Autoencoders for Amortized Joint Maximum Likelihood Estimation of Confirmatory Item Factor Models.

Abstract

Neural networks like variational autoencoders have been proposed as a statistical tool to fit item factor models to data. Advantages are that high dimensional models can be estimated more efficiently as compared to conventional approaches. In this study, we demonstrate advantages of a specific autoencoder as a tool for amortized joint maximum likelihood estimation of item factor models. Contrary to contemporary joint maximum likelihood estimation and marginal maximum likelihood estimation, no additional parameter constraints are necessary to ensure standard asymptotic theory to apply. In a simulation study, the performance of the autoencoder is compared to constrained joint maximum likelihood and various forms of marginal maximum likelihood under different distributions for the factor scores. Results show that the amortized joint maximum likelihood estimates of the factors scores are overall less biased as compared to the other approaches. We illustrate the use of the autoencoder in two real data examples.