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

Abstract

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.

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Notes

  1. 1.

    It is technically possible to add interaction effects between explanatory variables in a regression model but besides that it is a relatively uncommon practice, the multiplication of combinations quickly becomes unworkable. An interesting approach is developed by Judea Pearl in the framework of analytical sociology, based on structural causality (Pearl 2009).

  2. 2.

    There is already criticism of this assumption in Halbwachs’ The causes of suicide (2002 [1930]), about the relationship between religion and urbanization.

  3. 3.

    This argument is also very present in the epistemological reflections of Passeron (1991).

  4. 4.

    We cite here some of the main criticisms, leaving aside—among others—those of Abbott about temporality issues (2001).

  5. 5.

    One may ask if we would not understand better some scientific debates by analyzing these kinds of competitions on the "size" and "robustness" of effects as a form of male competition.

  6. 6.

    This is the same logic that explains the recent success, within state organizations or NGOs, of the "randomized evaluation" promoted by Esther Duflo (2010) to test the effectiveness of development assistance programs.

  7. 7.

    «This method [the elimination of structural effects] leads to the study and the comparison between the behaviors of a reindeer in the Sahara and of a camel at the North Pole» (cited in Maurice Halbwachs, «La statistique en sociologie», in Centre internationale de synthèse, La statistique. Ses applications. Les problèmes qu’elles soulèvent, Paris, PUF, pp. 113–160).

  8. 8.

    For a study of tastes for cinema in France, see Duval (2011).

  9. 9.

    We use “eta²” indicator here, which is similar to R² in linear regression analysis (Le Roux and Rouanet 2004).

  10. 10.

    In demography, one of the most widely used indicators to study mortality is the crude death rate. When comparing Sweden and Mexico, for example, we see that the crude death rate in Sweden is higher than that of Mexico, which may seem counterintuitive in that health conditions are better and life expectancy is higher in Sweden. This is due to the fact that the crude death rate is influenced by the age structure of the population under study: Sweden has an older population than Mexico, and the elderly have higher death rates than other categories of age, which leads to a relatively high crude death rate. Demographers thus use statistical techniques of "standardization" to neutralize the effect of the age structure, i.e. to calculate the mortality indicators that are net of this structural effect. More generally, SFA is applied to MCA in this article but it could apply to any other factor analysis technique, such as principal component analysis (PCA).

  11. 11.

    At this stage, one can choose to retain only the first principal components, those that contain the most information.

  12. 12.

    To the extent that the PCA is not performed directly on the variables of the original MCA, one can’t obtain the contributions of these variables. However, all the other tools for the interpretation of supplementary variables may be used (cos², v test, eta²).

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Acknowledgments

The authors gratefully acknowledge Gabriel Abend, Jérôme Deauvieau and Frédéric Lebaron as well as the anonymous reviewers for their proofreading, discussions and advice.

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Correspondence to Olivier Roueff.

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Bry, X., Robette, N. & Roueff, O. A dialogue of the deaf in the statistical theater? Adressing structural effects within a geometric data analysis framework. Qual Quant 50, 1009–1020 (2016). https://doi.org/10.1007/s11135-015-0187-z

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Keywords

  • Correspondence analysis
  • Regression models
  • Analysis of structural effects
  • Combination of geometrical and inferential statistics
  • Standardized factor analysis (SFA)