Continuous Time Structural Equation Modelling - Old 'OpenMx'-Based Version

Original 'ctsem' (continuous time structural equation modelling) functionality, based on the 'OpenMx' software, as described in Driver, Oud, Voelkle (2017) , with updated details in vignette. Combines stochastic differential equations representing latent processes with structural equation measurement models. This package is maintained for consistency with the original 'ctsem' paper, but for the much newer and more capable 'ctsem' package, see < https://cran.r-project.org/package=ctsem>.

Structural Equation Modeling with Deep Neural Network and Machine Learning Algorithms

Training and validation of a custom (or data-driven) Structural Equation Models using Deep Neural Networks or Machine Learning algorithms, which extend the fitting procedures of the 'SEMgraph' R package .

Case-Based Least Squares Estimation of Nonlinear Structural Equation Models

Estimates structural equation models by case-based least squares: the latent scores of every observation are treated as free variables of a constrained optimization problem, so that arbitrary nonlinear model equations, bounds and constraints on latent variables and inequality constraints on parameters become possible. Model equations are specified as plain text (e.g. "y == a*exp(b*eta)"). Gradients are obtained by automatic differentiation via 'RTMB', and the constrained problem is solved with 'nloptr' (SLSQP or augmented Lagrangian). Missing data are handled case-wise. The methodology is described in Oldenburg (2024) and Oldenburg (2025) .

Influential Case Detection Methods for Factor Analysis and Structural Equation Models

Tools for detecting and summarize influential cases that can affect exploratory and confirmatory factor analysis models as well as structural equation models more generally (Chalmers, 2015, ; Flora, D. B., LaBrish, C. & Chalmers, R. P., 2012, ).

Interactive Structural Equation Modeling (SEM) and Multi-Group Path Diagrams

Provides an interactive workflow for visualizing structural equation modeling (SEM), multi-group path diagrams, and network diagrams in R. Users can directly manipulate nodes and edges to create publication-quality figures while maintaining statistical model integrity. Supports integration with 'lavaan', 'OpenMx', 'tidySEM', and 'blavaan' etc. Features include parameter-based aesthetic mapping, generative AI assistance, and complete reproducibility by exporting metadata for script-based workflows.

Fused Sparse Structural Equation Models to Jointly Infer Gene Regulatory Network

An optimizer of Fused-Sparse Structural Equation Models, which is the state of the art jointly fused sparse maximum likelihood function for structural equation models proposed by Xin Zhou and Xiaodong Cai (2018 ).

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.

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) .

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.