Generate lavaan syntax for latent change score models
Source:vignettes/v1-lavaan-syntax.Rmd
v1-lavaan-syntax.Rmd
library(lcsm)
#> This is lcsm 0.3.2
#> Please report any issues or ideas at:
#> https://github.com/milanwiedemann/lcsm/issues
#> Univariate LCSM syntax
The example below shows how to specify a generic univariate latent
change score model using the function
specify_uni_lcsm().
uni_lcsm_syntax <- specify_uni_lcsm(timepoints = 5,
var = "x",
change_letter = "g",
model = list(alpha_constant = TRUE,
beta = TRUE,
phi = TRUE))
# To get a readable output use cat() function
cat(uni_lcsm_syntax)
#> # Specify latent true scores
#> lx1 =~ 1 * x1
#> lx2 =~ 1 * x2
#> lx3 =~ 1 * x3
#> lx4 =~ 1 * x4
#> lx5 =~ 1 * x5
#> # Specify mean of latent true scores
#> lx1 ~ gamma_lx1 * 1
#> lx2 ~ 0 * 1
#> lx3 ~ 0 * 1
#> lx4 ~ 0 * 1
#> lx5 ~ 0 * 1
#> # Specify variance of latent true scores
#> lx1 ~~ sigma2_lx1 * lx1
#> lx2 ~~ 0 * lx2
#> lx3 ~~ 0 * lx3
#> lx4 ~~ 0 * lx4
#> lx5 ~~ 0 * lx5
#> # Specify intercept of obseved scores
#> x1 ~ 0 * 1
#> x2 ~ 0 * 1
#> x3 ~ 0 * 1
#> x4 ~ 0 * 1
#> x5 ~ 0 * 1
#> # Specify variance of observed scores
#> x1 ~~ sigma2_ux * x1
#> x2 ~~ sigma2_ux * x2
#> x3 ~~ sigma2_ux * x3
#> x4 ~~ sigma2_ux * x4
#> x5 ~~ sigma2_ux * x5
#> # Specify autoregressions of latent variables
#> lx2 ~ 1 * lx1
#> lx3 ~ 1 * lx2
#> lx4 ~ 1 * lx3
#> lx5 ~ 1 * lx4
#> # Specify latent change scores
#> dx2 =~ 1 * lx2
#> dx3 =~ 1 * lx3
#> dx4 =~ 1 * lx4
#> dx5 =~ 1 * lx5
#> # Specify latent change scores means
#> dx2 ~ 0 * 1
#> dx3 ~ 0 * 1
#> dx4 ~ 0 * 1
#> dx5 ~ 0 * 1
#> # Specify latent change scores variances
#> dx2 ~~ 0 * dx2
#> dx3 ~~ 0 * dx3
#> dx4 ~~ 0 * dx4
#> dx5 ~~ 0 * dx5
#> # Specify constant change factor
#> g2 =~ 1 * dx2 + 1 * dx3 + 1 * dx4 + 1 * dx5
#> # Specify constant change factor mean
#> g2 ~ alpha_g2 * 1
#> # Specify constant change factor variance
#> g2 ~~ sigma2_g2 * g2
#> # Specify constant change factor covariance with the initial true score
#> g2 ~~ sigma_g2lx1 * lx1
#> # Specify proportional change component
#> dx2 ~ beta_x * lx1
#> dx3 ~ beta_x * lx2
#> dx4 ~ beta_x * lx3
#> dx5 ~ beta_x * lx4
#> # Specify autoregression of change score
#> dx3 ~ phi_x * dx2
#> dx4 ~ phi_x * dx3
#> dx5 ~ phi_x * dx4Add lavaan syntax
uni_lcsm_syntax_add <- specify_uni_lcsm(timepoints = 3,
var = "x",
change_letter = "g",
add = "# JUST ANOTHER COMMENT",
model = list(alpha_constant = TRUE,
beta = TRUE,
phi = TRUE))
# To get a readable output use cat() function
cat(uni_lcsm_syntax_add)
#> # Specify latent true scores
#> lx1 =~ 1 * x1
#> lx2 =~ 1 * x2
#> lx3 =~ 1 * x3
#> # Specify mean of latent true scores
#> lx1 ~ gamma_lx1 * 1
#> lx2 ~ 0 * 1
#> lx3 ~ 0 * 1
