An Empirical Investigation of Bayesian Hierarchical Modeling with Unidimensional IRT Models

Sheng, Yunlong

doi:10.2333/bhmk.40.19

Cited by 11 publications

(10 citation statements)

References 55 publications

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“…Even with proper non-informative prior densities, the procedure either fails to converge or requires an enormous number of iterations for the Markov chain to reach convergence (Sheng, 2010 ). Sheng ( 2013 ) shows that if one specifies prior distributions for the hyperparameters of the item parameters, instead of setting values for them, the problem can be resolved. This type of hierarchical modeling allows a more objective approach to inference by estimating the parameters of prior distributions from data rather than specifying them using subjective information.…”

Section: Introductionmentioning

confidence: 99%

Investigating a Weakly Informative Prior for Item Scale Hyperparameters in Hierarchical 3PNO IRT Models

Sheng

2017

Front. Psychol.

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The half-t family has been suggested for the scale hyperparameter in Bayesian hierarchical modeling. Two parameters define a half-t distribution: the scale s and the degree-of-freedom ν. When s is set at a finite value that is slightly larger than the actual standard deviation of the parameters, the half-t prior density can be vaguely informative. This paper focused on such densities, and applied them to the hierarchical three-parameter item response theory (IRT) model. Monte Carlo simulations were carried out to investigate the performance of such specifications in parameter recovery and model comparisons under situations where the actual variability of item parameters varied, and results suggest that the half-t family does offer advantages over the commonly adopted uniform or inverse-gamma prior density by allowing the variability for item parameters to be either very small or large. A real data example is also provided to further illustrate this.

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Section: Introductionmentioning

confidence: 99%

Investigating a Weakly Informative Prior for Item Scale Hyperparameters in Hierarchical 3PNO IRT Models

Sheng

2017

Front. Psychol.

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“…This hierarchical structure yields more accurate parameter estimates in small samples than their nonhierarchical counterparts by pooling information across parameters of the same type, depending on τ α and τ β (Fox, 2010; Jackman, 2009). This beneficial characteristic was demonstrated for the H2PL, for instance, by Sheng (2013) and Natesan et al (2016). Moreover, the hierarchical structure requires researchers to specify prior distributions only for the hyperparameters μ ξ and ∑ .…”

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confidence: 99%

“…Their specification, however, is not straightforward (Ames & Smith, 2018). Thus, utilizing a hierarchical approach alleviates this problem (Kim et al, 1994; Sheng, 2013). Nonetheless, the specification of prior distributions for ∑ and τ α and τ β still requires careful consideration.…”

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An Optimized Bayesian Hierarchical Two-Parameter Logistic Model for Small-Sample Item Calibration

König

Spoden

Frey

2019

Applied Psychological Measurement

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Accurate item calibration in models of item response theory (IRT) requires rather large samples. For instance, [Formula: see text] respondents are typically recommended for the two-parameter logistic (2PL) model. Hence, this model is considered a large-scale application, and its use in small-sample contexts is limited. Hierarchical Bayesian approaches are frequently proposed to reduce the sample size requirements of the 2PL. This study compared the small-sample performance of an optimized Bayesian hierarchical 2PL (H2PL) model to its standard inverse Wishart specification, its nonhierarchical counterpart, and both unweighted and weighted least squares estimators (ULSMV and WLSMV) in terms of sampling efficiency and accuracy of estimation of the item parameters and their variance components. To alleviate shortcomings of hierarchical models, the optimized H2PL (a) was reparametrized to simplify the sampling process, (b) a strategy was used to separate item parameter covariances and their variance components, and (c) the variance components were given Cauchy and exponential hyperprior distributions. Results show that when combining these elements in the optimized H2PL, accurate item parameter estimates and trait scores are obtained even in sample sizes as small as [Formula: see text]. This indicates that the 2PL can also be applied to smaller sample sizes encountered in practice. The results of this study are discussed in the context of a recently proposed multiple imputation method to account for item calibration error in trait estimation.

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“…The use of Bayesian MIRT models has been demonstrated on both simulated and real data examples (de la Torre & Patz, 2005;Sheng & Wikle, 2008), but they used large and complete samples. Sheng (2012) and König et al (2020) implemented Bayesian hierarchical univariate item response models for small samples, but both were simulation studies and they did not have sparse measurements. Only one example of a Bayesian hierarchical multidimensional item response model applied to small samples could be found in the literature (de la Torre & Hong, 2010); however, the smallest sample size used in the article was 500, which was part of a simulation study.…”

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confidence: 99%

Bayesian Hierarchical Multidimensional Item Response Modeling of Small Sample, Sparse Data for Personalized Developmental Surveillance

Gilholm

Mengersen

Thompson

2021

Educational and Psychological Measurement

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Developmental surveillance tools are used to closely monitor the early development of infants and young children. This study provides a novel implementation of a multidimensional item response model, using Bayesian hierarchical priors, to construct developmental profiles for a small sample of children ( N = 115) with sparse data collected through an online developmental surveillance tool. The surveillance tool records 348 developmental milestones measured from birth to three years of age, within six functional domains: auditory, hands, movement, speech, tactile, and vision. The profiles were constructed in three steps: (1) the multidimensional item response model, embedded in the Bayesian hierarchical framework, was implemented in order to measure both the latent abilities of the children and attributes of the milestones, while retaining the correlation structure among the latent developmental domains; (2) subsequent hierarchical clustering of the multidimensional ability estimates enabled identification of subgroups of children; and (3) information from the posterior distributions of the item response model parameters and the results of the clustering were used to construct a personalized profile of development for each child. These individual profiles support early identification of, and personalized early interventions for, children with developmental delay.

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An Empirical Investigation of Bayesian Hierarchical Modeling with Unidimensional IRT Models

Cited by 11 publications

References 55 publications

Investigating a Weakly Informative Prior for Item Scale Hyperparameters in Hierarchical 3PNO IRT Models

Investigating a Weakly Informative Prior for Item Scale Hyperparameters in Hierarchical 3PNO IRT Models

An Optimized Bayesian Hierarchical Two-Parameter Logistic Model for Small-Sample Item Calibration

Bayesian Hierarchical Multidimensional Item Response Modeling of Small Sample, Sparse Data for Personalized Developmental Surveillance

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