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Abstract
In the past, confirmatory factor analysis (CFA) techniques have routinely been used to test for measurement equivalence in longitudinal data. However, item response theory (IRT) techniques also can be used for this task. This study illustrates that a particular type IRT technique (likelihood ratio tests) are conceptually and pragmatically more appropriate for testing for measurement equivalence in longitudinal data than are the CFA analyses. Data were simulated using both CFA and IRT paradigms manipulating the number of items simulated, the number of items with simulated differences, and differences in sample size. The CFA simulated data also contained simulated differences in factor loadings, factor variance, and item intercepts. The IRT simulated data also contained simulated differences in item parameters and varying degrees of canceling differences. CFA and two IRT analyses, likelihood ratio (LR) tests and differential functioning of items and tests (DFIT), were used to analyze the data. Results show that the CFA analyses currently in use do not perform as well as the LR IRT tests for detecting differences in longitudinal data. Furthermore, the widely used DFIT IRT analyses showed extremely poor performance in detecting these simulated differences.