Unnecessary reliance on multilevel modelling to analyse nested data in neuroscience: When a traditional summary-statistics approach suffices

Abstract

Nested data structures create statistical dependence that influences the effective sample size and statistical power of a study. Several methods are available for dealing with nested data, including the summary-statistics approach and multilevel modelling (MLM). Recent publications have heralded MLM as the best method for analysing nested data, claiming benefits in power over summary-statistics approaches (e.g., the t-test). However, when cluster size is equal, these approaches are mathematically equivalent. We conducted statistical simulations demonstrating equivalence of MLM and summary-statistics approaches for analysing nested data and provide supportive cases for the utility of the conventional summary-statistics approach in nested experiments. Using statistical simulations, we demonstrate that losses in power in the summary-statistics approach discussed in the previous literature are unsubstantiated. We also show that MLM sometimes suffers from frequent singular fit errors, especially when intraclass correlation is low. There are indeed many situations in which MLM is more appropriate and desirable, but researchers should be aware of the possibility that simpler analysis (i.e., summary-statistics approach) does an equally good or even better job in some situations.

Keywords

• Hierarchical linear model
• Mixed model
• t-test
• Clustering