Estimating CDMs Using the Slice-Within-Gibbs Sampler

Abstract

In this paper, the slice-within-Gibbs sampler has been introduced as a method for estimating cognitive diagnosis models (CDMs). Compared with other Bayesian methods, the slice-within-Gibbs sampler can employ a wide-range of prior specifications; moreover, it can also be applied to complex CDMs with the aid of auxiliary variables, especially when applying different identifiability constraints. To evaluate its performances, two simulation studies were conducted. The first study confirmed the viability of the slice-within-Gibbs sampler in estimating CDMs, mainly including G-DINA and DINA models. The second study compared the slice-within-Gibbs sampler with other commonly used Markov Chain Monte Carlo algorithms, and the results showed that the slice-within-Gibbs sampler converged much faster than the Metropolis-Hastings algorithm and more flexible than the Gibbs sampling in choosing the distributions of priors. Finally, a fraction subtraction dataset was analyzed to illustrate the use of the slice-within-Gibbs sampler in the context of CDMs.

Knowledge Integration in Science Learning: Tracking Students' Knowledge Development and Skill Acquisition with Cognitive Diagnosis Models

“…The approach is based on cognitive diagnosis models (CDMs; de la Torre et al., 2018; Junker & Sijtsma, 2001; Rupp & Templin, 2008). CDMs have been employed in both educational and noneducational contexts (Chen et al., 2017; de la Torre et al., 2018; Guo et al., 2019; Iaconangelo et al., 2022; Lee & Sawaki, 2009; Xu et al., 2020; Wu et al., 2021). For example, CDMs have been employed to evaluate reading comprehension in English (Lee & Sawaki, 2009; Ravand, 2016; Ravand & Robitzsch, 2018) and to diagnose psychological disorders (de la Torre et al., 2018; Jaeger et al., 2006; Templin & Henson, 2006).…”

The Restricted DINA Model: A Comprehensive Cognitive Diagnostic Model for Classroom-Level Assessments

“…Firstly, it can be distinguished between parametric and nonparametric CDMs. The former are stochastic models that, under some specific assumptions, provide consistent estimates of both item and person parameters via marginalized maximum likelihood estimation (e.g., de la Torre, 2009de la Torre, , 2011 or Markov chain Monte Carlo algorithms (e.g., Liu et al, 2020;Xu et al, 2020). On the other hand, nonparametric CDMs are deterministic methods that classify students without relying on model parameter estimation.…”

Recent Development of Parameter Estimation Methods in Diagnostic Classification Models

“…Gibbs sampling)も提案されている(Yamaguchi and Templin, 2022a) ．さらに，スライスサ ンプリングを用いた方法(Xu et al, 2020) や，DINA モデルのパラメタ推定に Pólya-gamma 分布を用いた方法(Zhang et al, 2020) や，Pólya-gamma 分布を用いてモデルパラメタとＱ行 列の推定も同時に実行する方法も提案されている(Balamuta and Culpepper, .g., Jeon et al, 2017)．上記のように，変分ベイ et al, 2021) もあり，ますますの発展が見られる．変分ベイズ推定法について の理論的な解説は Nakajima et al (2019) においてなされている．また，入門的レビューに ついては Blei et al (2017) や Grimmer(2011) が参考になる． DCM においては，Yamaguchi and Okada(2020c) において変分ベイズ推定法に基づく DINA モデルの推定アルゴリズムが提案されている．さらに，Yamaguchi(2020) は多枝選 択式のデータに対する DINA モデル(multiple choice DINA model)について，Yamaguchi and Okada(2020b) は前述の MCMC 法で用いたモデルと事前分布を仮定した変分ベイズ推 定法を提案した．この他，Yamaguchi and Martinez(2023) は隠れマルコフモデルにもとづ く縦断的 DCM に対して変分ベイズ推定法を提案し，Yamaguchi (2023a) は外部情報を含め た DCM のうちの一つである二段階 DCM に対する変分ベイズ推定法を提案している．本 節では，Yamaguchi and Okada(2020b) にもとづいた DCM における変分ベイズ推定法のア ルゴリズムを示す．アルゴリズムの具体的な導出方法については，Yamaguchi and Okada (2020b) に詳細な記載がある．…”