A Deep Learning Algorithm for High-Dimensional Exploratory Item Factor Analysis

Deep learning methods are the gold standard for non-linear statistical modeling in computer vision and in natural language processing but are rarely used in psychometrics. To bridge this gap, we present a novel deep learning algorithm for exploratory item factor analysis (IFA). Our approach combines a deep artificial neural network (ANN) model called a variational autoencoder (VAE) with recent work that uses regularization for exploratory factor analysis. We first provide overviews of ANNs and VAEs. We then describe how to conduct exploratory IFA with a VAE and demonstrate our approach in two empirical examples and in two simulated examples. Our empirical results were consistent with existing psychological theory across random starting values. Our simulations suggest that the VAE consistently recovers the data generating factor pattern with moderate-sized samples. Secondary loadings were underestimated with a complex factor structure and intercept parameter estimates were moderately biased with both simple and complex factor structures. All models converged in minutes, even with hundreds of thousands of observations, hundreds of items, and tens of factors. We conclude that the VAE offers a powerful new approach to fitting complex statistical models in psychological and educational measurement.