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 OpenMx’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.