LCSM Parameters
In lcsm: Univariate and Bivariate Latent Change Score Modelling

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

library(lcsm)

Overview of estimated LCSM parameters

Univariate LCSM

Depending on the specified model, the following parameters can be estimated for univariate LCSMs:

|Parameter |Description | |:-----------|:-----------------------------------------------------------------------| |gamma_lx1 |Mean of latent true scores x (Intercept) | |sigma2_lx1 |Variance of latent true scores x | |sigma2_ux |Variance of observed scores x | |alpha_g2 |Mean of change factor (g2) | |alpha_g3 |Mean of change factor (g3) | |sigma2_g2 |Variance of change factor (g2) | |sigma2_g3 |Variance of change factor (g3) | |sigma_g2lx1 |Covariance of change factor (g2) with the initial true score x | |sigma_g3lx1 |Covariance of change factor (g3) with the initial true score x | |sigma_g2g3 |Covariance of change factors within construct x | |beta_x | Proportional change x | |phi_x |Autoregression of change scores x |

Bivariate LCSMs

For bivariate LCSMs, estimated parameters can be categorised into (1) Construct X, (2) Construct Y, and (3) Coupling between X and Y.

|Parameter |Description | |:------------|:-----------------------------------------------------------------------| |Construct X | |gamma_lx1 |Mean of latent true scores x (Intercept) | |sigma2_lx1 |Variance of latent true scores x | |sigma2_ux |Variance of observed scores x | |alpha_g2 |Mean of change factor (g2) | |alpha_g3 |Mean of change factor (g3) | |sigma2_g2 |Variance of change factor (g2) | |sigma2_g3 |Variance of change factor (g3) | | beta_x | Proportional change x | |sigma_g2lx1 |Covariance of change factor (g2) with the initial true score x (lx1) | |sigma_g3lx1 |Covariance of change factor (g3) with the initial true score x (lx1) | |sigma_g2g3 |Covariance of change factors within construct x | |phi_x |Autoregression of change scores x | |Construct Y | |gamma_ly1 |Mean of latent true scores y (Intercept) | |sigma2_ly1 |Variance of latent true scores y | |sigma2_uy |Variance of observed scores y | |alpha_j2 |Mean of change factor (j2) | |alpha_j3 |Mean of change factor (j3) | |sigma2_j2 |Variance of change factor (j2) | |sigma2_j3 |Variance of change factor (j3) | | beta_y | Proportional change y | |sigma_j2ly1 |Covariance of change factor (j2) with the initial true score y (ly1) | |sigma_j3ly1 |Covariance of change factor (j3) with the initial true score y (ly1) | |sigma_j2j3 |Covariance of change factors within construct y | |phi_y |Autoregression of change scores y | |Coupeling X & Y | |sigma_su |Covariance of residuals x and y | |sigma_ly1lx1 |Covariance of intercepts x and y | |sigma_g2ly1 |Covariance of change factor x (g2) with the initial true score y (ly1) | |sigma_g3ly1 |Covariance of change factor x (g3) with the initial true score y (ly1) | |sigma_j2lx1 |Covariance of change factor y (j2) with the initial true score x (lx1) | |sigma_j3lx1 |Covariance of change factor y (j3) with the initial true score x (lx1) | |sigma_j2g2 |Covariance of change factors y (j2) and x (g2) | |sigma_j2g3 | Covariance of change factors y (j2) and x (g3) | |sigma_j3g2 |Covariance of change factors y (j3) and x (g2) | |delta_con_xy |Change score x (t) determined by true score y (t) | |delta_con_yx |Change score y (t) determined by true score x (t) | |delta_lag_xy |Change score x (t) determined by true score y (t-1) | |delta_lag_yx |Change score y (t) determined by true score x (t-1) | |xi_con_xy |Change score x (t) determined by change score y (t) | |xi_con_yx |Change score y (t) determined by change score x (t) | |xi_lag_xy |Change score x (t) determined by change score y (t-1) | |xi_lag_yx |Change score y (t) determined by change score x (t-1) |