Score-based tests for detecting heterogeneity in linear mixed models

@article{Wang2019ScorebasedTF,
  title={Score-based tests for detecting heterogeneity in linear mixed models},
  author={Ting Wang and Edgar C. Merkle and Joaquin A. Anguera and Brandon M. Turner},
  journal={Behavior Research Methods},
  year={2019},
  volume={53},
  pages={216-231}
}
Cross-level interactions among fixed effects in linear mixed models (also known as multilevel models) can be complicated by heterogeneity stemming from random effects and residuals. When heterogeneity is present, tests of fixed effects (including cross-level interaction terms) are subject to inflated type I or type II error. While the impact of variance change/heterogeneity has been noticed in the literature, few methods have been proposed to detect this heterogeneity in a simple, systematic… 
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