#> # Specify variance of latent true scores
#> lx1 ~~ sigma2_lx1 * lx1
#> lx2 ~~ 0 * lx2
#> lx3 ~~ 0 * lx3
#> # Specify intercept of obseved scores
#> x1 ~ 0 * 1
#> x2 ~ 0 * 1
#> x3 ~ 0 * 1
#> # Specify variance of observed scores
#> x1 ~~ sigma2_ux * x1
#> x2 ~~ sigma2_ux * x2
#> x3 ~~ sigma2_ux * x3
#> # Specify autoregressions of latent variables
#> lx2 ~ 1 * lx1
#> lx3 ~ 1 * lx2
#> # Specify latent change scores
#> dx2 =~ 1 * lx2
#> dx3 =~ 1 * lx3
#> # Specify latent change scores means
#> dx2 ~ 0 * 1
#> dx3 ~ 0 * 1
#> # Specify latent change scores variances
#> dx2 ~~ 0 * dx2
#> dx3 ~~ 0 * dx3
#> # Specify constant change factor
#> g2 =~ 1 * dx2 + 1 * dx3
#> # Specify constant change factor mean
#> g2 ~ alpha_g2 * 1
#> # Specify constant change factor variance
#> g2 ~~ sigma2_g2 * g2
#> # Specify constant change factor covariance with the initial true score
#> g2 ~~ sigma_g2lx1 * lx1
#> # Specify proportional change component
#> dx2 ~ beta_x * lx1
#> dx3 ~ beta_x * lx2
#> # Specify autoregression of change score
#> dx3 ~ phi_x * dx2
#> # # # # # # # # # # # # # # # # # # # # # # #
#> # ---- Additaional Model Specifications ----
#> # # # # # # # # # # # # # # # # # # # # # # #
#> # JUST ANOTHER COMMENTBivariate LCSM syntax
True Score to Change Score
# Specify bivariate LCSM
lavaan_bi_lcsm_delta_01 <- specify_bi_lcsm(timepoints = 5,
var_x = "x",
model_x = list(alpha_constant = TRUE,
beta = TRUE,
phi = TRUE),
var_y = "y",
model_y = list(alpha_constant = TRUE,
beta = TRUE,
phi = TRUE),
coupling = list(delta_lag_xy = TRUE,
delta_lag_yx = TRUE),
change_letter_x = "g",
change_letter_y = "j")
# To get a readable output use cat() function
cat(lavaan_bi_lcsm_delta_01)
#> # # # # # # # # # # # # # # # # # # # # #
#> # Specify parameters for construct x ----
#> # # # # # # # # # # # # # # # # # # # # #
#> # Specify latent true scores
#> lx1 =~ 1 * x1
#> lx2 =~ 1 * x2
#> lx3 =~ 1 * x3
#> lx4 =~ 1 * x4
#> lx5 =~ 1 * x5
#> # Specify mean of latent true scores
#> lx1 ~ gamma_lx1 * 1
#> lx2 ~ 0 * 1
#> lx3 ~ 0 * 1
#> lx4 ~ 0 * 1
#> lx5 ~ 0 * 1
#> # Specify variance of latent true scores
#> lx1 ~~ sigma2_lx1 * lx1
#> lx2 ~~ 0 * lx2
#> lx3 ~~ 0 * lx3
#> lx4 ~~ 0 * lx4
#> lx5 ~~ 0 * lx5
#> # Specify intercept of obseved scores
#> x1 ~ 0 * 1
#> x2 ~ 0 * 1
#> x3 ~ 0 * 1
#> x4 ~ 0 * 1
#> x5 ~ 0 * 1
#> # Specify variance of observed scores
#> x1 ~~ sigma2_ux * x1
#> x2 ~~ sigma2_ux * x2
#> x3 ~~ sigma2_ux * x3
#> x4 ~~ sigma2_ux * x4
#> x5 ~~ sigma2_ux * x5
#> # Specify autoregressions of latent variables
#> lx2 ~ 1 * lx1
#> lx3 ~ 1 * lx2
#> lx4 ~ 1 * lx3
#> lx5 ~ 1 * lx4
#> # Specify latent change scores
#> dx2 =~ 1 * lx2
#> dx3 =~ 1 * lx3
#> dx4 =~ 1 * lx4
