Table 1.

Description of the four different levels of measurement equivalence tested.

Type of measurement invariance	Purpose of the test	Specific constraints applied in testing	Comparison allowed
Configural invariance	Tests whether a construct has a similar basic factorial structure in different groups	No constraints are applied on any parameter.	Comparison of basic structure allowed but no comparisons can be made on specific parameters.
Metric invariance	Tests the presence of a common metric by hypothesizing that scale intervals are equal in different groups	Factor loadings are constrained to be equal across groups.	Needed to compare structural relations linking latent variables (i.e., regression coefficients) and the variances and covariances of latent variables.
Scalar invariance	Tests whether two persons with the same level of a construct (e.g. self-care maintenance) but belonging to different groups have the same expected score on items.	Poses equality constraints on factor loadings and intercepts across groups.	Needed for a meaningful comparison of means and intercepts of latent variables.
Strict invariance	Tests for equality and full comparability of items factor loadings, intercepts and error variances across groups.	Poses equality constraints on factor loadings, intercepts and residual variances across groups.	Needed if observed variables are to be compared (e.g., through analysis of variance) across groups and when scale scores of single individuals are to be used for classification (e.g. high vs. low in self-care).