Abstract
Structural equation models comprise a large class of popular statistical models, including factor analysis models, certain mixed models, and extensions thereof. Model estimation is complicated by the fact that we typically have multiple interdependent response variables and multiple latent variables (which may also be called random effects or hidden variables), often leading to slow and inefficient MCMC samples. In this paper, we describe and illustrate a general, efficient approach to Bayesian SEM estimation in Stan, contrasting it with previous implementations in R package blavaan (Merkle & Rosseel, 2018). After describing the approaches in detail, we conduct a practical comparison under multiple scenarios. The comparisons show that the new approach is clearly better. We also discuss ways that the approach may be extended to other models that are of interest to psychometricians.
Highlights
Structural equation models (SEMs) are commonly used in the social sciences, where it is customary to measure unobservable traits such as cognitive abilities, attitudes, and proficiencies
We describe the three Markov chain Monte Carlo (MCMC) approaches that are implemented in blavaan: the original JAGS approach described in Merkle and Rosseel (2018), the original Stan approach that is being formally described in this paper for the first time, and the new Stan approach that is the primary focus of this paper
We briefly describe the three MCMC approaches implemented in blavaan: the original JAGS approach, the original Stan approach, and the new Stan approach that is the focus of this paper
Summary
Structural equation models (SEMs) are commonly used in the social sciences, where it is customary to (attempt to) measure unobservable traits such as cognitive abilities, attitudes, and proficiencies. Such models provide a formal way of connecting these unobservable traits to related, observed variables (e.g., test scores, Likert responses, etc), which has led to longstanding popularity of SEMs. SEMs are related to research on causality and directed acyclic graphs (e.g., Pearl 2013), to generalized linear mixed models A small number of more recent R (R Core Team 2021) packages, including sem (Fox, Nie, and Byrnes 2021), OpenMx (Boker et al 2011), and lavaan (Rosseel 2012), provide open source SEM functionality that utilize classical estimation methods including maximum likelihood or least squares
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