scholarly journals Estimating Explanatory Extensions of Dichotomous and Polytomous Rasch Models: The eirm Package in R

Psych ◽  
2021 ◽  
Vol 3 (3) ◽  
pp. 308-321
Author(s):  
Okan Bulut ◽  
Guher Gorgun ◽  
Seyma Nur Yildirim-Erbasli
Keyword(s):  
Item Response ◽  
Rating Scale ◽  
Real Data ◽  
R Package ◽  
Explanatory Models ◽  
Scale Model ◽  
Test Model ◽  
Partial Credit Model ◽  
Irt Models ◽  
Explanatory Irt

Explanatory item response modeling (EIRM) enables researchers and practitioners to incorporate item and person properties into item response theory (IRT) models. Unlike traditional IRT models, explanatory IRT models can explain common variability stemming from the shared variance among item clusters and person groups. In this tutorial, we present the R package eirm, which provides a simple and easy-to-use set of tools for preparing data, estimating explanatory IRT models based on the Rasch family, extracting model output, and visualizing model results. We describe how functions in the eirm package can be used for estimating traditional IRT models (e.g., Rasch model, Partial Credit Model, and Rating Scale Model), item-explanatory models (i.e., Linear Logistic Test Model), and person-explanatory models (i.e., latent regression models) for both dichotomous and polytomous responses. In addition to demonstrating the general functionality of the eirm package, we also provide real-data examples with annotated R codes based on the Rosenberg Self-Esteem Scale.

Optimal Calibration Designs for Tests of Polytomously Scored Items Described by Item Response Theory Models

2001 ◽  
Vol 26 (4) ◽  
pp. 361-380 ◽  
Author(s):  
Rebecca Holman ◽  
Martijn P. F. Berger
Keyword(s):  
Item Response Theory ◽  
Item Response ◽  
Rating Scale ◽  
Information Matrix ◽  
Scale Model ◽  
Partial Credit Model ◽  
Response Theory ◽  
Irt Models ◽  
Optimal Calibration ◽  
Fisher's Information

This article examines calibration designs, which maximize the determinant of Fisher’s information matrix on the item parameters (D-optimal), for sets of polytomously scored items. These items were analyzed using a number of item response theory (IRT) models, which are members of the “divide-by-total” family, including the nominal categories model, the rating scale model, the unidimensional polytomous Rasch model and the partial credit model. We extend the known results for dichotomous items, both singly and in tests to polytomous items. The structure of Fisher’s information matrix is examined in order to gain insights into the structure of D-optimal calibration designs for IRT models. A theorem giving an upper bound for the number of support points for such models is proved. A lower bound is also given. Finally, we examine a set of items, which have been analyzed using a number of different models. The locally D-optimal calibration design for each analysis is calculated using an exact numerical and a sequential procedure. The results are discussed both in general and in relation to each other.

scholarly journals A General Bayesian Multidimensional Item Response Theory Model for Small and Large Samples

2020 ◽  
Vol 80 (4) ◽  
pp. 665-694
Author(s):  
Ken A. Fujimoto ◽  
Sabina R. Neugebauer
Keyword(s):  
Item Response Theory ◽  
Item Response ◽  
Rating Scale ◽  
Real Data ◽  
Theory Model ◽  
Dimensional Structure ◽  
Small Scale ◽  
Response Theory ◽  
Large Samples ◽  
Irt Models

Although item response theory (IRT) models such as the bifactor, two-tier, and between-item-dimensionality IRT models have been devised to confirm complex dimensional structures in educational and psychological data, they can be challenging to use in practice. The reason is that these models are multidimensional IRT (MIRT) models and thus are highly parameterized, making them only suitable for data provided by large samples. Unfortunately, many educational and psychological studies are conducted on a small scale, leaving the researchers without the necessary MIRT models to confirm the hypothesized structures in their data. To address the lack of modeling options for these researchers, we present a general Bayesian MIRT model based on adaptive informative priors. Simulations demonstrated that our MIRT model could be used to confirm a two-tier structure (with two general and six specific dimensions), a bifactor structure (with one general and six specific dimensions), and a between-item six-dimensional structure in rating scale data representing sample sizes as small as 100. Although our goal was to provide a general MIRT model suitable for smaller samples, the simulations further revealed that our model was applicable to larger samples. We also analyzed real data from 121 individuals to illustrate that the findings of our simulations are relevant to real situations.

Mokken Scale Analysis: Discussion and Application

2021 ◽  
Vol 8 (3) ◽  
pp. 672-695
Author(s):  
Thomas DeVaney
Keyword(s):  
Item Response Theory ◽  
Item Response ◽  
Rating Scale ◽  
Scale Analysis ◽  
Guttman Scale ◽  
Response Theory ◽  
Data Set ◽  
Mokken Scale Analysis ◽  
Irt Models ◽  
Guttman Scaling

This article presents a discussion and illustration of Mokken scale analysis (MSA), a nonparametric form of item response theory (IRT), in relation to common IRT models such as Rasch and Guttman scaling. The procedure can be used for dichotomous and ordinal polytomous data commonly used with questionnaires. The assumptions of MSA are discussed as well as characteristics that differentiate a Mokken scale from a Guttman scale. MSA is illustrated using the mokken package with R Studio and a data set that included over 3,340 responses to a modified version of the Statistical Anxiety Rating Scale. Issues addressed in the illustration include monotonicity, scalability, and invariant ordering. The R script for the illustration is included.

