@article{TQMP22-1-1,
    author =    {Nylund-Gibson, Karen AND Arch, Dina Ali Naji AND Carter, Delwin },
    journal =   {The Quantitative Methods for Psychology},
    publisher = {TQMP},
    title =     {Latent transition analysis with Auxiliary Variables: A demonstration of the ML 3-Step and BCH in Mplus},
    year =      {2026},
    volume =    {22},
    number =    {1},
    url =       {http://www.tqmp.org/RegularArticles/vol22-1/p001/p001.pdf },
    pages =     {1-8},
    abstract =  {Latent transition analysis (LTA) is increasingly used to understand how individuals move among latent classes measured at multiple time points. LTA models often include auxiliary variables (e.g., covariates or distal outcomes) to explain class membership, predict transition probabilities, or examine later outcomes. Although measurement invariance is commonly assumed in LTA, it is not required for model estimation but is helpful for interpreting transitions as stability or change in the same construct. When auxiliary variables are included, testing and properly specifying measurement invariance becomes more complex if invariance is assumed. Implementing measurement invariance with recommended multi-step procedures, the ML three-step (ML 3-step) and the Bolck–Croon–Hagenaars (BCH) method, requires a sequence of model tests and modeling decisions. This tutorial provides a fully worked demonstration of how to evaluate measurement invariance in LTA and how to incorporate auxiliary variables using the ML 3-step and BCH approaches within Mplus. We introduce a practical workflow, address frequent modeling challenges, and provide annotated syntax using R and MplusAutomation for reproducibility. The goal of this tutorial is to offer applied researchers a transparent and accessible framework for drawing valid conclusions about subgroup stability and change.},
    doi =       {10.20982/tqmp.22.1.p001}
}