We first load the `semtree`

package and the
`OpenMx`

package for specifying our SEM.

Now, we simulate some data from a linear latent growth curve model
(that is, a random intercept and random slope over time). The dataset
will be called `growth.data`

. The dataset contains five
observations for each individual (`X1`

to `X5`

)
and one predictor `P1`

. The predictor is dichotomous and
predicts a (quite large) difference in mean slope.

```
set.seed(23)
N <- 1000
M <- 5
icept <- rnorm(N, 10, sd = 4)
slope <- rnorm(N, 3, sd = 1.2)
p1 <- sample(c(0, 1), size = N, replace = TRUE)
loadings <- 0:4
x <-
(slope + p1 * 5) %*% t(loadings) +
matrix(rep(icept, each = M), byrow = TRUE, ncol = M) +
rnorm(N * M, sd = .08)
growth.data <- data.frame(x, factor(p1))
names(growth.data) <- c(paste0("X", 1:M), "P1")
```

Now, we specify a linear latent growth curve model using OpenMxâ€™s path specification. The model has five observed variables. Residual variances are assumed to be identical over time.

```
manifests <- names(growth.data)[1:5]
growthCurveModel <- mxModel("Linear Growth Curve Model Path Specification",
type="RAM",
manifestVars=manifests,
latentVars=c("intercept","slope"),
mxData(growth.data, type="raw"),
# residual variances
mxPath(
from=manifests,
arrows=2,
free=TRUE,
values = c(.1, .1, .1, .1, .1),
labels=c("residual","residual","residual","residual","residual")
),
# latent variances and covariance
mxPath(
from=c("intercept","slope"),
arrows=2,
connect="unique.pairs",
free=TRUE,
values=c(2, 0, 1),
labels=c("vari", "cov", "vars")
),
# intercept loadings
mxPath(
from="intercept",
to=manifests,
arrows=1,
free=FALSE,
values=c(1, 1, 1, 1, 1)
),
# slope loadings
mxPath(
from="slope",
to=manifests,
arrows=1,
free=FALSE,
values=c(0, 1, 2, 3, 4)
),
# manifest means
mxPath(
from="one",
to=manifests,
arrows=1,
free=FALSE,
values=c(0, 0, 0, 0, 0)
),
# latent means
mxPath(
from="one",
to=c("intercept", "slope"),
arrows=1,
free=TRUE,
values=c(1, 1),
labels=c("meani", "means")
)
) # close model
# fit the model to the entire dataset
growthCurveModel <- mxRun(growthCurveModel)
#> Running Linear Growth Curve Model Path Specification with 6 parameters
```

Now, we grow a SEM tree using the `semtree`

function,
which takes the model and the dataset as input. If not specified
otherwise, SEM tree will assume that all variables in the dataset, which
are not observed variables in the dataset are potential predictors.