On the boundary problems in diagnostic classification models

Yamaguchi, Kazuhiro

doi:10.1007/s41237-022-00187-7

Cited by 5 publications

(5 citation statements)

References 59 publications

(87 reference statements)

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“…Due to this context, it is important to note that recently there have been articles pointing out that in situations of low sample size, MMLE-EM can have boundary problems, i.e., that the parameter estimate (in this case a probability of success bounded between 0 and 1) converges toward the boundary of the parameter space [25,26]. It is for this reason that different alternatives for estimating item parameters or classifying individuals have been proposed in the literature.…”

Section: Estimation Proceduresmentioning

confidence: 99%

Exploring Approaches for Estimating Parameters in Cognitive Diagnosis Models with Small Sample Sizes

Sorrel

Escudero

Nájera

et al. 2023

Psych

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Cognitive diagnostic models (CDMs) are increasingly being used in various assessment contexts to identify cognitive processes and provide tailored feedback. However, the most commonly used estimation method for CDMs, marginal maximum likelihood estimation with Expectation–Maximization (MMLE-EM), can present difficulties when sample sizes are small. This study compares the results of different estimation methods for CDMs under varying sample sizes using simulated and empirical data. The methods compared include MMLE-EM, Bayes modal, Markov chain Monte Carlo, a non-parametric method, and a parsimonious parametric model such as Restricted DINA. We varied the sample size, and assessed the bias in the estimation of item parameters, the precision in attribute classification, the bias in the reliability estimate, and computational cost. The findings suggest that alternative estimation methods are preferred over MMLE-EM under low sample-size conditions, whereas comparable results are obtained under large sample-size conditions. Practitioners should consider using alternative estimation methods when working with small samples to obtain more accurate estimates of CDM parameters. This study aims to maximize the potential of CDMs by providing guidance on the estimation of the parameters.

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Section: Estimation Proceduresmentioning

confidence: 99%

Exploring Approaches for Estimating Parameters in Cognitive Diagnosis Models with Small Sample Sizes

Sorrel

Escudero

Nájera

et al. 2023

Psych

View full text Add to dashboard Cite

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“…The core idea of two-level DCMs is to combine DCMs and latent class models using relationship probabilities that connect both measurement models. Figure 1 For the diagnostic measurement, we employed the latent class formulation and notations utilized in Yamaguchi and Okada (2020a) and Yamaguchi andTemplin (2022a, 2022b).…”

Section: Elements Of Two-level Dcmsmentioning

confidence: 99%

“…More detailed update rules follow. Several derivations of the update rules are provided in Yamaguchi (2023).…”

Section: 𝐾 𝑙=1mentioning

confidence: 99%

Bayesian Analysis Methods for Two-Level Diagnosis Classification Models

Yamaguchi

2023

Journal of Educational and Behavioral Statistics

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Understanding whether or not different types of students master various attributes can aid future learning remediation. In this study, two-level diagnostic classification models (DCMs) were developed to represent the probabilistic relationship between external latent classes and attribute mastery patterns. Furthermore, variational Bayesian (VB) inference and Gibbs sampling Markov chain Monte Carlo methods were developed for parameter estimation of the two-level DCMs. The results of a parameter recovery simulation study show that both techniques appropriately recovered the true parameters; Gibbs sampling in particular was slightly more accurate than VB, whereas VB performed estimation much faster than Gibbs sampling. The two-level DCMs with the proposed Bayesian estimation methods were further applied to fourth-grade data obtained from the Trends in International Mathematics and Science Study 2007 and indicated that mathematical activities in the classroom could be organized into four latent classes, with each latent class connected to different attribute mastery patterns. This information can be employed in educational intervention to focus on specific latent classes and elucidate attribute patterns.

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“…For example, Sen and Cohen (2021) set the intercept at −1.1, main effect at 1.3, and interaction effects at 3, which mimicked items with medium-quality. Madison et al (2023) assumed that intercepts were fixed at 0.2, main effects at 2.5 or 1.5, and interactions at 1. Madison and Bradshaw (2018) set intercepts at −2, main effects at 2 or 3, and interaction effects 1.…”

Section: Simulation Study 1 Simulation Settingsmentioning

confidence: 99%

Bayesian Diagnostic Classification Models for a Partially Known Q-matrix

Yamaguchi

2023

Preprint

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In this study, a Bayesian method for the diagnostic classification models (DCMs) for a partially known Q-matrix situation that is intermediate between exploratory and confirmatory is proposed. The partially known Q-matrix situation is practical and useful for application as test experts have some preknowledge of the Q-matrix, although they cannot readily specify them completely. The proposed methods employ priors for the Bayesian variable selection to simultaneously estimate the effects of active and nonactive attributes, and the simulation study obtains appropriate parameter recoveries. Furthermore, a real data example indicates that the proposed Bayesian estimation methods for the partially known Q-matrix fit better than a fully specified Q-matrix. Additionally, the extensions and future directions are discussed.

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On the boundary problems in diagnostic classification models

Abstract: The data analysis code is available at the open science framework website: https://osf.io/rwe5t/. There are no conflicts of interest to declare.

Cited by 5 publications

References 59 publications

Exploring Approaches for Estimating Parameters in Cognitive Diagnosis Models with Small Sample Sizes

Exploring Approaches for Estimating Parameters in Cognitive Diagnosis Models with Small Sample Sizes

Bayesian Analysis Methods for Two-Level Diagnosis Classification Models

Bayesian Diagnostic Classification Models for a Partially Known Q-matrix

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