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

Carolyn Beth Mcnabb,Kou Murayama

doi:10.1016/j.crneur.2021.100024

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.

Highlights

Nested data structures create statistical dependence that influences the effective sample size and statistical power of a study
We demonstrate that losses in power in the summary-statistics approach discussed in the previous literature are unsubstantiated
We show that multilevel modelling (MLM) sometimes suffers from frequent singular fit errors, especially when intraclass correlation is low

Summary

Debunking the myth of power loss with the summarystatistics approach

Aarts and colleagues suggested that, for hierarchical data where clusters are nested within conditions (such as Dataset A/Scenario 1),. Comparing t tests conducted on cluster-based means with MLM, they claimed a 40% loss of statistical power with the summary-statistics approach, depending on cluster size and intra-class correlation (Aarts et al, 2014). We conducted a simulation to estimate statistical power and Type I error rate using the log-likelihood ratio test, REML (t-test) and summary-statistics approach (simulations conducted in R version 4.0.2 (2020-06-22; R scripts and simulated data are avail able on our OSF page - https://osf.io/w6unc/). REML (t-test; Fig. S2) and the summary-statistics approach (Fig. 2), which showed identical results in the absence of singular fit or convergence errors, appropriately control for Type I error rate across all simulation conditions, even when sample size is small

Cost of multilevel modelling

Some complicated cases

Complex study designs for which multilevel models are optimal

Findings

Conclusion