Usefulness of pystan and numpyro in Bayesian item response theory

Abstract

AbstractPurpose:The purpose of this study is to compare two libraries dedicated to Markov chain Monte Carlo method: pystan and numpyro.Materials and methods:Bayesian item response theory (IRT), 1PL-IRT and 2PL-IRT, were implemented with pystan and numpyro. Then, the Bayesian 1PL-IRT and 2PL-IRT were applied to two types of medical data obtained from a published paper. The same prior distributions of latent parameters were used in both pystan and numpyro. Estimation results of latent parameters of 1PL-IRT and 2PL-IRT were compared between pystan and numpyro. Additionally, the computational cost of Markov chain Monte Carlo method was compared between the two libraries. To evaluate the computational cost of IRT models, simulation data were generated from the medical data and numpyro.Results:For all the combinations of IRT types (1PL-IRT or 2PL-IRT) and medical data types, the mean and standard deviation of the estimated latent parameters were in good agreement between pystan and numpyro. In most cases, the sampling time using Markov chain Monte Carlo method was shorter in numpyro than that in pystan. When the large-sized simulation data were used, numpyro with a graphics processing unit was useful for reducing the sampling time.Conclusion:Numpyro and pystan were useful for applying the Bayesian 1PL-IRT and 2PL-IRT.