This article was originally submitted for publication to the Editor of Advances in Methods and Practices in Psychological Science (AMPPS) in 2015. When the submitted manuscript was subsequently posted online (Silberzahn et al., 2015), it received some media attention, and two of the authors were invited to write a brief commentary in Nature advocating for greater crowdsourcing of data analysis by scientists. This commentary, arguing that crowdsourced research "can balance discussions, validate findings and better inform policy" (Silberzahn & Uhlmann, 2015, p. 189), included a new figure that displayed the analytic teams' effectsize estimates and cited the submitted manuscript as the source of the findings, with a link to the preprint. However, the authors forgot to add a citation of the Nature commentary to the final published version of the AMPPS article or to note that the main findings had been previously publicized via the commentary, the online preprint, research presentations at conferences and universities, and media reports by other people. The authors regret the oversight.

Testing for invariance of measurements across groups (such as countries or time points) is essential before meaningful comparisons may be conducted. However, when tested, invariance is often absent. As a result, comparisons across groups are potentially problematic and may be biased. In the current study, we propose utilizing a multilevel structural equation modeling (SEM) approach to provide a framework to explain item bias. We show how variation in a contextual variable may explain noninvariance. For the illustration of the method, we use data from the second round of the European Social Survey (ESS).

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