stepmix 1.0.0

A Python package for stepwise estimation of latent class models with measurement and structural components. The package can also be used to fit mixture models with various observed random variables.

StepMix

For StepMixR, please refer to this repository.

A Python package following the scikit-learn API for model-based clustering and generalized mixture modeling (latent class/profile analysis) of continuous and categorical data. StepMix handles missing values through Full Information Maximum Likelihood (FIML) and provides multiple stepwise Expectation-Maximization (EM) estimation methods based on pseudolikelihood theory. Additional features include support for covariates and distal outcomes, various simulation utilities, and non-parametric bootstrapping, which allows inference in semi-supervised and unsupervised settings.

Install

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

pip install stepmix

Tutorials

Detailed tutorials are available in notebooks :

1. Generalized Mixture Models with StepMix : an in-depth look at how latent class models can be defined with StepMix. The tutorial uses the Iris Dataset as an example and covers :
   1. Continuous LCA models (latent profile analysis/gaussian mixture model);
   2. Binary LCA models;
   3. Categorical LCA models;
   4. Mixed variables mixture models (continuous and categorical data);
   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.
3. Model Selection : a short tutorial discussing:
   1. Selecting the number of components in a mixture model (n_components);
   2. Comparing models with fit indices: AIC and BIC.
4. Parameters, Bootstrapping and CI : a tutorial discussing how to:
   1. Access StepMix parameters;
   2. Bootstrap StepMix estimators;
   3. Quickly plot confidence intervals.

Quickstart

A simple example for 3-step estimation on simulated data :

from stepmix.datasets import data_bakk_response
from stepmix.stepmix import StepMix

# Soft 3-step 
X, Y, _ = data_bakk_response(n_samples=1000, sep_level=.9, random_state=42)
model = StepMix(n_components=3, n_steps=3, measurement='bernoulli', structural='gaussian_unit', assignment='soft',
            random_state=42)
model.fit(X, Y)
print(model.score(X, Y))  # Average log-likelihood

# Equivalently, each step can be performed individually. See the code of the fit method for details.
model = StepMix(n_components=3, measurement='bernoulli', structural='gaussian_unit', random_state=42)
model.em(X)  # Step 1
probs = model.predict_proba(X)  # Step 2
model.m_step_structural(probs, Y)  # Step 3
print(model.score(X, Y))

1-step and 2-step estimation are simply a matter of changing of the n_steps argument. Additionally, some bias correction methods are available for 3-step estimation.

References

• Bolck, A., Croon, M., and Hagenaars, J. Estimating latent structure models with categorical variables: One-step versus three-step estimators. Political analysis, 12(1): 3–27, 2004.

• Vermunt, J. K. Latent class modeling with covariates: Two improved three-step approaches. Political analysis, 18 (4):450–469, 2010.

• Bakk, Z., Tekle, F. B., and Vermunt, J. K. Estimating the association between latent class membership and external variables using bias-adjusted three-step approaches. Sociological Methodology, 43(1):272–311, 2013.

• Bakk, Z. and Kuha, J. Two-step estimation of models between latent classes and external variables. Psychometrika, 83(4):871–892, 2018