#> dx5 =~ 1 * lx5
#> # Specify latent change scores means
#> dx2 ~ 0 * 1
#> dx3 ~ 0 * 1
#> dx4 ~ 0 * 1
#> dx5 ~ 0 * 1
#> # Specify latent change scores variances
#> dx2 ~~ 0 * dx2
#> dx3 ~~ 0 * dx3
#> dx4 ~~ 0 * dx4
#> dx5 ~~ 0 * dx5
#> # Specify constant change factor
#> g2 =~ 1 * dx2 + 1 * dx3 + 1 * dx4 + 1 * dx5
#> # Specify constant change factor mean
#> g2 ~ alpha_g2 * 1
#> # Specify constant change factor variance
#> g2 ~~ sigma2_g2 * g2
#> # Specify constant change factor covariance with the initial true score
#> g2 ~~ sigma_g2lx1 * lx1
#> # Specify proportional change component
#> dx2 ~ beta_x * lx1
#> dx3 ~ beta_x * lx2
#> dx4 ~ beta_x * lx3
#> dx5 ~ beta_x * lx4
#> # Specify autoregression of change score
#> dx3 ~ phi_x * dx2
#> dx4 ~ phi_x * dx3
#> dx5 ~ phi_x * dx4
#> # # # # # # # # # # # # # # # # # # # # #
#> # Specify parameters for construct y ----
#> # # # # # # # # # # # # # # # # # # # # #
#> # Specify latent true scores
#> ly1 =~ 1 * y1
#> ly2 =~ 1 * y2
#> ly3 =~ 1 * y3
#> ly4 =~ 1 * y4
#> ly5 =~ 1 * y5
#> # Specify mean of latent true scores
#> ly1 ~ gamma_ly1 * 1
#> ly2 ~ 0 * 1
#> ly3 ~ 0 * 1
#> ly4 ~ 0 * 1
#> ly5 ~ 0 * 1
#> # Specify variance of latent true scores
#> ly1 ~~ sigma2_ly1 * ly1
#> ly2 ~~ 0 * ly2
#> ly3 ~~ 0 * ly3
#> ly4 ~~ 0 * ly4
#> ly5 ~~ 0 * ly5
#> # Specify intercept of obseved scores
#> y1 ~ 0 * 1
#> y2 ~ 0 * 1
#> y3 ~ 0 * 1
#> y4 ~ 0 * 1
#> y5 ~ 0 * 1
#> # Specify variance of observed scores
#> y1 ~~ sigma2_uy * y1
#> y2 ~~ sigma2_uy * y2
#> y3 ~~ sigma2_uy * y3
#> y4 ~~ sigma2_uy * y4
#> y5 ~~ sigma2_uy * y5
#> # Specify autoregressions of latent variables
#> ly2 ~ 1 * ly1
#> ly3 ~ 1 * ly2
#> ly4 ~ 1 * ly3
#> ly5 ~ 1 * ly4
#> # Specify latent change scores
#> dy2 =~ 1 * ly2
#> dy3 =~ 1 * ly3
#> dy4 =~ 1 * ly4
#> dy5 =~ 1 * ly5
#> # Specify latent change scores means
#> dy2 ~ 0 * 1
#> dy3 ~ 0 * 1
#> dy4 ~ 0 * 1
#> dy5 ~ 0 * 1
#> # Specify latent change scores variances
#> dy2 ~~ 0 * dy2
#> dy3 ~~ 0 * dy3
#> dy4 ~~ 0 * dy4
#> dy5 ~~ 0 * dy5
#> # Specify constant change factor
#> j2 =~ 1 * dy2 + 1 * dy3 + 1 * dy4 + 1 * dy5
#> # Specify constant change factor mean
#> j2 ~ alpha_j2 * 1
#> # Specify constant change factor variance
#> j2 ~~ sigma2_j2 * j2
#> # Specify constant change factor covariance with the initial true score
#> j2 ~~ sigma_j2ly1 * ly1
#> # Specify proportional change component
#> dy2 ~ beta_y * ly1
#> dy3 ~ beta_y * ly2
#> dy4 ~ beta_y * ly3
#> dy5 ~ beta_y * ly4
#> # Specify autoregression of change score
#> dy3 ~ phi_y * dy2
#> dy4 ~ phi_y * dy3
#> dy5 ~ phi_y * dy4
#> # Specify residual covariances
#> x1 ~~ sigma_su * y1
#> x2 ~~ sigma_su * y2
#> x3 ~~ sigma_su * y3
#> x4 ~~ sigma_su * y4
