Symbolic Computation for Structural Equation Models

A collection of functions for symbolic computation using the 'caracas' package for structural equation models and other statistical analyses. Among its features is the ability to calculate the model-implied covariance (and correlation) matrix and the sampling covariance matrix of variable functions using the delta method.

Bootstrapping Helpers for Structural Equation Modelling

A collection of helper functions for forming bootstrapping confidence intervals and examining bootstrap estimates in structural equation modelling, introduced in Yang and Cheung (2026) The function currently support models fitted by the 'lavaan' package by Rosseel (2012) .

Composite-Based Structural Equation Modeling

Estimate, assess, test, and study linear, nonlinear, hierarchical and multigroup structural equation models using composite-based approaches and procedures, including estimation techniques such as partial least squares path modeling (PLS-PM) and its derivatives (PLSc, ordPLSc, robustPLSc), generalized structured component analysis (GSCA), generalized structured component analysis with uniqueness terms (GSCAm), generalized canonical correlation analysis (GCCA), principal component analysis (PCA), factor score regression (FSR) using sum score, regression or Bartlett scores (including bias correction using Croon’s approach), as well as several tests and typical postestimation procedures (e.g., verify admissibility of the estimates, assess the model fit, test the model fit etc.).

Influential Cases in Structural Equation Modeling

Sensitivity analysis in structural equation modeling using influence measures and diagnostic plots. Support leave-one-out casewise sensitivity analysis presented by Pek and MacCallum (2011) and approximate casewise influence using scores and casewise likelihood. An introduction to the package can be found in Cheung and Lai (2026) .

Recursive Partitioning for Structural Equation Models

SEM Trees and SEM Forests -- an extension of model-based decision trees and forests to Structural Equation Models (SEM). SEM trees hierarchically split empirical data into homogeneous groups each sharing similar data patterns with respect to a SEM by recursively selecting optimal predictors of these differences. SEM forests are an extension of SEM trees. They are ensembles of SEM trees each built on a random sample of the original data. By aggregating over a forest, we obtain measures of variable importance that are more robust than measures from single trees. A description of the method was published by Brandmaier, von Oertzen, McArdle, & Lindenberger (2013) and Arnold, Voelkle, & Brandmaier (2020) .

Exploratory Structural Equation Modeling ESEM

A collection of functions developed to support the tutorial on using Exploratory Structural Equiation Modeling (ESEM) (Asparouhov & Muthén, 2009) < https://www.statmodel.com/download/EFACFA810.pdf>) with Longitudinal Study of Australian Children (LSAC) dataset (Mohal et al., 2023) . The package uses 'tidyverse','psych', 'lavaan','semPlot' and provides additional functions to conduct ESEM. The package provides general functions to complete ESEM, including esem_c(), creation of target matrix (if it is used) make_target(), generation of the Confirmatory Factor Analysis (CFA) model syntax esem_cfa_syntax(). A sample data is provided - the package includes a sample data of the Strengths and Difficulties Questionnaire of the Longitudinal Study of Australian Children (SDQ LSAC) in sdq_lsac(). 'ESEM' package vignette presents the tutorial demonstrating the use of ESEM on SDQ LSAC data.

Structural Equation Modeling for the Social Relations Model

Provides functionality for structural equation modeling for the social relations model (Kenny & La Voie, 1984; ; Warner, Kenny, & Soto, 1979, ). Maximum likelihood estimation (Gill & Swartz, 2001, ; Nestler, 2018, ) and least squares estimation is supported (Bond & Malloy, 2018, ).

Structural Equation Modeling and Confirmatory Network Analysis

Multi-group (dynamical) structural equation models in combination with confirmatory network models from cross-sectional, time-series and panel data . Allows for confirmatory testing and fit as well as exploratory model search.

Non-Smooth Regularization for Structural Equation Models

Provides regularized structural equation modeling (regularized SEM) with non-smooth penalty functions (e.g., lasso) building on 'lavaan'. The package is heavily inspired by the ['regsem'](< https://github.com/Rjacobucci/regsem>) and ['lslx'](< https://github.com/psyphh/lslx>) packages.

Stable Specification Search in Structural Equation Models

An exploratory and heuristic approach for specification search in Structural Equation Modeling. The basic idea is to subsample the original data and then search for optimal models on each subset. Optimality is defined through two objectives: model fit and parsimony. As these objectives are conflicting, we apply a multi-objective optimization methods, specifically NSGA-II, to obtain optimal models for the whole range of model complexities. From these optimal models, we consider only the relevant model specifications (structures), i.e., those that are both stable (occur frequently) and parsimonious and use those to infer a causal model.