Blockwise Resampling for Robust Fixed Effects Inference in Linear Mixed Models

Linear mixed models (LMM) are widely used for analyzing clustered data but face challenges with model misspecification, convergence issues, and variance heterogeneity. Alternatively, semi-parametric approaches like generalized estimating equation (GEE) are used to estimate the parameters of a generalized LM in the case of dependent observations. While GEE is robust to covariance misspecification, it is inefficient in handling unbalanced designs and underestimates the true standard errors unless a large sample size is utilized. To address these challenges, we propose a robust extension of the score-based statistical test using sign-flipping transformations. Our approach handles within-variance structure and heteroscedasticity nonparametrically by leveraging whole-block exchangeability. The proposed method provides robust and efficient inference for fixed effects, overcoming the limitations of traditional methodologies, e.g., the specification of the random structure.