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Estimating Discrete Latent Variable Models Using Amortized Variational Inference
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DOI：10.1017/psy.2026.10105.png)
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Abstract
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Recent research shows that amortized variational inference (AVI) can be used to efficiently estimate high-dimensional latent variable models on large datasets. However; its use has remained limited to item response theory (IRT); and generalizing the approach to discrete latent variable models is not straightforward. We propose two ways to deal with this problem. In an initial simulation; we verify that these approaches can be used to estimate simple discrete latent variable models; such as latent class analysis and the generalized deterministic inputs; noisy and gate model. In these cases; AVI provides accurate parameter estimates; although the computational advantage over marginal maximum likelihood (MML) and standard variational inference (VI) is limited. We then apply the same approach to estimate mixture IRT models. In this case; AVI is computationally faster than MML estimation and standard VI. To demonstrate the practical applicability of our AVI approach; we use it to fit a seven-dimensional mixture IRT model to a narcissism inventory. Whereas quadrature-based methods cannot feasibly estimate models of this dimensionality; the efficient AVI approach even allows for computation of bootstrapped standard errors. We provide our code; along with an easy-to-use tool for fitting these models to new datasets.
Keywords:
amortized variational inference
discrete latent variables
high-dimensional models
latent class analysis
mixture IRT
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