  Despite the versatility of generalized linear mixed models in handling
complex experimental designs, they often suffer from misspecification and
convergence problems. This makes inference on the values of coefficients
problematic. To address these challenges, we propose a robust extension of the
score-based statistical test using sign-flipping transformations. Our approach
efficiently handles within-variance structure and heteroscedasticity, ensuring
accurate regression coefficient testing. The approach is illustrated by
analyzing the reduction of health issues over time for newly adopted children.
The model is characterized by a binomial response with unbalanced frequencies
and several categorical and continuous predictors. The proposed approach
efficiently deals with critical problems related to longitudinal nonlinear
models, surpassing common statistical approaches such as generalized estimating
equations and generalized linear mixed models.