scholarly journals IRTBEMM: An R Package for Estimating IRT Models With Guessing or Slipping Parameters

2020 ◽  
Vol 44 (7-8) ◽  
pp. 566-567
Author(s):  
Shaoyang Guo ◽  
Chanjin Zheng ◽  
Justin L. Kern
Keyword(s):  
Maximum Likelihood ◽  
Item Response Theory ◽  
Item Response ◽  
R Package ◽  
Response Theory ◽  
Estimation Algorithms ◽  
Irt Models ◽  
Irt Estimation

A recently released R package IRTBEMM is presented in this article. This package puts together several new estimation algorithms (Bayesian EMM, Bayesian E3M, and their maximum likelihood versions) for the Item Response Theory (IRT) models with guessing and slipping parameters (e.g., 3PL, 4PL, 1PL-G, and 1PL-AG models). IRTBEMM should be of interest to the researchers in IRT estimation and applying IRT models with the guessing and slipping effects to real datasets.

On Longitudinal Item Response Theory Models: A Didactic

2019 ◽  
Vol 45 (3) ◽  
pp. 339-368 ◽  
Author(s):  
Chun Wang ◽  
Steven W. Nydick
Keyword(s):  
Item Response Theory ◽  
Item Response ◽  
Real Data ◽  
Measurement Model ◽  
Higher Order ◽  
Response Theory ◽  
Latent Growth ◽  
Multidimensional Irt ◽  
Irt Model ◽  
Irt Models

Recent work on measuring growth with categorical outcome variables has combined the item response theory (IRT) measurement model with the latent growth curve model and extended the assessment of growth to multidimensional IRT models and higher order IRT models. However, there is a lack of synthetic studies that clearly evaluate the strength and limitations of different multilevel IRT models for measuring growth. This study aims to introduce the various longitudinal IRT models, including the longitudinal unidimensional IRT model, longitudinal multidimensional IRT model, and longitudinal higher order IRT model, which cover a broad range of applications in education and social science. Following a comparison of the parameterizations, identification constraints, strengths, and weaknesses of the different models, a real data example is provided to illustrate the application of different longitudinal IRT models to model students’ growth trajectories on multiple latent abilities.

scholarly journals Item Response Tree Models to Investigate Acquiescence and Extreme Response Styles in Likert-Type Rating Scales

2019 ◽  
Vol 79 (5) ◽  
pp. 911-930 ◽  
Author(s):  
Minjeong Park ◽  
Amery D. Wu
Keyword(s):  
Item Response ◽  
Rating Scales ◽  
Rating Scale ◽  
Explanatory Models ◽  
Response Styles ◽  
Modeling Framework ◽  
Typical Application ◽  
Item Response Models ◽  
Extreme Response ◽  
Tree Models

Item response tree (IRTree) models are recently introduced as an approach to modeling response data from Likert-type rating scales. IRTree models are particularly useful to capture a variety of individuals’ behaviors involving in item responding. This study employed IRTree models to investigate response styles, which are individuals’ tendencies to prefer or avoid certain response categories in a rating scale. Specifically, we introduced two types of IRTree models, descriptive and explanatory models, perceived under a larger modeling framework, called explanatory item response models, proposed by De Boeck and Wilson. This extends the typical application of IRTree models for studying response styles. As a demonstration, we applied the descriptive and explanatory IRTree models to examine acquiescence and extreme response styles in Rosenberg’s Self-Esteem Scale. Our findings suggested the presence of two distinct extreme response styles and acquiescence response style in the scale.

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.

scholarly journals Performance of Polytomous IRT Models With Rating Scale Data: An Investigation Over Sample Size, Instrument Length, and Missing Data

2021 ◽  
Vol 6 ◽  
Author(s):  
Shenghai Dai ◽  
Thao Thu Vo ◽  
Olasunkanmi James Kehinde ◽  
Haixia He ◽  
Yu Xue ◽  
...  
Keyword(s):  
Missing Data ◽  
Sample Size ◽  
Rating Scales ◽  
Rating Scale ◽  
Small Sample Size ◽  
Small Sample ◽  
Item Parameter ◽  
Partial Credit Model ◽  
Irt Models ◽  
Polytomous Irt Models

The implementation of polytomous item response theory (IRT) models such as the graded response model (GRM) and the generalized partial credit model (GPCM) to inform instrument design and validation has been increasing across social and educational contexts where rating scales are usually used. The performance of such models has not been fully investigated and compared across conditions with common survey-specific characteristics such as short test length, small sample size, and data missingness. The purpose of the current simulation study is to inform the literature and guide the implementation of GRM and GPCM under these conditions. For item parameter estimations, results suggest a sample size of at least 300 and/or an instrument length of at least five items for both models. The performance of GPCM is stable across instrument lengths while that of GRM improves notably as the instrument length increases. For person parameters, GRM reveals more accurate estimates when the proportion of missing data is small, whereas GPCM is favored in the presence of a large amount of missingness. Further, it is not recommended to compare GRM and GPCM based on test information. Relative model fit indices (AIC, BIC, LL) might not be powerful when the sample size is less than 300 and the length is less than 5. Synthesis of the patterns of the results, as well as recommendations for the implementation of polytomous IRT models, are presented and discussed.

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