# LCSM Parameters

    library(lcsm)
    #> This is lcsm 0.3.3
    #> Please report any issues or ideas at:
    #> https://github.com/milanwiedemann/lcsm/issues
    #>

## 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)