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.

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.

Goodness-of-Fit Testing for Structural Equation Models

Supports eigenvalue block-averaging p-values (Foldnes, Grønneberg, 2018) , penalized eigenvalue block-averaging p-values (Foldnes, Moss, Grønneberg, WIP), penalized regression p-values (Foldnes, Moss, Grønneberg, WIP), as well as traditional p-values such as Satorra-Bentler. All p-values can be calculated using unbiased or biased gamma estimates (Du, Bentler, 2022) and two choices of chi square statistics.

Generalized Structured Component Analysis Structural Equation Modeling

Implementing generalized structured component analysis (GSCA) and its basic extensions, including constrained single and multiple group analysis, and second order latent variable modeling. For a comprehensive overview of GSCA, see Hwang & Takane (2014, ISBN: 9780367738754).

Betas-Select in Structural Equation Models and Linear Models

It computes betas-select, coefficients after standardization in structural equation models and regression models, standardizing only selected variables. Supports models with moderation, with product terms formed after standardization. It also offers confidence intervals that account for standardization, including bootstrap confidence intervals as proposed by Cheung et al. (2022) .

Automatic Calculation of Effects for Piecewise Structural Equation Models

Automatically calculate direct, indirect, and total effects for piecewise structural equation models, comprising lists of fitted models representing structured equations (Lefcheck, 2016 ). Confidence intervals are provided via bootstrapping.

Decision Trees with Structural Equation Models Fit in 'Mplus'

Uses recursive partitioning to create homogeneous subgroups based on structural equation models fit in 'Mplus', a stand-alone program developed by Muthen and Muthen.

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) .