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

arXiv: https://arxiv.org/abs/2109.09500 · HTML: https://mlsanity.com/paper/2109.09500/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 99 references that are in the map.
- First posted on arXiv 20 Sep 2021.

## Builds on (most cited first, 18 of 18)

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- [All Models are Wrong, but Many are Useful: Learning a Variable's Importance by Studying an Entire Class of Prediction Models Simultaneously](https://mlsanity.com/paper/1801.01489/) (2018)
- [Revisiting Classifier Two-Sample Tests](https://mlsanity.com/paper/1610.06545/) (2016)
- [Advances in Variational Inference](https://mlsanity.com/paper/1711.05597/) (2017)
- [Explaining individual predictions when features are dependent: More accurate approximations to Shapley values](https://mlsanity.com/paper/1903.10464/) (2019)
- [On the Convergence of A Class of Adam-Type Algorithms for Non-Convex Optimization](https://mlsanity.com/paper/1808.02941/) (2018)
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- [not-MIWAE: Deep Generative Modelling with Missing not at Random Data](https://mlsanity.com/paper/2006.12871/) (2020)
- [Classification accuracy as a proxy for two sample testing](https://mlsanity.com/paper/1602.02210/) (2016)
- [Doubly Reparameterized Gradient Estimators for Monte Carlo Objectives](https://mlsanity.com/paper/1810.04152/) (2018)
- [Variational Item Response Theory: Fast, Accurate, and Expressive](https://mlsanity.com/paper/2002.00276/) (2020)
- [β3-IRT: A New Item Response Model and its Applications](https://mlsanity.com/paper/1903.04016/) (2019)
- [A General Family of Stochastic Proximal Gradient Methods for Deep Learning](https://mlsanity.com/paper/2007.07484/) (2020)
- [A Deep Learning Algorithm for High-Dimensional Exploratory Item Factor Analysis](https://mlsanity.com/paper/2001.07859/) (2020)
- [Multicollinearity Correction and Combined Feature Effect in Shapley Values](https://mlsanity.com/paper/2011.01661/) (2020)

## Abstract (arXiv)

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.