scholarly journals Exploring the Correlation Between Multiple Latent Variables and Covariates in Hierarchical Data Based on the Multilevel Multidimensional IRT Model

2019 ◽  
Vol 10 ◽  
Author(s):  
Jiwei Zhang ◽  
Jing Lu ◽  
Feng Chen ◽  
Jian Tao
Keyword(s):  
Latent Variables ◽  
Hierarchical Data ◽  
Multidimensional Irt ◽  
Irt Model

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.

A multidimensional IRT model for continuous and graded responses with error in persons and items

2020 ◽  
Author(s):  
Pere Ferrando ◽  
David Navarro-González
Keyword(s):  
Measurement Precision ◽  
Multidimensional Irt ◽  
Irt Model ◽  
Graded Responses ◽  
Factor Analytic ◽  
Continuous Responses ◽  
Categorical Responses ◽  
Ordered Categorical

This article proposes two multidimensional extensions of existing DMs: the M-DTCRM, intended for (approximately) continuous responses, and the M-DTGRM, intended for ordered-categorical responses (including binary). A rationale for the extension to the multiple-content-dimensions case, which is based on the concept of the multidimensional location index, is first proposed and discussed. Then, the models are described using both the factor-analytic and the IRT parameterizations. Procedures for (a) calibrating the items, (b) scoring individuals, (c) assessing model appropriateness, and (d) assessing measurement precision are finally discussed. The proposals are submitted to be of particular interest for the case of multidimensional questionnaires in which the number of items per scale would not be enough for arriving at stable estimates.

An Extended Multidimensional IRT Formulation for the Linear Item Factor Analysis Model

Methodology ◽  
2016 ◽  
Vol 12 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Pere J. Ferrando
Keyword(s):  
Item Response ◽  
Item Analysis ◽  
Analysis Model ◽  
Factor Analysis Model ◽  
Multidimensional Irt ◽  
Irt Model ◽  
Validity Assessment ◽  
Item Responses ◽  
Item Factor Analysis ◽  
Difficulty Index

Abstract. In previous research Spearman’s factor-analytic (FA) model has been formulated as a linear Item Response Theory (IRT) model for (approximately) continuous item responses. Furthermore, some generalized IRT-based indices have been proposed for multidimensional FA. However, to date no explicit IRT formulation has existed for this model. This article extends previous proposals in two directions. First, it proposes a Lord’s-type parameterization of the multidimensional FA model in which each item is characterized by a difficulty index in each dimension. Second, it proposes two multidimensional IRT-based item-person-distance indices. The characteristics and advantages of all the proposed measures as well as their relations to existing indices are discussed. The usefulness of the proposal in item analysis and validity assessment is also discussed and illustrated with two empirical examples.

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