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**Publication** The article was published in the *...* under the DOI . **Corresponding author** Florian Scharf (florian.scharf@uni-leipzig.de). **The following material is available:** 1. Original Figures 2. Scripts for simulations, analyses and figure generation 3. Sample results necessary to produce the results (i.e., loadings, effect sizes and factor correlation estimates as well as SRMR) 4. The scripts that are necessary to reproduce the data used for our illustrative example. 5. An open-source ESEM implementation as described in the Appendix of the manuscript including step-by-step comments. 6. A supplementary simulation (I) in which Geomin-rotated PCA was used to estimate the parameters. 7. A supplementary simulation (II) in which we verified the correctness of our bootstrap procedure. 8. A supplementary simulation (III) in which we investigated how the number of sampling points and the noise variance influence the factor scoring bias. All supplementary simulation directories contain summary files (PDFs or HTMLs, respectively) and archives that contain all the scripts and data to reproduce the results. If you have any questions, please do not hesitate to contact Florian Scharf.