Evaluation of the Role of Control Variables in Structural Equation Models

Various opportunities to evaluate the effects of including one or more control variable(s) in structural equation models onto model-implied variances, covariances, and parameter estimates. The derivation of the methodology employed in this package can be obtained from Blötner (2023) .

Genetic-Relationship-Matrix Structural Equation Modelling (GRMSEM)

Quantitative genetics tool supporting the modelling of multivariate genetic variance structures in quantitative data. It allows fitting different models through multivariate genetic-relationship-matrix (GRM) structural equation modelling (SEM) in unrelated individuals, using a maximum likelihood approach. Specifically, it combines genome-wide genotyping information, as captured by GRMs, with twin-research-based SEM techniques, St Pourcain et al. (2017) , Shapland et al. (2020) .

Likelihood-Based Confidence Interval in Structural Equation Models

Forms likelihood-based confidence intervals (LBCIs) for parameters in structural equation modeling, introduced in Cheung and Pesigan (2023) . Currently implements the algorithm illustrated by Pek and Wu (2018) , and supports the robust LBCI proposed by Falk (2018) .

Some Multivariate Analyses using Structural Equation Modeling

A set of functions for some multivariate analyses utilizing a structural equation modeling (SEM) approach through the 'OpenMx' package. These analyses include canonical correlation analysis (CANCORR), redundancy analysis (RDA), and multivariate principal component regression (MPCR). It implements procedures discussed in Gu and Cheung (2023) , Gu, Yung, and Cheung (2019) , and Gu et al. (2023) .

Monte Carlo Confidence Intervals in Structural Equation Modeling

Monte Carlo confidence intervals for free and defined parameters in models fitted in the structural equation modeling package 'lavaan' can be generated using the 'semmcci' package. 'semmcci' has three main functions, namely, MC(), MCMI(), and MCStd(). The output of 'lavaan' is passed as the first argument to the MC() function or the MCMI() function to generate Monte Carlo confidence intervals. Monte Carlo confidence intervals for the standardized estimates can also be generated by passing the output of the MC() function or the MCMI() function to the MCStd() function. A description of the package and code examples are presented in Pesigan and Cheung (2023) .

Network Analysis and Causal Inference Through Structural Equation Modeling

Estimate networks and causal relationships in complex systems through Structural Equation Modeling. This package also includes functions for importing, weight, manipulate, and fit biological network models within the Structural Equation Modeling framework as outlined in the Supplementary Material of Grassi M, Palluzzi F, Tarantino B (2022) .

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) (temporarily unavailable) 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."

Structural Equation Modeling with Deep Neural Network and Machine Learning

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

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.