Christopher J. Urban

Christopher J. Urban, Daniel J. Bauer

We investigate novel parameter estimation and goodness-of-fit (GOF) assessment methods for large-scale confirmatory item factor analysis (IFA) with many respondents, items, and latent factors. For parameter estimation, we extend Urban and Bauer's (2021) deep learning algorithm for exploratory IFA to the confirmatory setting by showing how to handle constraints on loadings and factor correlations. For GOF assessment, we explore simulation-based tests and indices that extend the classifier two-sample test (C2ST), a method that tests whether a deep neural network can distinguish between observed data and synthetic data sampled from a fitted IFA model. Proposed extensions include a test of approximate fit wherein the user specifies what percentage of observed and synthetic data should be distinguishable as well as a relative fit index (RFI) that is similar in spirit to the RFIs used in structural equation modeling. Via simulation studies, we show that: (1) the confirmatory extension of Urban and Bauer's (2021) algorithm obtains comparable estimates to a state-of-the-art estimation procedure in less time; (2) C2ST-based GOF tests control the empirical type I error rate and detect when the latent dimensionality is misspecified; and (3) the sampling distribution of the C2ST-based RFI depends on the sample size.

Christopher J. Urban, Daniel J. Bauer

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 an importance-weighted autoencoder (IWAE) for exploratory IFA. The IWAE approximates the MML estimator using an importance sampling technique wherein increasing the number of importance-weighted (IW) samples drawn during fitting improves the approximation, typically at the cost of decreased computational efficiency. We provide a real data application that recovers results aligning with psychological theory across random starts. Via simulation studies, we show that the IWAE yields more accurate estimates as either the sample size or the number of IW samples increases (although factor correlation and intercepts estimates exhibit some bias) and obtains 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.