Parametric and Semi-Parametric Bootstrap-Based Confidence Intervals for Robust Linear Mixed Models

Authors

  • Fabio Mason
    Faculty of Psychology and Educational Sciences, University of Geneva, Geneva, Switzerland
  • Eva Cantoni
    Research Center for Statistics and Geneva School of Economics and Management, University of Geneva, Geneva, Switzerland
  • Paolo Ghisletta
    Faculty of Psychology and Educational Sciences, University of Geneva, Geneva, Switzerland; Swiss National Centre of Competence in Research LIVES, University of Geneva, Geneva, Switzerland; Faculty of Psychology, UniDistance Suisse, Brig, Switzerland

Abstract

The linear mixed model (LMM) is a popular statistical model for the analysis of longitudinal data. However, the robust estimation of and inferential conclusions for the LMM in the presence of outliers (i.e., observations with very low probability of occurrence under Normality) is not part of mainstream longitudinal data analysis. In this work, we compared the coverage rates of confidence intervals (CIs) based on two bootstrap methods, applied to three robust estimation methods. We carried out a simulation experiment to compare CIs under three different conditions: data 1) without contamination, 2) contaminated by within-, or 3) between-participant outliers. Results showed that the semi-parametric bootstrap associated to the composite tau-estimator leads to valid inferential decisions with both uncontaminated and contaminated data. This being the most comprehensive study of CIs applied to robust estimators of the LMM, we provide fully commented R code for all methods applied to a popular example.