Likelihood Ratio Test P-Values for Structural Equation Models

Computes likelihood ratio test (LRT) p-values for free parameters in a structural equation model. Currently supports models fitted by the 'lavaan' package by Rosseel (2012) .

Latent Interaction (and Moderation) Analysis in Structural Equation Models (SEM)

Estimation of interaction (i.e., moderation) effects between latent variables in structural equation models (SEM). The supported methods are: The constrained approach (Algina & Moulder, 2001). The unconstrained approach (Marsh et al., 2004). The residual centering approach (Little et al., 2006). The double centering approach (Lin et al., 2010). The latent moderated structural equations (LMS) approach (Klein & Moosbrugger, 2000). The quasi-maximum likelihood (QML) approach (Klein & Muthén, 2007) The constrained- unconstrained, residual- and double centering- approaches are estimated via 'lavaan' (Rosseel, 2012), whilst the LMS- and QML- approaches are estimated via 'modsem' it self. Alternatively model can be estimated via 'Mplus' (Muthén & Muthén, 1998-2017). References: Algina, J., & Moulder, B. C. (2001). . "A note on estimating the Jöreskog-Yang model for latent variable interaction using 'LISREL' 8.3." Klein, A., & Moosbrugger, H. (2000). . "Maximum likelihood estimation of latent interaction effects with the LMS method." Klein, A. G., & Muthén, B. O. (2007). . "Quasi-maximum likelihood estimation of structural equation models with multiple interaction and quadratic effects." Lin, G. C., Wen, Z., Marsh, H. W., & Lin, H. S. (2010). . "Structural equation models of latent interactions: Clarification of orthogonalizing and double-mean-centering strategies." Little, T. D., Bovaird, J. A., & Widaman, K. F. (2006). . "On the merits of orthogonalizing powered and product terms: Implications for modeling interactions among latent variables." Marsh, H. W., Wen, Z., & Hau, K. T. (2004). . "Structural equation models of latent interactions: evaluation of alternative estimation strategies and indicator construction." Muthén, L.K. and Muthén, B.O. (1998-2017). "'Mplus' User’s Guide. Eighth Edition." < https://www.statmodel.com/>. Rosseel Y (2012). . "'lavaan': An R Package for Structural Equation Modeling."

Create Phantom Variables in Structural Equation Models for Sensitivity Analyses

Create phantom variables, which are variables that were not observed, for the purpose of sensitivity analyses for structural equation models. The package makes it easier for a user to test different combinations of covariances between the phantom variable(s) and observed variables. The package may be used to assess a model's or effect's sensitivity to temporal bias (e.g., if cross-sectional data were collected) or confounding bias.

Bayesian Structural Equation Modeling in Multiple Omics Data Integration

Provides Markov Chain Monte Carlo (MCMC) routine for the structural equation modelling described in Maity et. al. (2020) . This MCMC sampler is useful when one attempts to perform an integrative survival analysis for multiple platforms of the Omics data where the response is time to event and the predictors are different omics expressions for different platforms.

Path Component Fit Indices for Latent Structural Equation Models

Functions for computing fit indices for evaluating the path component of latent variable structural equation models. Available fit indices include RMSEA-P and NSCI-P originally presented and evaluated by Williams and O'Boyle (2011) and demonstrated by O'Boyle and Williams (2011) and Williams, O'Boyle, & Yu (2020) . Also included are fit indices described by Hancock and Mueller (2011) .

Within-Subject Mediation Analysis Using Structural Equation Modeling

Within-subject mediation analysis using structural equation modeling. Examine how changes in an outcome variable between two conditions are mediated through one or more variables. Supports within-subject mediation analysis using the 'lavaan' package by Rosseel (2012) , and extends Monte Carlo confidence interval estimation to missing data scenarios using the 'semmcci' package by Pesigan and Cheung (2023) .

Structural Equation Modeling Using the Reticular Action Model (RAM) Notation

We rewrite of RAMpath software developed by John McArdle and Steven Boker as an R package. In addition to performing regular SEM analysis through the R package lavaan, RAMpath has unique features. First, it can generate path diagrams according to a given model. Second, it can display path tracing rules through path diagrams and decompose total effects into their respective direct and indirect effects as well as decompose variance and covariance into individual bridges. Furthermore, RAMpath can fit dynamic system models automatically based on latent change scores and generate vector field plots based upon results obtained from a bivariate dynamic system. Starting version 0.4, RAMpath can conduct power analysis for both univariate and bivariate latent change score models.

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) .