Examination of Nonlinear Longitudinal Processes with Latent Variables, Latent Processes, Latent Changes, and Latent Classes in the Structural Equation Modeling Framework: The R package nlpsem

We introduce the R package nlpsem, a comprehensive toolkit for analyzing longitudinal processes within the structural equation modeling (SEM) framework, incorporating individual measurement occasions. This package emphasizes nonlinear longitudinal models, especially intrinsic ones, across four key scenarios: (1) univariate longitudinal processes with latent variables, optionally including covariates such as time-invariant covariates (TICs) and time-varying covariates (TVCs); (2) multivariate longitudinal analyses to explore correlations or unidirectional relationships between longitudinal variables; (3) multiple-group frameworks for comparing manifest classes in scenarios (1) and (2); and (4) mixture models for scenarios (1) and (2), accommodating latent class heterogeneity. Built on the OpenMx R package, nlpsem supports flexible model designs and uses the full information maximum likelihood method for parameter estimation. A notable feature is its algorithm for determining initial values directly from raw data, enhancing computational efficiency and convergence. Furthermore, nlpsem provides tools for goodness-of-fit tests, cluster analyses, visualization, derivation of p-values and three types of confidence intervals, as well as model selection for nested models using likelihood ratio tests and for non-nested models based on criteria such as Akaike Information Criterion and Bayesian Information Criterion. This article serves as a companion document to the nlpsem R package, providing a comprehensive guide to its modeling capabilities, estimation methods, implementation features, and application examples using synthetic intelligence growth data.