The present study examined the factor structure and measurement invariance of the revised version of the Athletic Coping Skills Inventory (ACSI-28), following adjustment of the wording of items such that they were appropriate to assess Coping Skills in an educational setting. A sample of middle school students (n = 1,037) completed the revised inventory. An initial confirmatory factor analysis led to the hypothesis of a better fitting model with two items removed. Reliability of the subscales and the instrument as a whole was acceptable. Items were examined for sex invariance with differential item functioning (DIF) using item response theory, and five items were flagged for significant sex non-invariance. Following removal of these items, comparison of the mean differences between male and female coping scores revealed that there was no significant difference between the two groups. Further examination of the generalizability of the coping construct and the potential transfer of psychosocial skills between athletic and academic settings are warranted.

The common practice for testing measurement invariance is to constrain parameters to be equal over groups, and then evaluate the model-data fit to reject or fail to reject the restrictive model. Posterior predictive checking (PPC) provides an alternative approach to evaluating model-data discrepancy. This paper explores the utility of PPC in estimating measurement invariance. The simulation results show that the posterior predictive p (PP p) values of item parameter estimates respond to various invariance violations, whereas the PP p values of item-fit index may fail to detect such violations. The current paper suggests comparing group estimates and restrictive model estimates with posterior predictive distributions in order to demonstrate the pattern of misfit graphically.