Estimation of a Simple Structure in a Multidimensional IRT Model Using Structure Regularization

We develop a method for estimating a simple matrix for a multidimensional item response theory model. Our proposed method allows each test item to correspond to a single latent trait, making the results easier to interpret. It also enables clustering of test items based on their corresponding latent...

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Bibliographic Details
Published inEntropy (Basel, Switzerland) Vol. 26; no. 1; p. 44
Main Authors Shimmura, Ryosuke, Suzuki, Joe
Format Journal Article
LanguageEnglish
Published Switzerland MDPI AG 31.12.2023
Subjects
Algorithms
Analysis
Clustering
Estimates
Estimation
Estimation theory
Factor analysis
Item response theory
lasso
Matrices
Monte Carlo simulation
Optimization
prenet penalty
Regularization
simple structure
stochastic EM algorithm
Variables
Japan
stochastic EM algorithm
simple structure
lasso
prenet penalty
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Summary:We develop a method for estimating a simple matrix for a multidimensional item response theory model. Our proposed method allows each test item to correspond to a single latent trait, making the results easier to interpret. It also enables clustering of test items based on their corresponding latent traits. The basic idea of our approach is to use the prenet (product-based elastic net) penalty, as proposed in factor analysis. For optimization, we show that combining stochastic EM algorithms, proximal gradient methods, and coordinate descent methods efficiently yields solutions. Furthermore, our numerical experiments demonstrate its effectiveness, especially in cases where the number of test subjects is small, compared to methods using the existing L1 penalty.
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ISSN:1099-4300
1099-4300
DOI:10.3390/e26010044