arXiv subjects

Daniel J. Bauer

Publications and source records attributed to Daniel J. Bauer.

3 recordsLinked to original sources

arXiv2026

Two-stage Estimation of Latent Variable Regression Models: A General, Root-N Consistent Solution

Latent variable (LV) models are widely used in psychological research to investigate relationships among unobservable constructs. When one-stage estimation of the overall LV model is challenging, two-stage factor score regression (FSR) serves as a convenient alternative: the measurement model is fitted to obtain factor scores in the first stage, which are then used to fit the structural model in the subsequent stage. However, naive application of FSR is known to yield biased estimates of structural parameters. In this paper, we develop a generic bias-correction framework for two-stage estimation of parametric statistical models and tailor it specifically to FSR. Unlike existing bias-corrected FSR solutions, the proposed method applies to a broader class of LV models and does not require computing specific types of factor scores. We establish the root-n consistency of the proposed bias-corrected two-stage estimator under mild regularity conditions. To ensure broad applicability and minimize reliance on complex analytical derivations, we introduce a stochastic approximation algorithm for point estimation and a Monte Carlo-based procedure for variance estimation. In a sequence of Monte Carlo experiments, we demonstrate that the bias-corrected FSR estimator performs comparably to the ``gold standard'' one-stage maximum likelihood estimator. These results suggest that our approach offers a straightforward yet effective alternative for estimating LV models.

stat.ME↗

arXiv2023

Deep Learning-Based Estimation and Goodness-of-Fit for Large-Scale Confirmatory Item Factor Analysis

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.

stat.ML↗

arXiv2020

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

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.

stat.ME↗