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. Author manuscript; available in PMC: 2013 Oct 30.
Published in final edited form as: J Clin Epidemiol. 2008 Oct 1;62(3):10.1016/j.jclinepi.2008.06.012. doi: 10.1016/j.jclinepi.2008.06.012

Table 1.

Taxonomy of measurement invariance

Measurement invariance Interpretations Statistical tests in multiple-group confirmatory factor analysis
Configural invariance There is an equivalent HRQOL construct between two groups Whether item clusters are identical between two groups?
Metric invariance Given configure invariance, there are equivalent associations between items and underlying HRQOL between two groups (or the same unit of measurement) Given configure invariance, whether factor loadings of specific items are identical between two groups?
Scalar invariance Given metric invariance, there are equivalent starting values of item ratings between two groups Given metric invariance, whether intercepts of specific items are identical between two groups?
Residual invariance Given scalar invariance, there are equivalent nonsystematic measurement errors in the item responses between two groups Given scalar invariance, whether residuals of specific items are identical between two groups?