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. 2019 Jul 2;17:114. doi: 10.1186/s12955-019-1166-1

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© The Author(s). 2019

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. 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.

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Fig. 1 — Example of MIMIC model permitting DIF for the ith item. The dashed arrow from each covariate to the ith item represents the direct effect; γ_k = regression coefficient for the effect of the kth covariate on the latent variable; λ_i = the regression coefficient for the latent variable and the ith item; β_ik = regression coefficient showing the effect of the kth covariate on the ith item; ε_i = measurement error for the ith item; η = residual for the latent variable