Graphical Extension with Accuracy in Parameter Estimation (GAIPE)

Implements graphical extension with accuracy in parameter estimation (AIPE) on RMSEA for sample size planning in structural equation modeling based on Lin, T.-Z. & Weng, L.-J. (2014) . And, it can also implement AIPE on RMSEA and power analysis on RMSEA.

Computationally Efficient Maximum Likelihood Identification of Linear Dynamical Systems

Provides implementations of computationally efficient maximum likelihood parameter estimation algorithms for models representing linear dynamical systems. Currently, two such algorithms (one offline and one online) are implemented for the single-output cumulative structural equation model with an additive-noise output measurement equation and assumptions of normality and independence. The corresponding scientific papers are referenced in the descriptions of the functions implementing these algorithms.

Regularized Mediation Analysis

Mediation analysis for multiple mediators by penalized structural equation models with different types of penalties depending on whether there are multiple mediators and only one exposure and one outcome variable (using sparse group lasso) or multiple exposures, multiple mediators, and multiple outcome variables (using lasso, L1, penalties).

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().

Latent Repeated Measures ANOVA

Latent repeated measures ANOVA (L-RM-ANOVA) is a structural equation modeling based alternative to traditional repeated measures ANOVA. L-RM-ANOVA extends the latent growth components approach by Mayer et al. (2012) and introduces latent variables to repeated measures analysis.

Multilevel Latent Time Series Models with 'R' and 'Stan'

Fit multilevel manifest or latent time-series models, including popular Dynamic Structural Equation Models (DSEM). The models can be set up and modified with user-friendly functions and are fit to the data using 'Stan' for Bayesian inference. Path models and formulas for user-defined models can be easily created with functions using 'knitr'. Asparouhov, Hamaker, & Muthen (2018) .

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>.

Power Analysis for Moderation and Mediation

Power analysis and sample size determination for moderation, mediation, and moderated mediation in models fitted by structural equation modelling using the 'lavaan' package by Rosseel (2012) or by multiple regression. The package 'manymome' by Cheung and Cheung (2024) is used to specify the indirect paths or conditional indirect paths to be tested.

Approximate Bayesian Latent Variable Analysis

Implements approximate Bayesian inference for Structural Equation Models (SEM) using a custom adaptation of the Integrated Nested Laplace Approximation as described in Rue et al. (2009) . Provides a computationally efficient alternative to Markov Chain Monte Carlo (MCMC) for Bayesian estimation, allowing users to fit latent variable models using the 'lavaan' syntax.

Latent Variable Network Modeling

Estimate, fit and compare Structural Equation Models (SEM) and network models (Gaussian Graphical Models; GGM) using OpenMx. Allows for two possible generalizations to include GGMs in SEM: GGMs can be used between latent variables (latent network modeling; LNM) or between residuals (residual network modeling; RNM). For details, see Epskamp, Rhemtulla and Borsboom (2017) .