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. 2021 Jul 7;21:139. doi: 10.1186/s12874-021-01333-7

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© The Author(s) 2021

Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated in a credit line to the data.

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Fig. 2 — Difference from “true” value of 1 of regression coefficients estimated from RI and OLS models ( $β_{1}^{RI}$ and $β_{1}^{OLS}$ ) plotted against dispersion (expressed as SD) of the mean value/prevalence of $x_{ij}$ across the clusters within each sample. Results for different levels of intraclass correlation coefficient are distinguished by shades of grey as indicated in the legend. A Continuous $x_{ij}$ . B Binary $x_{ij}$