#> x5 ~~ sigma_su * y5
#> # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
#> # Specify covariances betweeen specified change components (alpha) and intercepts (initial latent true scores lx1 and ly1) ----
#> # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
#> # Specify covariance of intercepts
#> lx1 ~~ sigma_ly1lx1 * ly1
#> # Specify covariance of constant change and intercept between constructs
#> ly1 ~~ sigma_g2ly1 * g2
#> # Specify covariance of constant change and intercept between constructs
#> lx1 ~~ sigma_j2lx1 * j2
#> # Specify covariance of constant change factors between constructs
#> g2 ~~ sigma_j2g2 * j2
#> # # # # # # # # # # # # # # # # # # # # # # # # # # #
#> # Specify between-construct coupling parameters ----
#> # # # # # # # # # # # # # # # # # # # # # # # # # # #
#> # Change score x (t) is determined by true score y (t-1)
#> dx2 ~ delta_lag_xy * ly1
#> dx3 ~ delta_lag_xy * ly2
#> dx4 ~ delta_lag_xy * ly3
#> dx5 ~ delta_lag_xy * ly4
#> # Change score y (t) is determined by true score x (t-1)
#> dy2 ~ delta_lag_yx * lx1
#> dy3 ~ delta_lag_yx * lx2
#> dy4 ~ delta_lag_yx * lx3
#> dy5 ~ delta_lag_yx * lx4Change Score to Change Score
# Specify bivariate LCSM
lavaan_bi_lcsm_xi_01 <- specify_bi_lcsm(timepoints = 5,
var_x = "x",
model_x = list(alpha_constant = TRUE,
beta = TRUE,
phi = TRUE),
var_y = "y",
model_y = list(alpha_constant = TRUE,
beta = TRUE,
phi = TRUE),
coupling = list(xi_lag_xy = TRUE,
xi_lag_yx = TRUE),
change_letter_x = "g",
change_letter_y = "j")
# To get a readable output use cat() function
cat(lavaan_bi_lcsm_xi_01)
#> # # # # # # # # # # # # # # # # # # # # #
#> # Specify parameters for construct x ----
#> # # # # # # # # # # # # # # # # # # # # #
#> # Specify latent true scores
#> lx1 =~ 1 * x1
#> lx2 =~ 1 * x2
#> lx3 =~ 1 * x3
#> lx4 =~ 1 * x4
#> lx5 =~ 1 * x5
#> # Specify mean of latent true scores
#> lx1 ~ gamma_lx1 * 1
#> lx2 ~ 0 * 1
#> lx3 ~ 0 * 1
#> lx4 ~ 0 * 1
#> lx5 ~ 0 * 1
#> # Specify variance of latent true scores
#> lx1 ~~ sigma2_lx1 * lx1
#> lx2 ~~ 0 * lx2
#> lx3 ~~ 0 * lx3
#> lx4 ~~ 0 * lx4
#> lx5 ~~ 0 * lx5
#> # Specify intercept of obseved scores
#> x1 ~ 0 * 1
#> x2 ~ 0 * 1
#> x3 ~ 0 * 1
#> x4 ~ 0 * 1
#> x5 ~ 0 * 1
#> # Specify variance of observed scores
#> x1 ~~ sigma2_ux * x1
#> x2 ~~ sigma2_ux * x2
#> x3 ~~ sigma2_ux * x3
#> x4 ~~ sigma2_ux * x4
#> x5 ~~ sigma2_ux * x5
#> # Specify autoregressions of latent variables
#> lx2 ~ 1 * lx1
#> lx3 ~ 1 * lx2
#> lx4 ~ 1 * lx3
#> lx5 ~ 1 * lx4
#> # Specify latent change scores
#> dx2 =~ 1 * lx2
#> dx3 =~ 1 * lx3
#> dx4 =~ 1 * lx4
#> dx5 =~ 1 * lx5
#> # Specify latent change scores means
#> dx2 ~ 0 * 1
#> dx3 ~ 0 * 1
#> dx4 ~ 0 * 1
#> dx5 ~ 0 * 1
