Chapter 3: Multigroup Factor Analysis

Assessing levels of non-invariance of measurement

Goodness of fit of models with different levels of non-invariance of measurement can be examined and compared, to assess whether it would be necessary to allow for some non-invariance to achieve a good fit to the data. In such comparisons, the model with full measurement invariance is the most restricted model, and models with different levels of non-invariance are less restricted and thus better-fitting models.

Standard likelihood ratio tests can be used for such comparisons, for example to compare the full invariance model to partial non-invariance models, or to compare nested pairs of non-invariance models (e.g. scalar invariance vs. full non-invariance for a given item, or non-invariance for one vs. two items) to each other. These tests are often quite sensitive in practice, so it is common for them to reject the full invariance model. Because of this sensitivity, the tests may be supplemented by other methods of model assessment such as the AIC and BIC statistics. Examples of the use of these statistics and likelihood ratio tests for such comparisons of different measurement models are given in Example 2 of this chapter.

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