Estimation of multidimensional item response theory models with correlated latent variables using variational autoencoders

Artificial neural networks with a specific autoencoding structure are capable of estimating parameters for the multidimensional logistic 2-parameter (ML2P) model in item response theory (Curi et al. in International joint conference on neural networks (IJCNN), 2019), but with limitations, such as uncorrelated latent traits. In this work, we extend variational auto encoders (VAE) to estimate item parameters and correlated latent abilities, and directly compare the ML2P-VAE method to more traditional parameter estimation methods, such as Monte Carlo expectation-maximization. The incorporation of a non-identity covariance matrix in a VAE requires a novel VAE architecture, which can be utilized in applications outside of education. In addition, we show that the ML2P-VAE method is capable of estimating parameters for models with a large number of latent variables with low computational cost, where traditional methods are infeasible for data with high-dimensional latent traits.