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.

Complex Survey Structural Equation Modeling (SEM)

Fit structural equation models (SEM) including factor analysis, multivariate regression models with latent variables and many other latent variable models while correcting estimates, standard errors, and chi-square-derived fit measures for a complex sampling design. Incorporate clustering, stratification, sampling weights, and finite population corrections into a SEM analysis. Wrapper around packages lavaan and survey.

Evaluate Structural Equation Model Identification Rules

Evaluates selected necessary and sufficient identification conditions in structural equation models (SEMs), including latent-variable scaling constraints. Output reports rule status and applicability and provides diagnostic messages to support model specification and respecification. The package is intended as a diagnostic aid and does not implement a universal identification algorithm. For more details, see Bollen (2026, ISBN:978-1009312820).

Distributed-Lag Linear Structural Equation Models

Inference functionalities for distributed-lag linear structural equation models (DLSEMs). DLSEMs are Markovian structural causal models where each factor of the joint probability distribution is a distributed-lag linear regression with constrained lag shapes (Magrini, 2018 ; Magrini et al., 2019 ). DLSEMs account for temporal delays in the dependence relationships among the variables through a single parameter per covariate, thus allowing to perform dynamic causal inference in a feasible fashion. Endpoint-constrained quadratic, quadratic decreasing, linearly decreasing and gamma lag shapes are available.

Structural Equation Model Effect Analysis and Visualization

Provides standardized effect decomposition (direct, indirect, and total effects) for three major structural equation modeling frameworks: 'lavaan', 'piecewiseSEM', and 'plspm'. Automatically handles zero-effect variables, generates publication-ready 'ggplot2' visualizations, and returns both wide-format and long-format effect tables. Supports effect filtering, multi-model object inputs, and customizable visualization parameters. For a general overview of the methods used in this package, see Rosseel (2012) and Lefcheck (2016) .

Robust Test Statistics for Structural Equation Models

Computes robust p-values for overall fit and nested comparisons of structural equation models fitted with 'lavaan'. Implements penalized eigenvalue block averaging and penalized regression (Foldnes, Moss, Grønneberg, 2025) , including their extension to nested models (Foldnes, Grønneberg, Moss, 2026) , alongside familiar corrections such as Satorra-Bentler. Supported settings include complete-data ML, GLS, and ULS, categorical DWLS and ULS, and full-information maximum likelihood with one or several groups. Score and criterion-difference tests of parameter restrictions are also available, including restrictions in misspecified models.

Monte Carlo Simulation for Structural Equation Modeling

Provides tools to conduct Monte Carlo simulations under different conditions (e.g., varying sample size, data normality) for structural equation models (SEMs). Data can be simulated based on user-defined factor loadings and correlations, with optional non-normality added via Fleishman's power method (1978) . Once generated, models can be estimated using 'lavaan'. This package facilitates testing model performance across multiple simulation scenarios. When data generation is completed (or when generated data sets are given) model tests can also be run. Please cite as "Orçan, F. (2021). MonteCarloSEM An R Package to Simulate Data for SEM. International Journal of Assessment Tools in Education, 8 (3), 704-713."

A Tool for Sensitivity Analysis in Structural Equation Modeling

Perform sensitivity analysis in structural equation modeling using meta-heuristic optimization methods (e.g., ant colony optimization and others). The references for the proposed methods are: (1) Leite, W., & Shen, Z., Marcoulides, K., Fish, C., & Harring, J. (2022). (2) Harring, J. R., McNeish, D. M., & Hancock, G. R. (2017) ; (3) Fisk, C., Harring, J., Shen, Z., Leite, W., Suen, K., & Marcoulides, K. (2022). ; (4) Socha, K., & Dorigo, M. (2008) . We also thank Dr. Krzysztof Socha for sharing his research on ant colony optimization algorithm with continuous domains and associated R code, which provided the base for the development of this package.

Semi-Supervised Generalized Structural Equation Modeling

Conducts a semi-gSEM statistical analysis (semi-supervised generalized structural equation modeling) on a data frame of coincident observations of multiple predictive or intermediate variables and a final continuous, outcome variable, via two functions sgSEMp1() and sgSEMp2(), representing fittings based on two statistical principles. Principle 1 determines all sensible univariate relationships in the spirit of the Markovian process. The relationship between each pair of variables, including predictors and the final outcome variable, is determined with the Markovian property that the value of the current predictor is sufficient in relating to the next level variable, i.e., the relationship is independent of the specific value of the preceding-level variables to the current predictor, given the current value. Principle 2 resembles the multiple regression principle in the way multiple predictors are considered simultaneously. Specifically, the relationship of the first-level predictors (such as Time and irradiance etc) to the outcome variable (such as, module degradation or yellowing) is fit by a supervised additive model. Then each significant intermediate variable is taken as the new outcome variable and the other variables (except the final outcome variable) as the predictors in investigating the next-level multivariate relationship by a supervised additive model. This fitting process is continued until all sensible models are investigated.

Nonlinear Longitudinal Process in Structural Equation Modeling

Provides computational tools for nonlinear longitudinal models, in particular the intrinsically nonlinear models, in four scenarios: (1) univariate longitudinal processes with growth factors, with or without covariates including time-invariant covariates (TICs) and time-varying covariates (TVCs); (2) multivariate longitudinal processes that facilitate the assessment of correlation or causation between multiple longitudinal variables; (3) multiple-group models for scenarios (1) and (2) to evaluate differences among manifested groups, and (4) longitudinal mixture models for scenarios (1) and (2), with an assumption that trajectories are from multiple latent classes. The methods implemented are introduced in Liu (2025) .