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It is necessary to examine the measurement invariance (MI) among groups in studies where different groups are compared by using a measurement instrument. Most of the studies, measurement invariance is tested with multiple group conrmatory factor analysis. This model applies many model adjustments based on the modication indexes. Therefore, it is not practical due to too many large modication indexes while testing MI over many groups. Besides scalar model is a poor model fit when comparing many groups and so does not hold MI. In this study, the aim is to explain the basic concepts and processes of the alignment method which is offered as a new method for testing MI and illustrate an application on the real data set. In this study, measurement invariance among 56 countries including Turkey is tested with alignment method in order to set an example for researchers. For this purpose, the Instrumental Motivation Scale data, which is one of the psychological measurement instruments used in PISA 2015, was used. As a result of MG-CFA, it was found that configural invariance was ensured. The fit indexes of CFI and TLI were calculated as 0.982 and 0.946 respectively in this stage. After that, metric invariance was tested by considering the difference of fit indices obtained for the two stages. It was found that the metric invariance could not be provided. Alignment results show which countries hold MI and which do not. Besides it provides information which items have the most invariants for groups that hold MI.

Measurement Invariance Testing with Alignment Method: Many Groups Comparison