Estimating and Fitting the Non-continuous category scored Polytomous Items under the Weighted Score Logistic Model and its Simulation Study

Abstract

This study presents a novel extension of the weighted score logistic model (WSLM). The WSLM is an advancement of the traditional dichotomous logistic model that incorporates an additional weighted score parameter. This model is specifically designed to analyze non-continuous category scored polytomous items in educational and psychological testing contexts. Within the WSLM framework, the mean difficulty parameter reflects the overall item difficulty, while both discrimination and mean difficulty parameters are estimated using marginal maximum likelihood estimation. A Monte Carlo simulation study was conducted to evaluate the performance of the WSLM, which demonstrated low levels of bias and root mean square error (RMSE) of item parameters, indicative of accurate parameter recovery. Under most simulation conditions, the fit statistics Q1 and Q4 for polytomous items under the WSLM remained below their respective critical chi-square values, suggesting acceptable model-data fit. These results support the applicability and robustness of the WSLM in practical assessment settings involving complex scoring schemes.

Keywords

polytomous models weighted score logistic model polytomous items model fit item response theory

Get full access to this article

View all access options for this article.

References

Belov

D. I.

Armstrong

R. D.

Weissman

(2008). A monte carlo approach for adaptive testing with content constraints. Applied Psychological Measurement, 32(6), 431–446. https://doi.org/10.1177/0146621607309081

Bock

R. D.

(1972). Estimating item parameters and latent ability when responses are scored in two or more nominal categories. Psychometrika, 37(1), 29–51. https://doi.org/10.1007/bf02291411

Bock

R. D.

Aitkin

(1981). Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm. Psychometrika, 46(4), 443–459. https://doi.org/10.1007/BF02293801

Bock

R. D.

Lieberman

(1970). Fitting a response model for n dichotomously scored items. Psychometrika, 35(2), 179–197. https://doi.org/10.1007/BF02291262

Elliott

C. D.

Murray

D. J.

Saunders

(1977). Goodness of fit to the Rasch model as a criterion of test unidimensionality. Manchester: University of Manchester.

Jian

(2026) “Estimating and fitting the Discrete-scored Polytomous Items under the Weighted-score Logistic Model and its Simulation Study”. https://share.weiyun.com/biSfTN5a

Jian

Dai

(2016). The weighted score logistic model and Monte Carlo simulation study. Acta Psychologica Sinica, 48(12), 1625–1630. https://doi.org/10.3724/SP.J.1041.2016.01625

Masters

G. N.

(1982). A Rasch model for partial credit scoring. Psychometrika, 47(2), 149–174. https://doi.org/10.1007/BF02296272

Muraki

(1992). A generalized partial credit model. Applied Psychological Measurement, 16(2), Article 159176.

10.

Orlando

Thissen

(2000). Likelihood-based item-fit indices for dichotomous item response theory models. Applied Psychological Measurement, 24(1), 50–64. https://doi.org/10.1177/01466216000241003

11.

Orlando

Thissen

(2003). Further investigation of the performance of S-X2: An item fit indices for use with dichotomous item response theory models. Applied Psychological Measurement, 27(4), 289–298. https://doi.org/10.1177/0146621603027004004

12.

Samejima

(1969). Estimation of latent ability using a response pattern of graded scores. Psychometrika Monograph Supplement, 34(4), 100–114. https://doi.org/10.1007/BF03372160

13.

Stone

C. A.

Zhang

(2003). Assessing goodness of fit of item response theory models: A comparison of traditional and alternative procedures. Journal of Educational Measurement, 40(4), 331–352. https://doi.org/10.1111/j.1745-3984.2003.tb01150.x

14.

Thissen

Steinberg

(1984). A response model for multiple choice items. Psychometrika, 49(4), 501–519. https://doi.org/10.1007/BF02302588

15.

Tutz

(1990). Sequential item response models with an ordered response. British Journal of Mathematical and Statistical Psychology, 43(1), 39–55. https://doi.org/10.1111/j.2044-8317.1990.tb00925.x

16.

van der Linden

W. J.

Hambleton

R. K.

(Eds.). (1997). Handbook of modern item response theory . Springer. https://doi.org/10.2307/2965612

17.

Verhelst

N. D.

Glas

C. A. W.

de Vries

H. H.

(1997). A steps model to analyze partial credit. In van der Linden

W. J.

Hambleton

R. K.

(Eds.), Handbook of modern item response theory. Springer. https://doi.org/10.1007/978-1-4757-2691-6_7

18.

Yen

W. M.

(1981). Using simulation results to choose a latent trait model. Applied Psychological Measurement, 5(2), 245–262. https://doi.org/10.1177/014662168100500212

Supplementary Material

Please find the following supplemental material available below.

For Open Access articles published under a Creative Commons License, all supplemental material carries the same license as the article it is associated with.

For non-Open Access articles published, all supplemental material carries a non-exclusive license, and permission requests for re-use of supplemental material or any part of supplemental material shall be sent directly to the copyright owner as specified in the copyright notice associated with the article.

0.20 MB

0.00 MB