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The present paper contrasts two related criteria for the evaluation of prior-data conflict: the Data Agreement Criterion (DAC, Bousquet, 2008) and the criterion of Nott et al. (2016). One aspect that these criteria have in common is that they depend on a distance measure, of which dozens are available, but so far, only the Kullback-Leibler has been used. We describe and compare both criteria to determine whether a different choice of distance measure might impact the results. By means of a simulation study, we investigate how the choice of a specific distance measure influences the detection of prior-data conflict. The DAC seems more susceptible to the choice of distance measure, while the criterion of Nott et al. seems to lead to reasonably comparable conclusions of prior-data conflict, regardless of the distance measure choice. We conclude with some practical suggestions for the user of the DAC and the criterion of Nott et al.

This chapter focuses on a practical analysis of the Bayesian approximate measurement invariance model using standard software. It introduces the concept of approximate measurement invariance and illustrates the use of its most basic variant. The chapter discusses the use of measurement invariance testing in latent variable measurement models. In such models, the response functions are estimated through presumed conditional independence assumptions, and investigation of measurement invariance proceeds through restrictions on the parameters of these estimated functions. The most common model for this test is the confirmatory factor model, but this framework also includes item response theory (IRT) models, latent class models, and generalized multitrait‐multimethod models. The chapter focuses on a multigroup confirmatory factor analysis (MGCFA). The methodological literature on cross‐cultural and cross‐country analysis has recommended testing for measurement equivalence to guarantee that differences across groups are due to substantive true differences and not methodological artifacts

The purpose of the current study was to apply and evaluate a procedure to elicit expert judgments about correlations, and to update this information with empirical data. The result is a face-to-face group elicitation procedure with as its central element a trial roulette question that elicits experts' judgments expressed as distributions. During the elicitation procedure, a concordance probability question was used to provide feedback to the experts on their judgments. We evaluated the elicitation procedure in terms of validity and reliability by means of an application with a small sample of experts. Validity means that the elicited distributions accurately represent the experts' judgments. Reliability concerns the consistency of the elicited judgments over time. Four behavioral scientists provided their judgments with respect to the correlation between cognitive potential and academic performance for two separate populations enrolled at a specific school in the Netherlands that provides special education to youth with severe behavioral problems: youth with autism spectrum disorder (ASD), and youth with diagnoses other than ASD. Measures of face-validity, feasibility, convergent validity, coherence, and intra-rater reliability showed promising results. Furthermore, the current study illustrates the use of the elicitation procedure and elicited distributions in a social science application. The elicited distributions were used as a prior for the correlation, and updated with data for both populations collected at the school of interest. The current study shows that the newly developed elicitation procedure combining the trial roulette method with the elicitation of correlations is a promising tool, and that the results of the procedure are useful as prior information in a Bayesian analysis.