The fixed effects approach as an alternative to multilevel analysis for cross-national analyses

Multilevel models that combine individual and contextual factors are increasingly popular in comparative social science research; however, their application in country-comparative studies is often associated with several problems. First of all, most data-sets utilized for multilevel modeling include only a small number (N<30) of macro-level units, and therefore, the estimated models have a small number of degrees of freedom on the country level. If models are correctly specified paying regard to the small, level-2 N, only a few macro-level indicators can be controlled for. Furthermore, the introduction of random slopes and cross-level interaction effects is then hardly possible. Consequently, (1) these models are likely to suffer from omitted variable bias regarding the country-level estimators, and (2) the advantages of multilevel modeling cannot be fully exploited. The fixed effects approach is a valuable alternative to the application of conventional multilevel methods in country-comparative analyses. This method is also applicable with a small number of countries and avoids the country-level omitted variable bias through controlling for country-level heterogeneity. Following common practice in panel regression analyses, the moderator effect of macro-level characteristics can be estimated also in fixed effects models by means of cross-level interaction effects. Despite the advantages of the fixed effects approach, it is rarely used for the analysis of cross-national data. In this paper, I compare the fixed effects approach with conventional multilevel regression models and give practical examples using data of the International Social Survey Programme (ISSP) from 2006. As it turns out, the results of both approaches regarding the effect of cross-level interactions are similar. Thus, fixed effects models can be used either as an alternative to multilevel regression models or to assess the robustness of multilevel results.