---
title: "Cross-lag demo"
output: html_notebook
---

First set it all up.

```{r}
library(lavaan)

sampsize <- 500

lower <- '
1
.7 1
.4 .3 1
.3 .4 .5 1 '

longit_data <- getCov(lower, names = c("x1", "x2", "y1", "y2"))
```

Fit a cross-lag model.

```{r}
crosslag_model <- '
  x2 ~ x1 + y1
  y2 ~ x1 + y1
  x1 ~~ y1
  x2 ~~ y2
'
fit_crosslag_model <- sem(crosslag_model, sample.cov = longit_data, sample.nobs = sampsize)
summary(fit_crosslag_model, standardized = TRUE)
```

Now fit a correlated-trait model.

```{r}
trait_model <- '
  X_latent =~ a*x1 + a*x2
  Y_latent =~ b*y1 + b*y2
  X_latent ~~ Y_latent
  x1 ~~ y1
  x2 ~~ y2
'
fit_trait_model <- sem(trait_model, sample.cov = longit_data, sample.nobs = sampsize, std.lv = TRUE)
summary(fit_trait_model, standardized = TRUE)
```