Fitting Structural Equation Mixture Models

Estimation of structural equation models with nonlinear effects and underlying nonnormal distributions.

Supplementary Item Response Theory Models

Supplementary functions for item response models aiming to complement existing R packages. The functionality includes among others multidimensional compensatory and noncompensatory IRT models (Reckase, 2009, ), MCMC for hierarchical IRT models and testlet models (Fox, 2010, ), NOHARM (McDonald, 1982, ), Rasch copula model (Braeken, 2011, ; Schroeders, Robitzsch & Schipolowski, 2014, ), faceted and hierarchical rater models (DeCarlo, Kim & Johnson, 2011, ), ordinal IRT model (ISOP; Scheiblechner, 1995, ), DETECT statistic (Stout, Habing, Douglas & Kim, 1996, ), local structural equation modeling (LSEM; Hildebrandt, Luedtke, Robitzsch, Sommer & Wilhelm, 2016, ).

Multivariate Spatio-Temporal Models using Structural Equations

Fits a wide variety of multivariate spatio-temporal models with simultaneous and lagged interactions among variables (including vector autoregressive spatio-temporal ('VAST') dynamics) for areal, continuous, or network spatial domains. It includes time-variable, space-variable, and space-time-variable interactions using dynamic structural equation models ('DSEM') as expressive interface, and the 'mgcv' package to specify splines via the formula interface. See Thorson et al. (2025) for more details.

Mediation, Moderation and Moderated-Mediation After Model Fitting

Computes indirect effects, conditional effects, and conditional indirect effects in a structural equation model or path model after model fitting, with no need to define any user parameters or label any paths in the model syntax, using the approach presented in Cheung and Cheung (2024) . Can also form bootstrap confidence intervals by doing bootstrapping only once and reusing the bootstrap estimates in all subsequent computations. Supports bootstrap confidence intervals for standardized (partially or completely) indirect effects, conditional effects, and conditional indirect effects as described in Cheung (2009) and Cheung, Cheung, Lau, Hui, and Vong (2022) . Model fitting can be done by structural equation modeling using lavaan() or regression using lm().

Generate Standardized Data

Creates simulated data from structural equation models with standardized loading. Data generation methods are described in Schneider (2013) .

Bayes Factors for Informative Hypotheses

Computes approximated adjusted fractional Bayes factors for equality, inequality, and about equality constrained hypotheses. For a tutorial on this method, see Hoijtink, Mulder, van Lissa, & Gu, (2019) . For applications in structural equation modeling, see: Van Lissa, Gu, Mulder, Rosseel, Van Zundert, & Hoijtink, (2021) . For the statistical underpinnings, see Gu, Mulder, and Hoijtink (2018) ; Hoijtink, Gu, & Mulder, J. (2019) ; Hoijtink, Gu, Mulder, & Rosseel, (2019) .

Easy Model-Builder Functions for 'OpenMx'

Utilities for building certain kinds of common matrices and models in the extended structural equation modeling package, 'OpenMx'.

Graphing Nonlinear Relations Among Latent Variables from Structural Equation Mixture Models

Contains a graphical user interface to generate the diagnostic plots proposed by Bauer (2005; ), Pek & Chalmers (2015; ), and Pek, Chalmers, R. Kok, & Losardo (2015; ) to investigate nonlinear bivariate relationships in latent regression models using structural equation mixture models (SEMMs).

Latent Structure Learning

Fits structural equation modeling via penalized likelihood.

Basic and Advanced Statistical Power Analysis

This is a collection of tools for conducting both basic and advanced statistical power analysis including correlation, proportion, t-test, one-way ANOVA, two-way ANOVA, linear regression, logistic regression, Poisson regression, mediation analysis, longitudinal data analysis, structural equation modeling and multilevel modeling. It also serves as the engine for conducting power analysis online at < https://webpower.psychstat.org>.