Problem
Research questions and friction points this paper is trying to address.
multilevel modeling
intraclass correlation coefficient
negligible effect
equivalence testing
sampling uncertainty
Do I Even Need a Multilevel Model? Negligible Effect Significance Testing for Intraclass Correlation Coefficients
🤖 AI Summary
Conventional approaches to deciding whether to use multilevel models based on point estimates of the intraclass correlation coefficient (ICC) ignore sampling uncertainty and lack a foundation in statistical inference. This study proposes the "Negligible Effect Significance Test" (NEST), which introduces equivalence testing into ICC assessment for the first time. By constructing an ICC pivotal quantity from the F-statistic and incorporating design effect considerations, NEST defines a threshold for a “negligible” ICC that quantifies an acceptable level of variance inflation. The method provides a statistically rigorous decision rule for determining when multilevel modeling is warranted, accompanied by an R implementation to help researchers evaluate whether clustering structures merit explicit modeling—thereby avoiding misjudgments arising from neglecting sampling variability.
📝 Abstract
In applied research, the decision to utilize multilevel modeling (MLM) is commonly guided by comparing a point estimate of the unconditional intraclass correlation coefficient (ICC) against some recommended threshold (e.g., 0.05). This naive approach, however, fails to account for sampling uncertainty and provides no formal inferential justification for a decision. The current work introduces negligible effect significance testing (NEST; or equivalence testing) for the ICC, proposing a framework that performs this test using a pivotal quantity of the ICC based on the F statistic. Furthermore, we offer guidance to help researchers define "negligible" that utilizes the design effect to characterize a tolerable level of variance inflation. R code illustrating the proposed procedure is provided.
Innovation
Methods, ideas, or system contributions that make the work stand out.
negligible effect significance testing
intraclass correlation coefficient
multilevel modeling
equivalence testing
design effect
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