Confronting Sociological Theory with Data: Regression Analysis, Goodman's Log-Linear Models and Comparative Research
Authors: Pescosolido Bernice A. , Kelley Jonathan 
Published: September 2003

Comparisons are central to sociology and prominent among them are comparisons between the way two variables are related in different contexts (e.g. the present compared to the past, blacks compared to whites, industrial societies compared to agrarian ones). It is crucial, therefore, that analytic techniques used to test for such differences accurately reflect the true situation. A variety of statistical approaches have been used, most notably, ordinary least squares (OLS) regression with dummy variables and interaction terms. Recently, however, Goodman's log-linear procedure has been advocated as a `better' way of dealing with certain types of comparisons and particular models have been widely used. However, there is some question as to their applicability in answering theoretical questions typically posed in comparative sociological research. In this paper, we address this issue. Using a Monte Carlo simulation, we set up a typical but hypothetical set of data that would be appropriate for testing comparative theories of socioeconomic achievement or intergenerational mobility. This allows us to examine the ramifications of choosing particular analytic techniques on the conclusions drawn about theoretical propositions. Following conventions established in the literature, we apply two analytic techniques to the same set of data under a variety of conditions. Specifically, we compare the use of widely applied OLS regression and log-linear models where we set (1) the slope differences and (2) the mean differences in the variables between the contexts to vary. The simulation suggests that the regression procedure is able to pick up differences which would be of theoretical interest to the sociologist while the log-linear procedure, given the particular situation modelled here, does not. This is more likely to occur in those cases where the contexts compared have very different distributions. This does not reflect any problems in the log-linear technique itself. Ordered models are more likely to detect these differences because they are parsimonious with respect to degrees of freedom. However, this is not the only factor, methodological or theoretical, that needs to be considered in the choice of techniques. In particular, the findings alert us to difficulties inherent in testing sociological theories where (1) operationalizations of important concepts can result in very different measures and (2) conventional applications of these techniques fail to provide a valid test of proposed theoretical questions. Focussing on factors which may account for the differences observed, we address issues in the existing debate over the use of log-linear and regression models. We discuss the theoretical questions in stratification research for which log-linear techniques can be a useful tool and those for which it is misleading. Finally, we outline the theoretical and methodological tradeoffs in using each technique and suggest another not commonly employed in sociological research.