and other items are relatively more difficult for females). In addition, to identify the variance of the scale the product of the discrimination parameters was fixed at 1. Allowing for such random fluctuations in difficulty and discrimination across cohorts is also referred to as the assumption of approximate measurement invariance. This Bayesian method was only applied to NEO-FFI and EPQ-R test items, as for those tests, the numbers of cohorts were sufficiently large. We randomly selected 1,000 individuals from each cohort (or all individuals if sample size was smaller) and determined which items showed considerable DIF across cohorts by computing Bayes factors (Verhagen and Fox 2013a, b). When testing invariance hypotheses, an advantage of the Bayes factor is that you can gather evidence in favor of the (null) hypothesis of invariance. A Bayes factor smaller than 0.3 was regarded as clear evidence of DIF. A Bayes factor larger than 3 was regarded as evidence of measurement invariance (i.e., no DIF). Taking into account possible DIF, all individuals with either NEO or EPQ data were mapped to a common scale for Neuroticism and Extraversion and mean Neuroticism and Extraversion scores and variances were estimated for each cohort.
