Effect of Q-matrix Misspecification on Variational Autoencoders (VAE) for Multidimensional Item Response Theory (MIRT) Models Estimation

Deep generative models with a specific variational autoencoding structure are capable of estimating parameters for the multidimensional logistic 2-parameter (ML2P) model in item response theory. In this work, we incorporated Q-matrix and variational autoencoder (VAE) to estimate item parameters with correlated and independent latent abilities, and we validate Q-matrix via the root mean square error (RMSE), bias, correlation, and AIC and BIC test score. 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 such as players performance evaluation, clinical trials assessment. Moreover, results show that the ML2P-VAE method is capable of estimating parameters and validating Q-matrix for models with a large number of latent variables with low computational cost, whereas traditional methods are infeasible for data with high-dimensional latent traits.