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.

Latent Variable Models

A general implementation of Structural Equation Models with latent variables (MLE, 2SLS, and composite likelihood estimators) with both continuous, censored, and ordinal outcomes (Holst and Budtz-Joergensen (2013) ). Mixture latent variable models and non-linear latent variable models (Holst and Budtz-Joergensen (2020) ). The package also provides methods for graph exploration (d-separation, back-door criterion), simulation of general non-linear latent variable models, and estimation of influence functions for a broad range of statistical models.

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) .

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.

Power Analyses for SEM

Provides a-priori, post-hoc, and compromise power-analyses for structural equation models (SEM).

Easy Model-Builder Functions for 'OpenMx'

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

'SEM Shiny'

Interactive 'shiny' application for working with Structural Equation Modelling technique. Runtime examples are provided in the package function as well as at < https://kartikeyab.shinyapps.io/semwebappk/> .