The application of multilevel regression models has become common practice in the field of social sciences. Multilevel regression models take into account that observations on individual respondents are nested within higher-level groups such as schools, classrooms, states, and countries.

In the application of multilevel models in country-comparative studies, however, it has long been overlooked that on the country-level only a limited number of observations are available. As a result, measurements on single countries can easily overly influence the regression outcomes.

Diagnostic tools for detecting influential data in multilevel regression are becoming available (including our own influence.ME), but what are your experiences with influential cases in country-comparative (multilevel) studies? How do you deal with influential cases if you encounter them?