If a researcher applies the conventional tests of scale-level measurement invariance through multi-group confirmatory factor analysis of a PC matrix and MLE to test hypotheses of strong and full measurement invariance when the researcher has a rating scale response format wherein the item characteristics are different for the two groups of respondents, do these scale-level analyses reflect (or ignore) differences in item threshold characteristics? Results of the current study demonstrate the inadequacy of judging the suitability of a measurement instrument across groups by only investigating the factor structure of the measure for the different groups with a PC matrix and MLE. Evidence is provided that item level bias can still be present when a CFA of the two different groups reveals an equivalent factorial structure of rating scale items using a PC matrix and MLE.
Zumbo, Bruno D. and Koh, Kim H.
"Manifestation Of Differences In Item-Level Characteristics In Scale-Level Measurement Invariance Tests Of Multi-Group Confirmatory Factor Analyses,"
Journal of Modern Applied Statistical Methods:
1, Article 24.
Available at: http://digitalcommons.wayne.edu/jmasm/vol4/iss1/24