Linking individuals and societies

How do individuals shape societies? How do societies shape individuals? This paper develops a framework for studying the connections between micro and macro phenomena. The framework builds on two ingredients widely used in social science - population and variable. Starting with the simplest case of one population and one variable, we systematically introduce additional variables and additional populations. This approach enables simple and natural introduction and exposition of such operations as pooling, matching, regression, hierarchical and multilevel modeling, calculating summary measures, finding the distribution of a function of random variables, and choosing between two or more distributions. To illustrate the procedures we draw on problems from a variety of topical domains in social science, including an extended illustration focused on residential racial segregation. Three useful features of the framework are: First, similarities in the mathematical structure underlying distinct substantive questions, spanning different levels of aggregation and different substantive domains, become apparent. Second, links between distinct methodological procedures and operations become apparent. Third, the framework has a potential for growth, as new models and operations become incorporated into the framework.