Most international studies like TIMSS, PIRLS, PISA, CIVED or ICCS make use of item response modeling for the scaling of student responses to test questionnaire items. Using IRT enables researchers to use rotated test booklets, equate tests, describe performance scales and obtain proficiency estimates from multiple imputation (plausible values). In addition, an increasing number of studies employ IRT to obtain scale scores from questionnaire items. One important assumption for using IRT scaling (or other scaling methods) in cross-national research is measurement invariance because typically international parameters are used for obtaining scale scores that are used for between-country comparisons. However, it is widely recognized that language differences may have a powerful effect on equivalence (or non-equivalence). Most international studies (see for example Grisay, 2002; Chrostowski & Malak, 2004) implement rigorous translation verifications to achieve a maximum of "linguistic equivalence". However, it is well known that even slight deviations in wording (sometimes due to linguistic differences between source and target language) may lead to differences in item responses. Furthermore, non-equivalence can also be caused by the cultural differences among participating countries in international studies (van de Veijver and Tanzer, 1997; Byrne, 2003). This paper outlines how Rasch modeling can be used for testing assumption about measurement equivalence in international studies. Based on the Rasch model (Rasch, 1960) for dichotomous items and the Partial Credit model for polytomous items (Masters/Wright, 1982), so-called item-by-country interactions can be estimated that provide useful information about the level of measurement invariance in parameter estimates. It should be noted that item-by-country interactions are one form of differential item functioning (DIF) where groups vary in their probability of answering questions even after controlling for their levels of ability (see Hambleton, Swaminathan and Rogers, 1991). Item-by-country interactions can be obtained from comparing separate calibrations for national sub-samples or estimated directly through the inclusion of additional model parameters (see examples in Walker, 2008 and Schulz, 2009). Using field trial data from the IEA International Civic and Citizenship Education Study ICCS (for more information see: http://iccs.acer.edu.au/) the paper will outline ways of obtaining estimates of measurement invariance and will discuss their interpretation as well as the limitations of these analyses. In particular, the paper will illustrate the analysis of item-by-country interactions for test items and the estimation of country effects when scaling questionnaire (Likert-type) items. ... continues in Methodology ...

... The scaling software ACER ConQuest (Wu, Adams, Wilson and Haldane, 2007) was used for the analysis of data from 19,858 students at 734 schools in 32 countries that participated in an international field trial of ICCS instruments in late 2007. The analyses of item-by-country interactions undertaken with ICCS field trial data showed a noticeable but limited amount of country DIF. Information on item-by-country interaction helped to select items for the main survey that showed lower levels of parameter variation across countries.