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

Abstract

The Bayesian literature has shown that the Hamiltonian Monte Carlo (HMC) algorithm is powerful and efficient for statistical model estimation, especially for complicated models. Stan, a software program built upon HMC, has been introduced as a means of psychometric modeling estimation. However, there are no systemic guidelines for implementing Stan with the log-linear cognitive diagnosis model (LCDM), which is the saturated version of many cognitive diagnostic model (CDM) variants. This article bridges the gap between Stan application and Bayesian LCDM estimation: Both the modeling procedures and Stan code are demonstrated in detail, such that this strategy can be extended to other CDMs straightforwardly.