Studies aiming to make cross-cultural comparisons first should establish measurement invariance in the groups to be compared because results obtained from such comparisons may be artificial in the event that measurement invariance cannot be established. The purpose of this study is to investigate the measurement invariance of the data obtained from the "Mathematics Liking Scale" in TIMSS 2015through Multiple Group CFA, Multiple Group LCA and Mixed Rasch Model, which are based on different theoretical foundations and to compare the obtained results. To this end, TIMSS 2015 data for students in the USA and Canada, who speak the same language and data for students in the USA and Turkey, who speak different languages, are used. The study is conducted through a descriptive study approach. The study revealed that all measurement invariance levels were established in Multiple Group CFA for the USA-Canada comparison. In Multiple Group LCA, on the other hand, measurement invariance was established up to partial homogeneity. However, it was not established in the Mixed Rasch Model. As for the USA-Turkey comparison, metric invariance was established in Multiple Group CFA whereas in Multiple Group LCA it stopped at the heterogeneity level. Measurement invariance for data failed to be established for the relevant sample in the Mixed Rasch Model. The foregoing findings suggest that methods with different theoretical foundations yield different measurement invariance results. In this regard, when deciding on the method to be used in measurement invariance studies, it is recommended to examine the necessary assumptions and consider the variable structure.