semtree

What is this?

An R package for estimating Structural Equation Model (SEM) Trees and Forests. They are a fusion of SEM and decision trees, or SEM and random forests respectively. While SEM is a confirmatory modeling technique, SEM trees and forests allow to explore whether there are predictors that provide further information about an initial, theory-based model. Potential use cases are the search for potential predictors that explain individual differences, finding omitted variables in a model, or exploring measurement invariance over a large set of predictors. A recent overview is in our latest book chapter in the SEM handbook (Brandmaier & Jacobucci, 2023).

Install

Install the latest stable version from CRAN:

install.packages("semtree")

To install the latest semtree package directly from GitHub, copy the following line into R:

library(devtools)
devtools::install_github("brandmaier/semtree")

# even better: install with package vignette (extra documentation)
devtools::install_github("brandmaier/semtree",force=TRUE, build_opts = c())

Usage

Package documentation and use-cases with runnable R code can be found on our github pages: https://brandmaier.github.io/semtree/.

Package vignettes (shipped with the package) contain documentation on how to use the package. Simply type this in R once you have loaded the package:

browseVignettes("semtree")

Example

First, we load the birthwt data frame from the MASS package, which contains risk factors associated with low infant birth weight. We extract the variables presence of uterine irritability (ui), history of hypertension (ht), smoke status during pregnancy (smoke) and birth weight (btw):

 library(semtree)
#> Lade nötiges Paket: OpenMx

  bw <- with(MASS::birthwt, {
  ui <- factor(ui, labels=c("no","yes"))
  ht <- factor(ht, labels=c("no","yes"))
  smoke <- factor(smoke, labels=c("no","yes"))
  data.frame( bwt, uterine_irritability=ui, hypertension=ht, smoke, num_premature_labours=ptl, physician_visits=ftv )
 })

Next, we set up a simple univariate model that estimates mean and variance of birth weight

 model <- lavaan::lavaan("bwt~~bwt; bwt~1")

Last, we estimate a SEM tree with a maximum depth of two, a significance criterion of 1% and splits based on score-based tests, and plot the resulting tree:

ctrl <- semtree_control(method="score", max.depth = 2, alpha = 0.01)

tree <- semtree(model = model, data = bw, control = ctrl)
plot(tree)
 

#> ✖ Variable num_premature_labours is numeric but has only few unique values. Consider recoding as ordered factor.
#> ✖ Variable physician_visits is numeric but has only few unique values. Consider recoding as ordered factor.
#> ✔ Tree construction finished [took less than a second].

Robustness checklist for end users

To make analyses with semtree more robust and reproducible, we recommend the following:

1. Set a seed in semtree_control(seed = ...) before tree growth so randomized split procedures are reproducible.
2. Set explicit stopping rules (min.N, optionally min.bucket, and max.depth) instead of relying on defaults.
3. Choose split method intentionally (naive, fair, or score) and report the choice in manuscripts.
4. Use conservative split testing where appropriate with bonferroni = TRUE when many predictors are screened.
5. Inspect convergence behavior by keeping check.convergence = TRUE and increasing report.level for diagnostics.
6. Handle missing split variables explicitly (missing, use.all) and document your choice.
7. Pick and report likelihood computation (loglik = "model" vs "mvn") especially when comparing engines.
8. Use pruning for interpretation to avoid over-reading deep, unstable branches (prune(tree, max.depth = ...)).
9. Validate findings with forests (semforest) to check whether important predictors recur across trees.
10. Archive session metadata (at the very least document sessionInfo(), package versions, and control settings) alongside analysis outputs, or use packages such as reproducibleRchunks or repro to improve reproducibility chances.

References

Theory and method:

• Brandmaier, A. M., & Jacobucci, R. C. (2023). Machine-learning approaches to structural equation modeling. In R. H. Hoyle (Ed.), Handbook of structural equation modeling (2nd rev. ed., pp. 722–739). Guilford Press.

• Arnold, M., Voelkle, M.C., and Brandmaier, A.M. (2021). Score-guided structural equation model trees. Frontiers in psychology, 11, 564403.

• Brandmaier, A. M., Driver, C., & Voelkle, M. C. (2019). Recursive partitioning in continuous time analysis. In K. van Montfort, J. Oud, & M. C. Voelkle (Eds.), Continuous time modeling in the behavioral and related sciences. New York: Springer.

• Brandmaier, A. M., Prindle, J. J., McArdle, J. J., & Lindenberger, U. (2016). Theory-guided exploration with structural equation model forests. Psychological Methods, 21, 566-582.

• Brandmaier, A. M., von Oertzen, T., McArdle, J. J., & Lindenberger, U. (2014). Exploratory data mining with structural equation model trees. In J. J. McArdle & G. Ritschard (Eds.), Contemporary issues in exploratory data mining in the behavioral sciences (pp. 96-127). New York: Routledge.

• Brandmaier, A. M., von Oertzen, T., McArdle, J. J., & Lindenberger, U. (2013). Structural equation model trees. Psychological Methods, 18, 71-86.

Applied examples (there are many more):

Brandmaier, A. M., Ram, N., Wagner, G. G., & Gerstorf, D. (2017). Terminal decline in well-being: The role of multi-indicator constellations of physical health and psychosocial correlates. Developmental Psychology.