There are two papers related to `{INLAvaan}` and its underlying methodology. To cite `{INLAvaan}` in publications, please consider citing both.

To cite the methodological contribution exclusively, please cite:

Jamil H, Rue H (2026). “Approximate Bayesian inference for structural equation models using integrated nested Laplace approximations.” doi:10.48550/arXiv.2603.25690, 2603.25690.

To cite the software implementation and workflows, please cite:

Jamil H, Rue H (2026). “Implementation and workflows for INLA-based approximate Bayesian structural equation modelling.” doi:10.48550/arXiv.2604.00671, 2604.00671.

Corresponding BibTeX entries:

  @Misc{jamil2026approximate,
    title = {Approximate Bayesian inference for structural equation
      models using integrated nested Laplace approximations},
    author = {Haziq Jamil and Håvard Rue},
    year = {2026},
    number = {2603.25690 [stat.ME]},
    eprint = {2603.25690},
    primaryclass = {stat.ME},
    publisher = {arXiv},
    doi = {10.48550/arXiv.2603.25690},
    abstract = {Markov chain Monte Carlo (MCMC) methods remain the
      mainstay of Bayesian estimation of structural equation models
      (SEM); however they often incur a high computational cost. We
      present a bespoke approximate Bayesian approach to SEM, drawing
      on ideas from the integrated nested Laplace approximation (INLA;
      Rue et al., 2009, J. R. Stat. Soc. Series B Stat. Methodol.)
      framework. We implement a simplified Laplace approximation that
      efficiently profiles the posterior density in each parameter
      direction while correcting for asymmetry, allowing for parametric
      skew-normal estimation of the marginals. Furthermore, we apply a
      variational Bayes correction to shift the marginal locations,
      thereby better capturing the posterior mass. Essential
      quantities, including factor scores and model-fit indices, are
      obtained via an adjusted Gaussian copula sampling scheme. For
      normal-theory SEM, this approach offers a highly accurate
      alternative to sampling-based inference, achieving near-'maximum
      likelihood' speeds while retaining the precision of full Bayesian
      inference.},
    archiveprefix = {arXiv},
    copyright = {Creative Commons Attribution Non Commercial Share
      Alike 4.0 International},
  }

  @Misc{jamil2026implementation,
    title = {Implementation and workflows for INLA-based approximate
      Bayesian structural equation modelling},
    author = {Haziq Jamil and Håvard Rue},
    year = {2026},
    number = {2604.00671 [stat.CO]},
    eprint = {2604.00671},
    primaryclass = {stat.CO},
    publisher = {arXiv},
    doi = {10.48550/arXiv.2604.00671},
    abstract = {Bayesian structural equation modelling (BSEM) offers
      many advantages such as principled uncertainty quantification,
      small-sample regularisation, and flexible model specification.
      However, the Markov chain Monte Carlo (MCMC) methods on which it
      relies are computationally prohibitive for the iterative cycle of
      specification, criticism, and refinement that careful
      psychometric practice demands. We present INLAvaan, an R package
      for fast, approximate Bayesian SEM built around the Integrated
      Nested Laplace Approximation (INLA) framework for structural
      equation models developed by Jamil & Rue (2026, arXiv:2603.25690
      [stat.ME]). This paper serves as a companion manuscript that
      describes the architectural decisions and computational
      strategies underlying the package. Two substantive applications
      -- a 256-parameter bifactor circumplex model and a multilevel
      mediation model with full-information missing-data handling --
      demonstrate the approach on specifications where MCMC would
      require hours of run time and careful convergence work. In
      constrast, INLAvaan delivers calibrated posterior summaries in
      seconds.},
    archiveprefix = {arXiv},
    copyright = {Creative Commons Attribution Non Commercial Share
      Alike 4.0 International},
  }