used to visit the website
Cookies are small text files that are placed on your computer by websites that you visit. Websites use cookies to help users navigate efficiently and perform certain functions. Cookies that are required for the website to operate properly are allowed to be set without your permission. All other cookies need to be approved before they can be set in the browser.
You can change your consent to cookie usage at any time on our Privacy Policy page.
