MplusTrees {MplusTrees}

Recursive partitioning trees with Mplus models

Description

Generates recursive partitioning trees using Mplus models. MplusTrees() takes an Mplus model written in the form of an MplusAutomation script, uses MplusAutomation to fit the model in Mplus, and performs recursive partitioning using rpart.

Usage

MplusTrees(
  script,
  data,
  rPartFormula,
  catvars = NULL,
  group = ~id,
  control = rpart.control(),
  se = F,
  psplit = F,
  palpha = 0.05,
  cv = F,
  k = 5
)

Arguments

script

An MplusAutomation script file

data

Dataset that is specified in the script

rPartFormula

Formula of the form ~ variable names

catvars

Vector of names of categorical covariates

group

id variable. If not specified an id variable is created for each row

control

Control object for rpart

se

Whether to print standard errors and p values. In general should be set to FALSE

psplit

Whether to use likelihood ratio p values as a splitting criterion

palpha

Type I error rate (alpha level) for rejecting with likelihood ratio test when psplit set to TRUE

cv

Performs k-fold cross-validation to select value of cp

k

number of folds for cross-validation

Details

The function temporarily changes the working directory to the temporary directory. Files used and generated by Mplus are stored here and can be accessed using tempdir().

By default MplusTrees() only splits on the criteria specified in the control argument, the most important of which is the cp parameter. The user can also split on the p value generated from the likelihood ratio test comparing the parent node to a multiple group model consisting of 2 groups (the daughter nodes). This p value criterion is used in addition to the cp criterion in that both must be met for a split to be made. The psplit argument turns this option on, and palpha sets the alpha level criterion for rejection.

Cross-validation (CV) can also be used to choose the cp parameter. If this option is used, any user-specified cp value will be overridden by the optimal cp value chosen by CV. CV fits the model to the training set and calculates an expected minus 2 log-likelihood (-2LL) for each terminal node. In the test set, individuals are assigned to terminal nodes based on the tree structure found in the training set. Their "expected" values are the -2LL values from the respective training set terminal nodes. The "observed" values are the -2LL values from fitting a multiple group model, with each terminal node as a group. The cp value chosen is the one that produces the smallest MSE.

CV should only be used when (1) the Mplus model can be fit relatively quickly, (2) there are only a few covariates with a few response options, and (3) the sample size is large enough that the user is confident the model can be fit without issue in a sample of size N/k and a tree that partitions this sample further. If these conditions are not met, the process could take prohibitively long to arrive at a solution. Note that if even a single model fails to produce a valid log-likelihood value, the function will terminate with an error.

Value

An object of class 'mplustree'. rpart_out provides the tree structure, terminal gives a vector of terminal nodes, where shows the terminal node of each id, and estimates gives the parameter estimates for each terminal node.

Author(s)

Ross Jacobucci and Sarfaraz Serang

References

Serang, S., Jacobucci, R., Stegmann, G., Brandmaier, A. M., Culianos, D., & Grimm, K. J. (2021). Mplus Trees: Structural equation model trees using Mplus. Structural Equation Modeling, 28, 127-137.

Examples

## Not run: 
library(lavaan)

script = mplusObject(
   TITLE = "Example #1 - Factor Model;",
   MODEL = "f1 BY x1-x3; f2 BY x4-x6; f3 BY x7-x9;",
   usevariables = c('x1','x2','x3','x4','x5','x6','x7','x8','x9'),
   rdata = HolzingerSwineford1939)

fit = MplusTrees(script, HolzingerSwineford1939, group=~id,
   rPartFormula=~sex+school+grade,
   control=rpart.control(minsplit=100, minbucket=100, cp=.01))

fit

## End(Not run)