Comparative analysis may take different forms: It may involve comparisons across national groups, cultural groups, time points, or samples collected using different modes, just to name a few possibilities. In these types of studies, measurement invariance (MI, also often called measurement equivalence) is a necessary condition to allow meaningful comparisons of means or associations such as covariances and unstandardized regression coefficients across groups. In recent years, the concept of approximate measurement invariance (AMI) gained considerable attention. The AMI postulates that the estimation of reliable and comparable parameters for the groups in multiple-group models is possible even though there exist small “natural” differences between item parameters from different groups or a few completely non-invariant item parameters. The presentation will show some new developments in this approach including alignment optimization (including new generalizations) and BSEM models. It will show connections between linking, measurement invariance analysis, and regularization techniques.
Artur Pokropek is an associate professor at the Institute of Philosophy and Sociology of the Polish Academy of Sciences and the Head of Data Science, Statistics and Machine Learning Group (DSMLG) at the Educational Research Institute in Warsaw. The main area of his research is statistics, psychometry and research methodology. Currently, he is working on various aspects of compatibility in large scale cross-country surveys and modeling response biases (including response times and other paradata). He is involved in PISA, PIAAC, TIMSS and PIRLS research in Poland. He was visiting scholar at the Educational Testing Service (Princeton, USA) and EC Joint Research Center (Ispra, Italy). He is the author of several dozen articles in international journals such as Structural Equation Modeling, British Journal of Mathematical and Statistical Psychology, Journal of Educational Psychology, Stata Journal, and Sociological Methods & Research.