#> # Specify latent change scores variances
#> dx2 ~~ 0 * dx2
#> dx3 ~~ 0 * dx3
#> dx4 ~~ 0 * dx4
#> dx5 ~~ 0 * dx5
#> # Specify constant change factor
#> g2 =~ 1 * dx2 + 1 * dx3 + 1 * dx4 + 1 * dx5
#> # Specify constant change factor mean
#> g2 ~ alpha_g2 * 1
#> # Specify constant change factor variance
#> g2 ~~ sigma2_g2 * g2
#> # Specify constant change factor covariance with the initial true score
#> g2 ~~ sigma_g2lx1 * lx1
#> # Specify proportional change component
#> dx2 ~ beta_x * lx1
#> dx3 ~ beta_x * lx2
#> dx4 ~ beta_x * lx3
#> dx5 ~ beta_x * lx4
#> # Specify autoregression of change score
#> dx3 ~ phi_x * dx2
#> dx4 ~ phi_x * dx3
#> dx5 ~ phi_x * dx4
#> # # # # # # # # # # # # # # # # # # # # #
#> # Specify parameters for construct y ----
#> # # # # # # # # # # # # # # # # # # # # #
#> # Specify latent true scores
#> ly1 =~ 1 * y1
#> ly2 =~ 1 * y2
#> ly3 =~ 1 * y3
#> ly4 =~ 1 * y4
#> ly5 =~ 1 * y5
#> # Specify mean of latent true scores
#> ly1 ~ gamma_ly1 * 1
#> ly2 ~ 0 * 1
#> ly3 ~ 0 * 1
#> ly4 ~ 0 * 1
#> ly5 ~ 0 * 1
#> # Specify variance of latent true scores
#> ly1 ~~ sigma2_ly1 * ly1
#> ly2 ~~ 0 * ly2
#> ly3 ~~ 0 * ly3
#> ly4 ~~ 0 * ly4
#> ly5 ~~ 0 * ly5
#> # Specify intercept of obseved scores
#> y1 ~ 0 * 1
#> y2 ~ 0 * 1
#> y3 ~ 0 * 1
#> y4 ~ 0 * 1
#> y5 ~ 0 * 1
#> # Specify variance of observed scores
#> y1 ~~ sigma2_uy * y1
#> y2 ~~ sigma2_uy * y2
#> y3 ~~ sigma2_uy * y3
#> y4 ~~ sigma2_uy * y4
#> y5 ~~ sigma2_uy * y5
#> # Specify autoregressions of latent variables
#> ly2 ~ 1 * ly1
#> ly3 ~ 1 * ly2
#> ly4 ~ 1 * ly3
#> ly5 ~ 1 * ly4
#> # Specify latent change scores
#> dy2 =~ 1 * ly2
#> dy3 =~ 1 * ly3
#> dy4 =~ 1 * ly4
#> dy5 =~ 1 * ly5
#> # Specify latent change scores means
#> dy2 ~ 0 * 1
#> dy3 ~ 0 * 1
#> dy4 ~ 0 * 1
#> dy5 ~ 0 * 1
#> # Specify latent change scores variances
#> dy2 ~~ 0 * dy2
#> dy3 ~~ 0 * dy3
#> dy4 ~~ 0 * dy4
#> dy5 ~~ 0 * dy5
#> # Specify constant change factor
#> j2 =~ 1 * dy2 + 1 * dy3 + 1 * dy4 + 1 * dy5
#> # Specify constant change factor mean
#> j2 ~ alpha_j2 * 1
#> # Specify constant change factor variance
#> j2 ~~ sigma2_j2 * j2
#> # Specify constant change factor covariance with the initial true score
#> j2 ~~ sigma_j2ly1 * ly1
#> # Specify proportional change component
#> dy2 ~ beta_y * ly1
#> dy3 ~ beta_y * ly2
#> dy4 ~ beta_y * ly3
#> dy5 ~ beta_y * ly4
#> # Specify autoregression of change score
#> dy3 ~ phi_y * dy2
#> dy4 ~ phi_y * dy3
#> dy5 ~ phi_y * dy4
#> # Specify residual covariances
#> x1 ~~ sigma_su * y1
#> x2 ~~ sigma_su * y2
#> x3 ~~ sigma_su * y3
#> x4 ~~ sigma_su * y4
#> x5 ~~ sigma_su * y5
#> # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
