stepmix 0.5.0

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

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. Latent Class Analysis 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;
   2. Binary LCA models;
   3. Categorical LCA models;
   4. Mixed LCA models (continuous and categorical data);
   5. Missing Values.
2. Stepwise Estimation with StepMix : a tutorial demonstrating how to define measurement and structural models. The tutorial discusses:
   1. LCA models with response variables;
   2. LCA models with covariates;
   3. 1-step, 2-step and 3-step estimation;
   4. Corrections and other options for 3-step estimation.
3. Model Selection : a short tutorial discussing:
   1. Selecting the number of latent classes (n_components);
   2. Comparing models with 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