Item-Weighted Likelihood Method for Measuring Growth in Longitudinal Study With Tests Composed of Both Dichotomous and Polytomous Items

Xuemei Xue; Jing Lu; Jiwei Zhang

doi:10.3389/fpsyg.2021.580015

Item-Weighted Likelihood Method for Measuring Growth in Longitudinal Study With Tests Composed of Both Dichotomous and Polytomous Items

Front Psychol. 2021 Jul 27:12:580015. doi: 10.3389/fpsyg.2021.580015. eCollection 2021.

Authors

Xuemei Xue¹, Jing Lu², Jiwei Zhang³

Affiliations

¹ School of Mathematical Sciences, Xiamen University, Xiamen, China.
² Key Laboratory of Applied Statistics of MOE, School of Mathematics and Statistics, Northeast Normal University, Changchun, China.
³ Key Lab of Statistical Modeling and Data Analysis of Yunnan Province, School of Mathematics and Statistics, Yunnan University, Kunming, China.

Abstract

In this paper, a new item-weighted scheme is proposed to assess examinees' growth in longitudinal analysis. A multidimensional Rasch model for measuring learning and change (MRMLC) and its polytomous extension is used to fit the longitudinal item response data. In fact, the new item-weighted likelihood estimation method is not only suitable for complex longitudinal IRT models, but also it can be used to estimate the unidimensional IRT models. For example, the combination of the two-parameter logistic (2PL) model and the partial credit model (PCM, Masters, 1982) with a varying number of categories. Two simulation studies are carried out to further illustrate the advantages of the item-weighted likelihood estimation method compared to the traditional Maximum a Posteriori (MAP) estimation method, Maximum likelihood estimation method (MLE), Warm's (1989) weighted likelihood estimation (WLE) method, and type-weighted maximum likelihood estimation (TWLE) method. Simulation results indicate that the improved item-weighted likelihood estimation method better recover examinees' true ability level for both complex longitudinal IRT models and unidimensional IRT models compared to the existing likelihood estimation (MLE, WLE and TWLE) methods and MAP estimation method, with smaller bias, root-mean-square errors, and root-mean-square difference especially at the low-and high-ability levels.

Keywords: dichotomous item response; item-weighted likelihood; longitudinal model; mixed-format test; polytomous item response.