Order selection and sparsity in latent variable models via the ordered factor LASSO.

Area of Science:

• Statistics
• Ecology
• Bioinformatics

Background:

• Generalized linear latent variable models (GLLVMs) are powerful for analyzing multiple response data.
• Key challenges in GLLVMs include determining the number of latent factors and achieving sparsity in the loading matrix.
• Existing methods lack specific penalties for simultaneous order selection and sparsity in latent variable models.

Purpose of the Study:

• To introduce the Ordered Factor LASSO (OFAL) penalty for simultaneous order selection and sparsity in GLLVMs.
• To address the limitations of current methods in latent variable model fitting.
• To apply the OFAL penalty to analyze marine species assemblages in the Southern Ocean.

Main Methods:

• The OFAL penalty utilizes a hierarchically structured group LASSO penalty to zero out entire columns of the loading matrix.
• It ensures non-zero loadings are concentrated on lower-order factors.
• Adaptive LASSO is employed for individual element sparsity, complemented by an information criterion for aggressive shrinkage.

Main Results:

• Simulations demonstrate that OFAL outperforms standard methods in order selection, sparsity, and prediction for GLLVMs.
• Application to Southern Ocean marine species data revealed that environmental predictors explain approximately half of the species covariation.
• This resulted in a reduced number of latent variables and increased sparsity in the loading matrix compared to models without covariates.

Conclusions:

• The OFAL penalty provides an effective solution for order selection and sparsity in GLLVMs.
• It offers improved model interpretability and predictive performance.
• The method successfully identified key environmental drivers in the Southern Ocean marine ecosystem analysis.