Robust Inference for Generalized Linear Mixed Models: A “Two-Stage Summary Statistics” Approach Based on Score Sign Flipping

Psychometrika, vol. 90, pp. 531–553

Abstract

Abstract 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. In addition, the researcher’s choice of random and fixed effects directly affects statistical inference correctness. To address these challenges, we propose a robust extension of the “two-stage summary statistics” approach using sign-flipping transformations of the score statistic in the second stage. Our approach efficiently handles within-variance structure and heteroscedasticity, ensuring accurate regression coefficient testing for 2-level hierarchical data structures. 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.

Authors 4

1. Angela Andreella corresponding

   University of Trento

   Affiliation as printed

   University of Trento, Italy

2. Jelle J. Goeman Aachen

   Leiden University Medical Center

   Affiliation as printed

   Leiden University Medical Center, The Netherlands

3. Jesse Hemerik

   Erasmus University Rotterdam

   Affiliation as printed

   Erasmus University Rotterdam, The Netherlands

4. Livio Finos

   University of Padua

   Affiliation as printed

   University of Padova, Italy