Load nlpsem package, dependent packages and set CSOLNP as the optimizer | Load pre-computed models | Load example data and preprocess data | Example 1: Fit nonparametric LCSMs to assess the development of reading ability from Kindergarten to Grade 5, both with and without incorporating baseline teacher-reported approach to learning and attentional focus. The getSummary() function is used to generate a comprehensive summary table for these two models. Additionally, the visual representations of the growth rate and change from the baseline for both models. | Example 2: Fit LCSMs with quadratic, negative exponential and Jenss-Bayley functional forms. Additionally, the visual representations change from the baseline for three models.

Load nlpsem package, dependent packages and set CSOLNP as the optimizer | Load pre-computed models | Load example data and preprocess data | Example 1: Fit bilinear spline LGCMs with both a random and a fixed knot to evaluate the development of mathematics ability from Kindergarten to Grade 5. These models are then compared using a likelihood ratio test (LRT) utilizing the getLRT() function. | Example 2: Fit the full bilinear spline LGCM to assess the development of mathematics skill from Kindergarten to Grade 5. This model includes two growth time-invariant covariates (TICs), baseline values of teacher-reported approach to learning and attentional focus. Point estimates and corresponding standard errors (SEs) of all parameters are presented within the original parameter space. The plot of the growth status of mathematics ability is also provided.

Load nlpsem package, dependent packages and set CSOLNP as the optimizer | Load pre-computed models | Load example data and preprocess data | Example 1: Fit longitudinal mediation model with a bilinear spline functional form to assess how the baseline teacher-reported approach to learning influences the development of mathematics ability, mediated through the development of reading ability. | Example 2: Fit longitudinal mediation model with a bilinear spline functional form to assess how the development of reading ability influences the development of science ability, mediated through the development of mathematics ability.

Load nlpsem package, dependent packages and set CSOLNP as the optimizer | Load pre-computed models | Load example data and preprocess data | Example 1: Fit multivariate bilinear spline LGCMs fixed knots to evaluate the development of reading and mathematics ability from Kindergarten to Grade 5. | Example 2: Fit multivariate bilinear spline LGCMs with random knots to evaluate the development of reading and mathematics ability from Kindergarten to Grade 5.

Load nlpsem package, dependent packages and set CSOLNP as the optimizer | Load pre-computed models | Load example data and preprocess data | Example 1: Fit multiple group bilinear spline LGCM to evaluate the difference in the development of mathematics ability | Example 2: Fit multiple group negative exponential LGCM with time-invariant covariates (TICs) to evaluate the difference in the development of reading ability. This model includes two growth TICs, baseline values of teacher-reported approach to learning and attentional focus. Point estimates and corresponding standard errors (SEs) of all parameters are presented within the original parameter space.

Load nlpsem package, dependent packages and set CSOLNP as the optimizer | Load pre-computed models | Load example data and preprocess data | Example 1: Fit bilinear spline LGCMs with 1-, 2-, and 3- latent classes to examine the heterogeneity in the development of mathematics skills. The enumeration process is conducted using the getSummary() function, with HetModels = TRUE specified. | Example 2: Fit reduced bilinear spline bivariate LGCMs with three latent classes to analyze the heterogeneity in the co-development of reading and mathematics skills.

Load nlpsem package, dependent packages and set CSOLNP as the optimizer | Load pre-computed models | Load example data and preprocess data | Example 1: This example includes two models. Model 1 is a full bilinear spline LGCM with a TVC to examine the influence of baseline teacher-reported approach to learning and the development in reading ability on the development of mathematics ability. It also includes a visualization showcasing the growth status of mathematics ability. Model 2 is a full bilinear spline LGCM with a decomposed TVC (interval-specific slopes) to examine the influence of baseline teacher-reported approach to learning and the development in reading ability on the development of mathematics ability. P values and Wald confidence intervals of all parameters are provided. It also includes a visualization showcasing the growth status of mathematics ability. | Example 2: Fit reduced bilinear spline LGCMs with a decomposed TVC (interval-specific slopes, interval-specific changes, and change from baseline) to examine the influence of baseline teacher-reported approach to learning and the development in reading ability on the development of mathematics ability. It also includes a visualization showcasing the growth status of mathematics ability.

Overview | Modeling Scenarios | Supported Growth Curve Functions | Quick-Start Example | Data Preparation | Fitting a Latent Growth Curve Model | Post-Processing | Model Fit Summary | Parameter Inference | Visualization | Other Useful Functions | Further Reading