Structure detection of semiparametric structural equation models with Bayesian adaptive group lasso

Area of Science:

• Statistics
• Biostatistics
• Machine Learning

Background:

• Structural equation models (SEMs) are crucial for analyzing latent variable relationships.
• Semiparametric SEMs offer flexibility but require advanced estimation techniques.
• Simultaneous model selection and estimation remain a challenge in complex statistical modeling.

Purpose of the Study:

• To develop a novel Bayesian adaptive group least absolute shrinkage and selection operator (LASSO) procedure.
• To enable simultaneous model selection and estimation for semiparametric SEMs.
• To automatically detect variable effects (linear, nonlinear, or none) in structural equations.

Main Methods:

• Utilized basis expansions to approximate unknown nonparametric functions.
• Introduced adaptive penalties to groups of basis expansions for variable selection.
• Employed a Bayesian framework for robust estimation and uncertainty quantification.

Main Results:

• The proposed Bayesian adaptive group LASSO procedure demonstrated satisfactory performance in simulations.
• The method successfully identified and estimated relationships among observed and latent variables.
• Successfully applied to reveal risk factors for diabetic kidney disease.

Conclusions:

• The developed method provides an effective tool for semiparametric SEMs.
• It facilitates automated detection of variable effects, enhancing model interpretability.
• Offers a promising approach for identifying complex risk factors in diseases like diabetic kidney disease.