Structural equation model (SEM) trees are a combination of SEM and decision trees (also known as classification and regression trees or recursive partitioning). SEM trees hierarchically split empirical data into homogeneous groups sharing similar data patterns with respect to a SEM by recursively selecting optimal predictors of these differences from a potentially large set of predictors.
semtree(
model,
data = NULL,
control = NULL,
constraints = NULL,
predictors = NULL,
...
)A template model specification from OpenMx using
the mxModel function (or a lavaan model
using the lavaan function with option fit=FALSE).
Model must be syntactically correct within the framework chosen, and
converge to a solution.
Data.frame used in the model creation using
mxModel or lavaan are input here. Order
of modeled variables and predictors is not important when providing a
dataset to semtree.
semtree model specifications from
semtree.control are input here. Any changes from the default
setting can be specified here.
A semtree.constraints object setting model
parameters as constrained from the beginning of the semtree
computation. This includes options to globally or locally set equality
constraints and to specify focus parameters (i.e., parameter subsets that
exclusively go into the function evaluating splits). Also, options for
measurement invariance testing in trees are included.
A vector of variable names matching variable names in
dataset. If NULL (default) all variables that are in dataset and not part of
the model are potential predictors. Optional function input to select a
subset of the unmodeled variables to use as predictors in the semtree
function.
Optional arguments passed to the tree growing function.
A semtree object is created which can be examined with
summary, plot, and print.
Calling semtree with an OpenMx or
lavaan model creates a tree that recursively
partitions a dataset such that the partitions maximally differ with respect
to the model-predicted distributions. Each resulting subgroup (represented
as a leaf in the tree) is represented by a SEM with a distinct set of
parameter estimates.
Predictors (yet unmodeled variables) can take on any form for the splitting algorithm to function (categorical, ordered categories, continuous). Care must be taken in choosing how many predictors to include in analyses because as the number of categories grows for unordered categorical variables, the number of multigroup comparisons increases exponentially for unordered categories.
Currently available evaluation methods for assessing partitions:
1. "naive" selection method compares all possible split values to one another over all predictors included in the dataset.
2. "fair" selection uses a two step procedure for analyzing split values on predictors at each node of the tree. The first phase uses half of the sample to examine the model improvement for each split value on each predictor, and retains the the value that presents the largest improvement for each predictor. The second phase then evaluates these best split points for each predictor on the second half of the sample. The best improvement for the c splits tested on c predictors is selected for the node and the dataset is split from this node for further testing.
3. "score" uses score-based test statistics. These statistics are much faster than the classic SEM tree approach while having favorable statistical properties.
All other parameters controlling the tree growing process are available
through a separate semtree.control object.
Brandmaier, A.M., Oertzen, T. v., McArdle, J.J., & Lindenberger, U. (2013). Structural equation model trees. Psychological Methods, 18(1), 71-86.
Arnold, M., Voelkle, M. C., & Brandmaier, A. M. (2021). Score-guided structural equation model trees. Frontiers in Psychology, 11, Article 564403. https://doi.org/10.3389/fpsyg.2020.564403
semtree.control, summary.semtree,
parameters, se, prune.semtree,
subtree, OpenMx,
lavaan