[论文解读] StepMix: A Python Package for Pseudo-Likelihood Estimation of Generalized Mixture Models with External Variables

Sacha Morin, Robin Legault+5 more|arXiv (Cornell University)|Apr 7, 2023

Bayesian Methods and Mixture Models被引用 8

一句话总结

tldr: StepMix 是一个开源 Python 包，实现带协变量和远端结果的广义有限混合模型的偏差调整的一步、两步和三步伮信似似似 likelihood 估计器，具有 scikit-learn 风格 API 及一个 R 封装。

ABSTRACT

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.

研究动机与目标

• Provide an open-source Python package for estimating generalized finite mixture models with external variables (covariates and distal outcomes).
• Offer one-step and bias-adjusted stepwise estimators (two-step and three-step) within a unified EM-based framework.
• Promote interpretability of latent classes by enabling stepwise estimation that decouples the measurement and structural models.
• Bridge usability between Python and R by offering a wrapper and a scikit-learn–style interface to facilitate adoption in the data science community.

提出的方法

• Unify likelihood and pseudo-likelihood formulations for the measurement model (MM) and structural model (SM) within a complete model (CM).
• Implement EM algorithm-based subroutines to perform one-step, two-step, and bias-adjusted three-step estimation as pseudo-likelihoods.
• Support missing data via full information maximum likelihood (FIML) within the EM framework.
• Provide class responsibilities tau(i,k) = P(X=i|observations; current parameters) in the E-step and update CM parameters in the M-step.
• Offer an object-oriented API aligned with scikit-learn, plus an R wrapper for broader accessibility.
• Include handling of covariates Z^p, indicators Y, and distal outcomes Z^o with conditional independence given latent class X.]
• research_questions:[

实验结果

研究问题

• RQ1 How can bias-adjusted stepwise estimators be implemented within a unified EM framework for generalized mixture models with external variables?
• RQ2 What are the practical and theoretical benefits of one-step versus stepwise estimators (two-step and three-step) in terms of interpretability and estimation stability?
• RQ3 Can open-source Python software robustly implement bias-adjusted three-step estimators and support covariates and non-Gaussian components?
• RQ4 How does StepMix compare to existing R and Python packages in terms of features, accessibility, and API design?

主要发现

• StepMix provides open-source implementation of bias-adjusted three-step estimators for generalized mixture models with covariates and both Gaussian and non-Gaussian components.
• The package implements one-, two-, and three-step estimation within a unified EM-based pseudo-likelihood framework, including FIML for missing data.
• StepMix follows the scikit-learn API, enabling straightforward integration with Python’s ML tools and also offers an R wrapper.
• It is the first open-source package to natively implement bias-adjusted three-step methods and to enable pseudo-likelihood estimation of mixture models in Python.
• The tool aids interpretability by decoupling the measurement and structural models, facilitating exploratory analyses without conflating latent class definitions with distal outcomes.