A dialogue of the deaf in the statistical theater? Adressing structural effects within a geometric data analysis framework

摘要

Since their introduction in the late 1960s, the "moderate", and moreover "metrological" and "hypermetrological" uses of regression models quickly became the dominant quantitative approach in the Anglo-Saxon social sciences. This "sociology of the variables" has been the subject of many critical insights, with little impact on its dominance. By contrast, the French situation is quite different, mainly because of the strong association between Pierre Bourdieu's research program and the correspondence analysis methods. In this context, the relationship between geometric data analysis and regression models has turned into a "dialogue of the deaf". Complementarity is sometimes emphasized, correspondence analysis being associated with exploration and description of the data, and regressions being used to explain, reject or confirm assumptions. But regression models may also be used in order to analyze structural effects within a framework of geometrical data analysis, e.g. by visualizing graphically the results of a regression (Rouanet et al. in Math Sci Hum 160:13-46, 2002; Lebaron 2013). We propose a new multi-step approach, "Standardized Factor Analysis", which relies on geometric analysis and uses linear regression in a second stage in order to uncover structural effects in the original space. We illustrate it with data about tastes for cinema in France. We conclude by raising a more general set of questions about causality: social determinisms, even well established, are partial in the sense that they produce their effects only when associated with each other.