Original Article
Graphical Tools for Detecting Departures from Linear Mixed Model Assumptions and Some Remedial Measures
Julio M. Singer,
Francisco M.M. Rocha,
Juvêncio S. Nobre,
Corresponding Author
Julio M. Singer
Departamento de Estatística, Universidade de São Paulo, São Paulo, Brazil
Search for more papers by this authorFrancisco M.M. Rocha
Escola Paulista de Política, Economia e Negócios, Universidade Federal de São Paulo, São Paulo, Brazil
Search for more papers by this authorJuvêncio S. Nobre
Departamento de Estatística e Matemática Aplicada, Universidade Federal do Ceará, Fortaleza, Brazil
Search for more papers by this authorJulio M. Singer,
Francisco M.M. Rocha,
Juvêncio S. Nobre,
Corresponding Author
Julio M. Singer
Departamento de Estatística, Universidade de São Paulo, São Paulo, Brazil
Search for more papers by this authorFrancisco M.M. Rocha
Escola Paulista de Política, Economia e Negócios, Universidade Federal de São Paulo, São Paulo, Brazil
Search for more papers by this authorJuvêncio S. Nobre
Departamento de Estatística e Matemática Aplicada, Universidade Federal do Ceará, Fortaleza, Brazil
Search for more papers by this authorSummary
We review some results on the analysis of longitudinal data or, more generally, of repeated measures via linear mixed models starting with some exploratory statistical tools that may be employed to specify a tentative model. We follow with a summary of inferential procedures under a Gaussian set-up and then discuss different diagnostic methods focusing on residual analysis but also addressing global and local influence. Based on the interpretation of diagnostic plots related to three types of residuals (marginal, conditional and predicted random effects) as well as on other tools, we proceed to identify remedial measures for possible violations of the proposed model assumptions, ranging from fine-tuning of the model to the use of elliptically symmetric or skew-elliptical linear mixed models as well as of robust estimation methods. We specify many results available in the literature in a unified notation and highlight those with greater practical appeal. In each case, we discuss the availability of model diagnostics as well as of software and give general guidelines for model selection. We conclude with analyses of three practical examples and suggest further directions for research.
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