Linear mixed-effect panel data models are widely used in longitudinal biomedical, environmental, and social studies, but are often sensitive to data contamination and numerous covariates. To address these challenges, we propose a robust variable selection approach based on a least squares approximation (LSA) of the density power divergence (DPD) objective function combined with the Adaptive LASSO penalty. The LSA converts the nonlinear DPD objective into a computationally efficient quadratic approximation while preserving the robustness of DPD estimation. Under suitable regularity conditions, the proposed DPD Adaptive LASSO-LSA estimator is shown to possess oracle properties, including selection consistency and asymptotic normality. Simulation studies demonstrate improved robustness, better sparsity recovery, and significantly enhanced computational efficiency than penalized likelihood methods, while maintaining performance comparable to existing DPD-based approaches. An application to the SWAN bone mineral density dataset illustrates the practical relevance of the proposed methodology for robust estimation and reliable identification of important covariates.

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