Accelerating item factor analysis on GPU with Python package xifa.

Item parameter estimation is a crucial step when conducting item factor analysis (IFA). From the view of frequentist estimation, marginal maximum likelihood (MML) seems to be the gold standard. However, fitting a high-dimensional IFA model by MML is still a challenging task. The current study demonstrates that with the help of a GPU (graphics processing unit) and carefully designed vectorization, the computational time of MML could be largely reduced for large-scale IFA applications. In particular, a Python package called xifa (accelerated item factor analysis) is developed, which implements a vectorized Metropolis-Hastings Robbins-Monro (VMHRM) algorithm. Our numerical experiments show that the VMHRM on a GPU may run 33 times faster than its CPU version. When the number of factors is at least five, VMHRM (on GPU) is much faster than the Bock-Aitkin expectation maximization, MHRM implemented by mirt (on CPU), and the importance-weighted autoencoder (on GPU). The GPU-implemented VMHRM is most appropriate for high-dimensional IFA with large data sets. We believe that GPU computing will play a central role in large-scale psychometric modeling in the near future.