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. 2023 Mar 31;13:5310. doi: 10.1038/s41598-023-32150-1

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© The Author(s) 2023

Open Access This 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/.

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Visual representation of the model in Latent Heritable Confounder Mendelian Randomization (LHC-MR). G = Genetic instruments; CF = general cognitive functioning; (a) For moderate physical activity (ModPA); (b) For vigorous physical activity (VigPA); U = Latent heritable confounder; h² = direct heritability. Each figure includes the bidirectional causal effects between the two traits as well as the confounder effects on each of them. Coefficients are beta values. P-values are indicated in brackets. The models were adjusted for age, sex, genotyping chip, first ten genomic principal components, center, and season (month) of wearing an accelerometer.