# StepMix: A Python Package for Pseudo-Likelihood Estimation of Generalized Mixture Models with External Variables

arXiv: https://arxiv.org/abs/2304.03853 · HTML: https://mlsanity.com/paper/2304.03853/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 68 references that are in the map.
- First posted on arXiv 7 Apr 2023.

## Builds on (most cited first, 2 of 2)

- [Gaussian Parsimonious Clustering Models with Covariates and a Noise Component](https://mlsanity.com/paper/1711.05632/) (2017)
- [AutoGMM: Automatic Gaussian Mixture Modeling in Python](https://mlsanity.com/paper/1909.02688/) (2019)

## Built on by (most cited first, 5 of 5)

- [Tutorial: a priori estimation of sample size, effect size, and statistical power for cluster analysis, latent class analysis, and multivariate mixture models](https://mlsanity.com/paper/2309.00866/) (2023)
- [Quantifying the Cross-sectoral Intersecting Discrepancies within Multiple Groups Using Latent Class Analysis Towards Fairness](https://mlsanity.com/paper/2407.03133/) (2024)
- [AI-based response assessment and prediction in longitudinal imaging for brain metastases treated with stereotactic radiosurgery](https://mlsanity.com/paper/2509.06396/) (2025)
- [LLM-Augmented Computational Phenotyping of Long Covid](https://mlsanity.com/paper/2603.18115/) (2026)
- [How Do People Challenge Racial Stereotypes Online? Counter-Story Detection Across Reddit Communities](https://mlsanity.com/paper/2610.04803/) (2026)

## Abstract (arXiv)

StepMix is an open-source Python package for the pseudo-likelihood estimation (one-, two- and three-step approaches) of generalized finite mixture models (latent profile and latent class analysis) with external variables (covariates and distal outcomes). In many applications in social sciences, the main objective is not only to cluster individuals into latent classes, but also to use these classes to develop more complex statistical models. These models generally divide into a measurement model that relates the latent classes to observed indicators, and a structural model that relates covariates and outcome variables to the latent classes. The measurement and structural models can be estimated jointly using the so-called one-step approach or sequentially using stepwise methods, which present significant advantages for practitioners regarding the interpretability of the estimated latent classes. In addition to the one-step approach, StepMix implements the most important stepwise estimation methods from the literature, including the bias-adjusted three-step methods with Bolk-Croon-Hagenaars and maximum likelihood corrections and the more recent two-step approach. These pseudo-likelihood estimators are presented in this paper under a unified framework as specific expectation-maximization subroutines. To facilitate and promote their adoption among the data science community, StepMix follows the object-oriented design of the scikit-learn library and provides an additional R wrapper.