Example of a three-variable cross lagged panel model in R using {lavaan}

lav-clpm-3var.R

## generate data set
x2 <- rnorm(200)
x1 <- x2 + rnorm(200)
y2 <- rnorm(200) + x2
y1 <- y2 + rnorm(200)
z2 <- rnorm(200) + y2
z1 <- z2 + rnorm(200)
d <- data.frame(x1, x2, y1, y2, z1, z2)

## specify null and full models
null_mod_syntax <- '
  x2 ~ 0*x1 + 0*y1 + 0*z1
  y2 ~ 0*x1 + 0*y1 + 0*z1
  z2 ~ 0*x1 + 0*y1 + 0*z1
'
full_mod_syntax <- '
  x2 ~ x1 + y1 + z1
  y2 ~ x1 + y1 + z1
  z2 ~ x1 + y1 + z1
'

## estimate models
m0 <- lavaan::sem(null_mod_syntax, data = d)
m1 <- lavaan::sem(full_mod_syntax, data = d)

## compare models (see degrees of freedom)
lavaan::anova(m0, m1)

## view full model summary
lavaan::summary(m1)

## compare DV correlations...
with(d, cor(data.frame(x2, y2, z2)))
##  with residual correlations
subset(
  lavaan::parameterEstimates(m1),
  op == "~~" & lhs %in% c("x2", "y2", "z2")
)

Thanks a lot ！Can you give a reference for this method?