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.

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) .

Dynamic Panel Models Fit with Maximum Likelihood

Implements the dynamic panel models described by Allison, Williams, and Moral-Benito (2017 ) in R. This class of models uses structural equation modeling to specify dynamic (lagged dependent variable) models with fixed effects for panel data. Additionally, models may have predictors that are only weakly exogenous, i.e., are affected by prior values of the dependent variable. Options also allow for random effects, dropping the lagged dependent variable, and a number of other specification choices.

Omega-Generic: Composite Reliability of Multidimensional Measures

It is a computer tool to estimate the item-sum score's reliability (composite reliability, CR) in multidimensional scales with overlapping items. An item that measures more than one domain construct is called an overlapping item. The estimation is based on factor models allowing unlimited cross-factor loadings such as exploratory structural equation modeling (ESEM) and Bayesian structural equation modeling (BSEM). The factor models include correlated-factor models and bi-factor models. Specifically for bi-factor models, a type of hierarchical factor model, the package estimates the CR hierarchical subscale/hierarchy and CR subscale/scale total. The CR estimator 'Omega-generic' was proposed by Mai, Srivastava, and Krull (2021) < https://whova.com/embedded/subsession/enars_202103/1450751/1452993/>. The current version can only handle continuous data. Yujiao Mai contributes to the algorithms, R programming, and application example. Deo Kumar Srivastava contributes to the algorithms and the application example. Kevin R. Krull contributes to the application example. The package 'OmegaG' was sponsored by American Lebanese Syrian Associated Charities (ALSAC). However, the contents of 'OmegaG' do not necessarily represent the policy of the ALSAC.