#> # Specify covariances betweeen specified change components (alpha) and intercepts (initial latent true scores lx1 and ly1) ----
#> # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
#> # Specify covariance of intercepts
#> lx1 ~~ sigma_ly1lx1 * ly1
#> # Specify covariance of constant change and intercept between constructs
#> ly1 ~~ sigma_g2ly1 * g2
#> # Specify covariance of constant change and intercept between constructs
#> lx1 ~~ sigma_j2lx1 * j2
#> # Specify covariance of constant change factors between constructs
#> g2 ~~ sigma_j2g2 * j2
#> # # # # # # # # # # # # # # # # # # # # # # # # # # #
#> # Specify between-construct coupling parameters ----
#> # # # # # # # # # # # # # # # # # # # # # # # # # # #
#> # Change score x (t) is determined by change score y (t-1)
#> dx3 ~ xi_lag_xy * dy2
#> dx4 ~ xi_lag_xy * dy3
#> dx5 ~ xi_lag_xy * dy4
#> # Change score y (t) is determined by change score x (t-1)
#> dy3 ~ xi_lag_yx * dx2
#> dy4 ~ xi_lag_yx * dx3
#> dy5 ~ xi_lag_yx * dx4Add model specifications to lavaan code
# Specify bivariate LCSM
lavaan_bi_lcsm_xi_add <- specify_bi_lcsm(timepoints = 3,
var_x = "x",
model_x = list(alpha_constant = TRUE,
beta = TRUE,
phi = TRUE),
var_y = "y",
model_y = list(alpha_constant = TRUE,
beta = TRUE,
phi = TRUE),
coupling = list(xi_lag_xy = TRUE,
xi_lag_yx = TRUE),
add = "age ~~ age_j2 * j2",
change_letter_x = "g",
change_letter_y = "j")
# To get a readable output use cat() function
cat(lavaan_bi_lcsm_xi_add)
#> # # # # # # # # # # # # # # # # # # # # #
#> # Specify parameters for construct x ----
#> # # # # # # # # # # # # # # # # # # # # #
#> # Specify latent true scores
#> lx1 =~ 1 * x1
#> lx2 =~ 1 * x2
#> lx3 =~ 1 * x3
#> # Specify mean of latent true scores
#> lx1 ~ gamma_lx1 * 1
#> lx2 ~ 0 * 1
#> lx3 ~ 0 * 1
#> # Specify variance of latent true scores
#> lx1 ~~ sigma2_lx1 * lx1
#> lx2 ~~ 0 * lx2
#> lx3 ~~ 0 * lx3
#> # Specify intercept of obseved scores
#> x1 ~ 0 * 1
#> x2 ~ 0 * 1
#> x3 ~ 0 * 1
#> # Specify variance of observed scores
#> x1 ~~ sigma2_ux * x1
#> x2 ~~ sigma2_ux * x2
#> x3 ~~ sigma2_ux * x3
#> # Specify autoregressions of latent variables
#> lx2 ~ 1 * lx1
#> lx3 ~ 1 * lx2
#> # Specify latent change scores
#> dx2 =~ 1 * lx2
#> dx3 =~ 1 * lx3
#> # Specify latent change scores means
#> dx2 ~ 0 * 1
#> dx3 ~ 0 * 1
#> # Specify latent change scores variances
#> dx2 ~~ 0 * dx2
#> dx3 ~~ 0 * dx3
#> # Specify constant change factor
#> g2 =~ 1 * dx2 + 1 * dx3
#> # Specify constant change factor mean
#> g2 ~ alpha_g2 * 1
#> # Specify constant change factor variance
#> g2 ~~ sigma2_g2 * g2
#> # Specify constant change factor covariance with the initial true score
#> g2 ~~ sigma_g2lx1 * lx1
#> # Specify proportional change component
