Distal outcomes in mixture modeling: A guide for pairwise comparisons, multiplicity control, and effect size...

Despite the widespread use of mixture models in psychology, education, and the behavioral sciences, there is little consolidated guidance on how distal outcome differences should be tested, corrected for multiplicity, and reported once a latent class or profile solution has been selected. In practice, applied researchers often report omnibus tests without follow-up comparisons, conduct uncorrected pairwise tests, or omit effect sizes and confidence intervals altogether, limiting the interpretability and reproducibility of findings. Consistent with this concern, a targeted reporting-practice audit of recent applied person-centered studies showed that multiplicity adjustment, global distal outcome effect sizes, pairwise effect sizes, and confidence intervals for pairwise effects were rarely reported. The present paper synthesizes recommendations from the general statistical literature and adapts them to the context of mixture modeling, focusing primarily on continuous distal outcomes and comparisons of class-specific means. We propose a principled framework for (a) defining appropriate families of pairwise comparisons for distal outcomes, (b) selecting and implementing multiplicity corrections with Benjamini-Hochberg recommended as the default procedure for applied distal outcome comparisons, and (c) computing and reporting global and pairwise effect sizes and confidence intervals using quantities readily available from standard mixture modeling software (e.g., Mplus). Through worked examples and a software-agnostic Quarto/R supplement, we demonstrate how these practices can be implemented transparently and consistently across common auxiliary-variable approaches, including maximum likelihood (ML) three-step and Bolck-Croon-Hagenaars (BCH) methods.