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

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.