Log-Linear Analysis of Contingency Tables: An Introduction for Historians with an application to Thernstrom on the "Floating Proletariat"

Abstract

For historians or other social scientists whose data is available in discreet (nominal- or ordinal-level) form, recently developed “log-linear” multivariate statistical techniques offer considerable advantages over commonsensical devices and are in many respects superior to such multivariate methods as multiple classification analysis, weighted least-squares, and logit. Reanalyzing Thernstrom’s Boston data on geographic mobility, we explain the ideas behind and the procedure of log-linear analysis explicitly, step-by-step. Intended for people who are already somewhat familiar with statistics (say, through multiple regression), the paper is self-contained and as simple as we could make it. After reading it carefully, one should be well prepared to perform such an analysis himself. Substantively, we sketch a simple economic model which points to age as an important determinant of the decision to move or stay, and our results cast doubt on Thernstrom’s tentatively offered notion of a “floating proletariat.”