Latent variable two time-point model

Question

I have a latent variable that was measured at 2 time points, and I want to model the growth in this latent variable. I then want to examine how variations in slope and intercept differ by latent and non-latent covariates, allowing for interactions between these covariates as well. What is the best way to do this? I can't do a latent growth model because there are only 2 time points.

Answer 1

You can do a latent growth model with two variables.

Example:

library(dplyr)
library(lavaan)

d <- data.frame(y1 = rnorm(1000)) %>%
  dplyr::mutate(y2 = rnorm(1000) * y1 + 1)

model <- "
  int =~ 1 * y1 + 1 * y2
  slope =~ 1 * y2
  int ~~ int
  slope ~~ slope
  y1 ~ 0
  y2 ~ 0
  int ~ 1
  slope ~ 1
  y1 ~~ 0 * y1
  y2 ~~ 0 * y2
  
  "

fit <- lavaan::sem(model, d)
summary(fit)

Edit:

Here's the output which shows the slope and intercept variances.

Latent Variables:
                   Estimate  Std.Err  z-value  P(>|z|)
  int =~                                              
    y1                1.000                           
    y2                1.000                           
  slope =~                                            
    y2                1.000                           

Covariances:
                   Estimate  Std.Err  z-value  P(>|z|)
  int ~~                                              
    slope            -1.049    0.059  -17.861    0.000

Intercepts:
                   Estimate  Std.Err  z-value  P(>|z|)
   .y1                0.000                           
   .y2                0.000                           
    int              -0.004    0.032   -0.113    0.910
    slope             1.022    0.047   21.543    0.000

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)
    int               1.043    0.047   22.361    0.000
    slope             2.251    0.101   22.361    0.000
   .y1                0.000                           
   .y2                0.000