scholarly journals Polytomous Item Explanatory Item Response Theory Models

2019 ◽  
Vol 80 (4) ◽  
pp. 726-755 ◽  
Author(s):  
Jinho Kim ◽  
Mark Wilson
Keyword(s):  
Item Response Theory ◽  
Item Response ◽  
Rasch Model ◽  
Explanatory Models ◽  
Partial Credit Model ◽  
Partial Credit ◽  
Response Theory ◽  
Polytomous Item ◽  
Item Properties ◽  
Item Response Theory Models

This study investigates polytomous item explanatory item response theory models under the multivariate generalized linear mixed modeling framework, using the linear logistic test model approach. Building on the original ideas of the many-facet Rasch model and the linear partial credit model, a polytomous Rasch model is extended to the item location explanatory many-facet Rasch model and the step difficulty explanatory linear partial credit model. To demonstrate the practical differences between the two polytomous item explanatory approaches, two empirical studies examine how item properties explain and predict the overall item difficulties or the step difficulties each in the Carbon Cycle assessment data and in the Verbal Aggression data. The results suggest that the two polytomous item explanatory models are methodologically and practically different in terms of (a) the target difficulty parameters of polytomous items, which are explained by item properties; (b) the types of predictors for the item properties incorporated into the design matrix; and (c) the types of item property effects. The potentials and methodological advantages of item explanatory modeling are discussed as well.

Using Item Response Theory Models to Evaluate the Practice Environment Scale

2014 ◽  
Vol 22 (2) ◽  
pp. 323-341 ◽  
Author(s):  
Dheeraj Raju ◽  
Xiaogang Su ◽  
Patricia A. Patrician
Keyword(s):  
Item Response Theory ◽  
Item Response ◽  
Information Criterion ◽  
Partial Credit Model ◽  
Practice Environment ◽  
Partial Credit ◽  
Response Theory ◽  
Environment Scale ◽  
Graded Response ◽  
Item Response Theory Models

Background and Purpose: The purpose of this article is to introduce different types of item response theory models and to demonstrate their usefulness by evaluating the Practice Environment Scale. Methods: Item response theory models such as constrained and unconstrained graded response model, partial credit model, Rasch model, and one-parameter logistic model are demonstrated. The Akaike information criterion (AIC) and Bayesian information criterion (BIC) indices are used as model selection criterion. Results: The unconstrained graded response and partial credit models indicated the best fit for the data. Almost all items in the instrument performed well. Conclusions: Although most of the items strongly measure the construct, there are a few items that could be eliminated without substantially altering the instrument. The analysis revealed that the instrument may function differently when administered to different unit types.

scholarly journals Item Response Theory Models for the Fuzzy TOPSIS in the Analysis of Survey Data

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 223
Author(s):  
Bartłomiej Jefmański ◽  
Adam Sagan
Keyword(s):  
Item Response Theory ◽  
Item Response ◽  
Fuzzy Numbers ◽  
Fuzzy Topsis ◽  
Partial Credit Model ◽  
Response Model ◽  
Partial Credit ◽  
Triangular Fuzzy Numbers ◽  
Response Theory ◽  
Irt Models

The fuzzy TOPSIS (The Technique for Order of Preference by Similarity to Ideal Solution) is an attractive tool for measuring complex phenomena based on uncertain data. The original version of the method assumes that the object assessments in terms of the adopted criteria are expressed as triangular fuzzy numbers. One of the crucial stages of the fuzzy TOPSIS is selecting the fuzzy conversion scale, which is used to evaluate objects in terms of the adopted criteria. The choice of a fuzzy conversion scale may influence the results of the fuzzy TOPSIS. There is no uniform approach in constructing and selecting the fuzzy conversion scale for the fuzzy TOPSIS. The choice is subjective and made by researchers. Therefore, the aim of the article is to present a new, objective approach to the construction of fuzzy conversion scales based on Item Response Theory (IRT) models. The following models were used in the construction of fuzzy conversion scales: Polychoric Correlation Model (PM), Polytomous Rasch Model (PRM), Rating Scale Model (RSM), Partial Credit Model (PCM), Generalized Partial Credit Model (GPCM), Graded Response Model (GRM), Nominal Response Model (NRM). The usefulness of the proposed approach is presented on the example of the analysis of a survey’s results on measuring the quality of professional life of inhabitants of selected communes in Poland. The obtained results indicate that the choice of the fuzzy conversion scale has a large impact on the closeness coefficient values. A large difference was also observed in the spreads of triangular fuzzy numbers between scales based on IRT models and those used in the literature on the subject. The use of the fuzzy TOPSIS with fuzzy conversion scales built based on PRM, RSM, PCM, GPCM, and GRM models gives results with a greater range of variability than in the case of fuzzy conversion scales used in empirical research.

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