StepMix

For StepMixR, please refer to this repository.

A Python package following the scikit-learn API for generalized mixture modeling. The package supports categorical data (Latent Class Analysis) and continuous data (Gaussian Mixtures/Latent Profile Analysis). StepMix can be used for both clustering and supervised learning.

Additional features include:

• Support for missing values through Full Information Maximum Likelihood (FIML);
• Multiple stepwise Expectation-Maximization (EM) estimation methods based on pseudolikelihood theory;
• Covariates and distal outcomes;
• Parametric and non-parametric bootstrapping.

Reference

If you find StepMix useful, please leave a ⭐ and consider citing our Journal of Statistical Software paper:

@Article{,
  title = {{StepMix}: A {Python} Package for Pseudo-Likelihood
    Estimation of Generalized Mixture Models with External
    Variables},
  author = {Sacha Morin and Robin Legault and F{\'e}lix Lalibert{\'e}
    and Zsuzsa Bakk and Charles-{\'E}douard Gigu{\`e}re and Roxane
    {de la Sablonni{\`e}re} and {\'E}ric Lacourse},
  journal = {Journal of Statistical Software},
  year = {2025},
  volume = {113},
  number = {8},
  pages = {1--39},
  doi = {10.18637/jss.v113.i08},
}

Install

You can install StepMix with pip, preferably in a virtual environment:

pip install stepmix

Quickstart

A StepMix mixture using categorical variables on a preloaded data matrix. StepMix accepts either numpy.arrayor pandas.DataFrame. Categories should be integer-encoded and 0-indexed.

from stepmix.stepmix import StepMix

# Categorical StepMix Model with 3 latent classes
model = StepMix(n_components=3, measurement="categorical")
model.fit(data)

# Allow missing values
model_nan = StepMix(n_components=3, measurement="categorical_nan")
model_nan.fit(data_nan)

For binary data you can also use measurement="binary" or measurement="binary_nan". For continuous data, you can fit a Gaussian Mixture with diagonal covariances using measurement="continuous" or measurement="continuous_nan".

Set verbose=1 for a detailed output.

Please refer to the StepMix tutorials to learn how to combine continuous and categorical data in the same model.

Tutorials

Detailed tutorials are available in notebooks:

1. Generalized Mixture Models with StepMix: an in-depth look at how mixture models can be defined with StepMix. The tutorial uses the Iris Dataset as an example and covers:
   1. Gaussian Mixtures (Latent Profile Analysis);
   2. Binary Mixtures (LCA);
   3. Categorical Mixtures (LCA);
   4. Mixed Categorical and Continuous Mixtures;
   5. Missing Values through Full-Information Maximum Likelihood.
2. Stepwise Estimation with StepMix: a tutorial demonstrating how to define measurement and structural models. The tutorial discusses:
   1. LCA models with distal outcomes;
   2. LCA models with covariates;
   3. 1-step, 2-step and 3-step estimation;
   4. Corrections (BCH or ML) and other options for 3-step estimation;
   5. Putting it All Together: A Complete Model with Missing Values
3. Model Selection:
   1. Selecting the number of components in a mixture model (n_components) with cross-validation;
   2. Selecting the number of components with the Parametric Bootstrapped Likelihood Ratio Test (BLRT);
   3. Fit indices: AIC, BIC and other metrics.
4. Parameters, Bootstrapping and CI: a tutorial discussing how to:
   1. Access StepMix parameters;
   2. Bootstrap StepMix estimators;
   3. Quickly plot confidence intervals.
5. Supervised and Semi-Supervised Learning with StepMix:
   1. Binary Classification;
   2. Multiclass Classification;
   3. Semi-Supervised Learning;
   4. Cross-Validation.
6. Deriving p-values in StepMix: a tutorial demonstrating how to transform SM parameters into conventional regression coefficients and how to derive p-values. The tutorial covers models with:
   1. Continuous covariate;
   2. Binary covariate;
   3. Categorical covariate;
   4. Multiple covariates (different distributions);
   5. Binary distal outcome;