Semi-Confirmatory Structural Equation Modeling via Penalized Likelihood or Least Squares

Fits semi-confirmatory structural equation modeling (SEM) via penalized likelihood (PL) or penalized least squares (PLS). For details, please see Huang (2020) .

Elastic Net Penalized Maximum Likelihood for Structural Equation Models with Network GPT Framework

Provides elastic net penalized maximum likelihood estimator for structural equation models (SEM). The package implements `lasso` and `elastic net` (l1/l2) penalized SEM and estimates the model parameters with an efficient block coordinate ascent algorithm that maximizes the penalized likelihood of the SEM. Hyperparameters are inferred from cross-validation (CV). A Stability Selection (STS) function is also available to provide accurate causal effect selection. The software achieves high accuracy performance through a `Network Generative Pre-trained Transformer` (Network GPT) Framework with two steps: 1) pre-trains the model to generate a complete (fully connected) graph; and 2) uses the complete graph as the initial state to fit the `elastic net` penalized SEM.

Latent Variable Models

A general implementation of Structural Equation Models with latent variables (MLE, 2SLS, and composite likelihood estimators) with both continuous, censored, and ordinal outcomes (Holst and Budtz-Joergensen (2013) ). Mixture latent variable models and non-linear latent variable models (Holst and Budtz-Joergensen (2020) ). The package also provides methods for graph exploration (d-separation, back-door criterion), simulation of general non-linear latent variable models, and estimation of influence functions for a broad range of statistical models.

Bayesian Latent Variable Analysis

Fit a variety of Bayesian latent variable models, including confirmatory factor analysis, structural equation models, and latent growth curve models. References: Merkle & Rosseel (2018) ; Merkle et al. (2021) .

Fitting Structural Equation Mixture Models

Estimation of structural equation models with nonlinear effects and underlying nonnormal distributions.

Supplementary Item Response Theory Models

Supplementary functions for item response models aiming to complement existing R packages. The functionality includes among others multidimensional compensatory and noncompensatory IRT models (Reckase, 2009, ), MCMC for hierarchical IRT models and testlet models (Fox, 2010, ), NOHARM (McDonald, 1982, ), Rasch copula model (Braeken, 2011, ; Schroeders, Robitzsch & Schipolowski, 2014, ), faceted and hierarchical rater models (DeCarlo, Kim & Johnson, 2011, ), ordinal IRT model (ISOP; Scheiblechner, 1995, ), DETECT statistic (Stout, Habing, Douglas & Kim, 1996, ), local structural equation modeling (LSEM; Hildebrandt, Luedtke, Robitzsch, Sommer & Wilhelm, 2016, ).

Multivariate Spatio-Temporal Models using Structural Equations

Fits a wide variety of multivariate spatio-temporal models with simultaneous and lagged interactions among variables (including vector autoregressive spatio-temporal ('VAST') dynamics) for areal, continuous, or network spatial domains. It includes time-variable, space-variable, and space-time-variable interactions using dynamic structural equation models ('DSEM') as expressive interface, and the 'mgcv' package to specify splines via the formula interface. See Thorson et al. (2025) for more details.

Generate Standardized Data

Creates simulated data from structural equation models with standardized loading. Data generation methods are described in Schneider (2013) .

Mediation, Moderation and Moderated-Mediation After Model Fitting

Computes indirect effects, conditional effects, and conditional indirect effects in a structural equation model or path model after model fitting, with no need to define any user parameters or label any paths in the model syntax, using the approach presented in Cheung and Cheung (2024) . Can also form bootstrap confidence intervals by doing bootstrapping only once and reusing the bootstrap estimates in all subsequent computations. Supports bootstrap confidence intervals for standardized (partially or completely) indirect effects, conditional effects, and conditional indirect effects as described in Cheung (2009) and Cheung, Cheung, Lau, Hui, and Vong (2022) . Model fitting can be done by structural equation modeling using lavaan() or regression using lm().

Bayes Factors for Informative Hypotheses

Computes approximated adjusted fractional Bayes factors for equality, inequality, and about equality constrained hypotheses. For a tutorial on this method, see Hoijtink, Mulder, van Lissa, & Gu, (2019) . For applications in structural equation modeling, see: Van Lissa, Gu, Mulder, Rosseel, Van Zundert, & Hoijtink, (2021) . For the statistical underpinnings, see Gu, Mulder, and Hoijtink (2018) ; Hoijtink, Gu, & Mulder, J. (2019) ; Hoijtink, Gu, Mulder, & Rosseel, (2019) .