Various levels of measurement equivalence, part 1

In the MGCFA approach, measurement equivalence can be tested by examining how similar the measurement models are across groups. Obviously, the more similar the models are, the greater the comparability. Several levels of measurement equivalence can be distinguished, each with its own implications for the comparability of scores. These levels are ordered hierarchically, in the sense that higher equivalence levels presuppose lower ones. Higher equivalence levels are harder to obtain as they present a stronger test of cross-cultural equivalence, but also allow a more extensive form of cross-cultural or cross-time comparison.

The lowest level of equivalence is called configural equivalence [Hor92 [Ste98]]. Configural equivalence means that the measurement model for the latent concept has the same factor structure across groups. In other words, configural equivalence implies that, if an item that loads strongly on the latent factor in one group, it also has a high factor loading in other groups. However, the strength of the factor loadings can differ across countries and time points, as no restrictions are placed on the magnitude of these parameters [Ste98]. Generally, this basic level of measurement equivalence is relatively easy to reach. The other side of the coin is that configural equivalence does not guarantee comparability across groups. Configural equivalence only means that the latent concepts can be meaningfully discussed in all groups. Since configural equivalence is a prerequisite for further equivalence testing, it is often used as a baseline [Van00].

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