#> dx2 ~ beta_x * lx1
#> dx3 ~ beta_x * lx2
#> # Specify autoregression of change score
#> dx3 ~ phi_x * dx2
#> # # # # # # # # # # # # # # # # # # # # #
#> # Specify parameters for construct y ----
#> # # # # # # # # # # # # # # # # # # # # #
#> # Specify latent true scores
#> ly1 =~ 1 * y1
#> ly2 =~ 1 * y2
#> ly3 =~ 1 * y3
#> # Specify mean of latent true scores
#> ly1 ~ gamma_ly1 * 1
#> ly2 ~ 0 * 1
#> ly3 ~ 0 * 1
#> # Specify variance of latent true scores
#> ly1 ~~ sigma2_ly1 * ly1
#> ly2 ~~ 0 * ly2
#> ly3 ~~ 0 * ly3
#> # Specify intercept of obseved scores
#> y1 ~ 0 * 1
#> y2 ~ 0 * 1
#> y3 ~ 0 * 1
#> # Specify variance of observed scores
#> y1 ~~ sigma2_uy * y1
#> y2 ~~ sigma2_uy * y2
#> y3 ~~ sigma2_uy * y3
#> # Specify autoregressions of latent variables
#> ly2 ~ 1 * ly1
#> ly3 ~ 1 * ly2
#> # Specify latent change scores
#> dy2 =~ 1 * ly2
#> dy3 =~ 1 * ly3
#> # Specify latent change scores means
#> dy2 ~ 0 * 1
#> dy3 ~ 0 * 1
#> # Specify latent change scores variances
#> dy2 ~~ 0 * dy2
#> dy3 ~~ 0 * dy3
#> # Specify constant change factor
#> j2 =~ 1 * dy2 + 1 * dy3
#> # Specify constant change factor mean
#> j2 ~ alpha_j2 * 1
#> # Specify constant change factor variance
#> j2 ~~ sigma2_j2 * j2
#> # Specify constant change factor covariance with the initial true score
#> j2 ~~ sigma_j2ly1 * ly1
#> # Specify proportional change component
#> dy2 ~ beta_y * ly1
#> dy3 ~ beta_y * ly2
#> # Specify autoregression of change score
#> dy3 ~ phi_y * dy2
#> # Specify residual covariances
#> x1 ~~ sigma_su * y1
#> x2 ~~ sigma_su * y2
#> x3 ~~ sigma_su * y3
#> # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
#> # Specify covariances betweeen specified change components (alpha) and intercepts (initial latent true scores lx1 and ly1) ----
#> # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
#> # Specify covariance of intercepts
#> lx1 ~~ sigma_ly1lx1 * ly1
#> # Specify covariance of constant change and intercept between constructs
#> ly1 ~~ sigma_g2ly1 * g2
#> # Specify covariance of constant change and intercept between constructs
#> lx1 ~~ sigma_j2lx1 * j2
#> # Specify covariance of constant change factors between constructs
#> g2 ~~ sigma_j2g2 * j2
#> # # # # # # # # # # # # # # # # # # # # # # # # # # #
#> # Specify between-construct coupling parameters ----
#> # # # # # # # # # # # # # # # # # # # # # # # # # # #
#> # Change score x (t) is determined by change score y (t-1)
#> dx3 ~ xi_lag_xy * dy2
#> # Change score y (t) is determined by change score x (t-1)
#> dy3 ~ xi_lag_yx * dx2
#> # # # # # # # # # # # # # # # # # # # # # # #
#> # ---- Additaional Model Specifications ----
#> # # # # # # # # # # # # # # # # # # # # # # #
#> age ~~ age_j2 * j2