Marginal maximum likelihood (MML) estimation is the preferred approach to fitting item response theory models in psychometrics due to the MML estimator's consistency, normality, and efficiency as the sample size tends to infinity. However, state-of-the-art MML estimation procedures such as the Metropolis-Hastings Robbins-Monro (MH-RM) algorithm as well as approximate MML estimation procedures such as variational inference (VI) are computationally time-consuming when the sample size and the number of latent factors are very large. In this work, we investigate a deep learning-based VI algorithm for exploratory item factor analysis (IFA) that is computationally fast even in large data sets with many latent factors. The proposed approach applies a deep artificial neural network model called a variational autoencoder for exploratory IFA. An importance sampling technique to help the variational estimator better approximate the MML estimator is explored. We provide a real data application that recovers results aligning with psychological theory across random starts. Via simulation studies, we empirically demonstrate that the variational estimator is consistent (although factor correlation estimates exhibit some bias) and yields similar results to MH-RM in less time. Our simulations also suggest that the proposed approach performs similarly to and is potentially faster than constrained joint maximum likelihood estimation, a fast procedure that is consistent when the sample size and the number of items simultaneously tend to infinity.
Combining Maximum-Likelihood with Deep Learning for Event Reconstruction in IceCube
