SwE

Sandwich Estimator Toolbox for Longitudinal & Repeated Measures Data

A toolbox for SPM

By Bryan Guillaume & Thomas Nichols

Introduction

Why use SwE?

This approach has a number of advantages over traditional linear mixed effect models:

• Easy random effects
  

  Only the population model is specified, meaning that no random effects (e.g. random slopes) need to be specified.

  • Despite having no explicit specification, all possible random effects are accounted for through the use of an unstructured error covariance.
  • For moderate sample sizes, the "Hom"ogeneous sandwich estimator assumes each subject in a group shares the same visit-based covariance structure.
  • For large sample sizes, the "Het"ergoeneous (traditional) sandwich estimator doesn't even assume common covariance over subjects.
  • When comparing multiple groups, each group automatically has its own covariance structure.
  • Different from usual approaches in SPM and FSL, it doesn't require per-subject dummy variables, and so allows between-subject covariates like age and sex.
  • There is no need to have a balanced design, and in fact, singleton subjects can be modeled along with subjects with multiple measures.

• No convergence problems
  

  The population model is estimated with Ordinary Least Squares, meaning that the method is non-iterative and thus is immune to convergence failures not uncommon in complex mixed effects models.

• Built for neuroimaging
  • Toolbox for widely used SPM software
  • While the traditional sandwich estimator techniques often assume large samples, SwE implements carefully evaluated (and in some cases novel) degrees of freedom estimator and small sample adjustments.
  • Familywise error-corrected voxel and cluster inferences are available with the Wild Bootstrap, avoiding any parametric (e.g. random field theory) distributional assumptions.