Variable Selection in Mixed-Effects Location-Scale and Location-Shift Models.

Area of Science:

• Statistics
• Econometrics
• Social Sciences

Background:

• Ordinal regression models are crucial for Likert scale data.
• Heterogeneity in response variability across subgroups poses analytical challenges.
• Clustered data introduces within-cluster variance requiring specific modeling.

Purpose of the Study:

• To present location-scale and location-shift regression models for ordinal data with differing subgroup variability.
• To incorporate cluster-level random effects for clustered ordinal data.
• To develop a variable selection procedure using adaptive fused LASSO-type regularization to simplify complex models.

Main Methods:

• Application of cumulative models for ordinal responses, assessing location, scale, dispersion, and random effects.
• Implementation of adaptive fused LASSO-type regularization for variable selection.
• Utilizing data from the Survey of Health, Ageing and Retirement in Europe (SHARE) for a case study.
• Conducting a simulation study to evaluate the regularization approach's performance.

Main Results:

• The proposed models effectively handle ordinal responses with varying subgroup variability and clustering.
• Adaptive fused LASSO regularization yields stable and interpretable parameter estimates across all model components.
• The case study demonstrates the practical applicability of the developed methods.

Conclusions:

• The presented regression framework provides a robust approach for analyzing complex ordinal survey data.
• Regularization significantly enhances model interpretability and stability, facilitating better insights from large datasets.
• The methods are valuable for researchers dealing with heterogeneous and clustered ordinal outcomes.