Estimating the DINA model parameters using the No‐U‐Turn Sampler

Abstract

The deterministic inputs, noisy, "and" gate (DINA) model is a popular cognitive diagnosis model (CDM) in psychology and psychometrics used to identify test takers' profiles with respect to a set of latent attributes or skills. In this work, we propose an estimation method for the DINA model with the No-U-Turn Sampler (NUTS) algorithm, an extension to Hamiltonian Monte Carlo (HMC) method. We conduct a simulation study in order to evaluate the parameter recovery and efficiency of this new Markov chain Monte Carlo method and to compare it with two other Bayesian methods, the Metropolis Hastings and Gibbs sampling algorithms, and with a frequentist method, using the Expectation-Maximization (EM) algorithm. The results indicated that NUTS algorithm employed in the DINA model properly recovers all parameters and is accurate for all simulated scenarios. We apply this methodology in the mental health area in order to develop a new method of classification for respondents to the Beck Depression Inventory. The implementation of this method for the DINA model applied to other psychological tests has the potential to improve the medical diagnostic process.

Integrating Differential Evolution Optimization to Cognitive Diagnostic Model Estimation

“…Traditionally, estimating LCDMs refers to the expectation maximization (EM) algorithm (Bock and Aitkin, 1981 ) that maximizes the marginal likelihood; this is the most commonly-seen algorithm in the CDM literature. In addition to the EM algorithm, Markov chain Monte Carlo (MCMC) techniques can be, theoretically, used to estimate the LCDM, but to date its application remains upon simpler CDMs such as the DINA model (da Silva et al, 2017 ; Jiang and Carter, 2018a ). This study focuses on the EM algorithm due to its practicality and popularity.…”

The Impact of Sample Attrition on Longitudinal Learning Diagnosis: A Prolog

“…The posterior distribution of model parameters will be affected by their prior distribution, particularly for a small sample size or a limited number of items. The choice of prior distribution is also worthy of attention (da Silva et al, 2018;Jiang and Carter, 2019). In practice, we recommend that the data analyst selects appropriate prior distributions based on the actual situation rather than copy those given in the Supplementary Table S1.…”

Using Hamiltonian Monte Carlo to estimate the log-linear cognitive diagnosis model via Stan

“…An LCDM (G-DINA with a logit link) provides great flexibility such as (1) subsuming most latent attributes, (2) enabling both additive and non-additive relationships between attributes and items simultaneously, and (3) syncing with other psychometric models, increasing insightfulness. Given these advantages, this article extends the DINA-HMC work by da Silva et al (2017) to a more applicable situation via an LCDM strategy.…”

“…On the other hand, simulation studies conducted by Almond (2014) show that in a simple model JAGS can converge in a shorter time, despite Stan provides more effective sample sizes. Da Silva, de Oliveira, von Davier, and Bazán (2017) claim that a tailored Gibbs sampler, incorporated in the R package dina (Culpepper, 2015) can be more efficient than HMC in Stan, where OpenBUGS is less efficient. Note that the efficiency comparison result can vary from model to model and/or condition to condition.…”