“Generative Mechanisms and Multivariate Statistical Analysis: Modeling Educational Opportunity Inequality with a Multi-Matrix Log-Linear Topological Model: Contributions and Limitations”

摘要

Among techniques for the quantitative analysis of categorical data, log-linear models at present occupy a central place in social statistics, their sophistication and complexity having rapidly evolved over the past three decades. The article examines a specific variant of this approach to modeling which consists of log-linear topological models. It starts from the debate which followed introduction of the latter at the end of the 1970s to offer a new evaluation of the heuristic and methodological utility of this technique in light of recent discussion more generally concerned with the quantitative variables-based approach. In this regard, the article puts forward two arguments. It first maintains that log-linear topological models, especially in their multi-matrix variant, are extremely useful in integrating sociological theory with empirical quantitative analysis. It then shows that the principal shortcoming of these models is that they only partially allow the accurate modeling of the generative mechanisms underlying all the empirical regularities observed in aggregate data. These models are thus very attractive in that they go beyond the descriptive level of numerous works in quantitative sociology, and yet they are incapable of yielding explanations founded on the notion of generative mechanisms. In order not to remain at the abstract level of epistemological reflection, the article will attempt to show the well-foundedness of this thesis by constructing a multi-matrix log-linear topological model for the analysis of a contingency table which cross-classifies social origin with the educational qualification. The model is then tested against French survey data. To the extent that this model attempts to express ideas drawn from a specific theoretical approach – that of ‘rational educational choice’ – the analysis can contribute to both the study and understanding of inequalities in educational opportunity.