Locating Event-Based Causal Effects: A Configural Perspective

Article

Abstract

Statistical models for the analysis of hypotheses that are compatible with direction dependence were originally specified based on the linear model. In these models, relations among variables reflected directional or causal hypotheses. In a number of causal theories, however, effects are defined as resulting from causes that did versus did not occur. To accommodate this type of theory, the present article proposes analyzing directional or causal hypotheses at the level of configurations. Causes thus have the effect that, in a particular sector of the data space, the density of cases increases or decreases. With reference to log-linear models of direction dependence, this article specifies base models for the configural analysis of directional or causal hypotheses. In contrast to standard configural analysis, the models are applied in a confirmatory context. Specific direction dependence hypotheses are analyzed. In a simulation study, it is shown that the proposed methods have good power to identify the sectors in the data space in which density exceeds or falls below expectation. In a data example, it is shown that the evolutionary hypothesis that body size determines brain size is confirmed in particular for higher vertebrates.

Keywords

Event-based causation Direction of dependence Configural frequency analysis Log-linear model 

Notes

Compliance with Ethical Standards

Conflict of Interest

All authors declare that there are no conflicts of interest.

Ethical Approval

This article does not contain any studies with human participants or animals performed by any of the authors.

References

  1. Agresti, A. (2013). Categorical data analysis (3rd ed.). New York: Wiley.Google Scholar
  2. Bateson, P. (2015). Ethology and human development. In W. F. Overton & P. C. M. Molenaar (Eds.), Handbook of child psychology and developmental science (pp. 208–243). Wiley: Hoboken.Google Scholar
  3. Beebee, H., Hitchcock, C., & Menzies, P. (Eds.). (2009). The Oxford handbook of causation. New York: Oxford University Press.Google Scholar
  4. Bergman, L. R., & Magnusson, D. (1997). A person-oriented approach in research on developmental psychopathology. Development and Psychopathology, 9, 291–319.CrossRefPubMedGoogle Scholar
  5. Bergman, L. R., & Trost, K. (2006). The person-oriented versus the variable-oriented approach: Are they complementary, opposites, or exploring different worlds? Merrill-Palmer Quarterly, 52, 601–632.CrossRefGoogle Scholar
  6. Bradley, J. V. (1978). Robustness? British Journal of Mathematical and Statistical Psychology, 31, 144–152.CrossRefGoogle Scholar
  7. Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). New Jersey: Lawrence Erlbaum Associates.Google Scholar
  8. Crile, G., & Quiring, D. P. (1940). A record of the body weight and certain organ and gland weights of 3690 animals. Ohio Journal of Science, 40, 219–259.Google Scholar
  9. Darlington, R. B., & Hayes, A. F. (2000). Combining independent p-values: Extensions of the Stouffer and binomial methods. Psychological Methods, 5, 496–515.Google Scholar
  10. Dodge, Y., & Rousson, V. (2000). Direction dependence in a regression line. Communications in Statistics: Theory and Methods, 32, 2053–2057.Google Scholar
  11. Dodge, Y., & Rousson, V. (2001). On asymmetric properties of the correlation coefficient in the regression setting. The American Statistician, 55, 51–54.CrossRefGoogle Scholar
  12. Dodge, Y., & Rousson, V. (2016). Statistical inference for direction of dependence in linear models. In W. Wiedermann & A. von Eye (Eds.), Statistics and causality: Methods for applied empirical research (pp. 45–62). Wiley: Hoboken.Google Scholar
  13. Dunbar, R. I. M., & Shultz, S. (2017). Why are there so many explanations for primate brain evolution? Philosophical Transactions of the Royal Society B, 372, 20160244.CrossRefGoogle Scholar
  14. Fisher, R. A. (1925). Statistical methods for research workers. Edinburgh: Oliver and Boyd.Google Scholar
  15. Goodman, L. A. (1973). Causal analysis of data from panel studies and other kinds of surveys. American Journal of Sociology, 78, 1135–1191.CrossRefGoogle Scholar
  16. Hagenaars, J. A. (1998). Categorical causal modeling: Latent class analysis and directed log-linear models with latent variables. Sociological Methods & Research, 26, 436–486.CrossRefGoogle Scholar
  17. Hall, E. J., & Paul, L. A. (2013). Causation: A user’s guide. Oxford: Oxford University Press.Google Scholar
  18. Hausman, D. M. (1999). The mathematical theory of causation. British Journal of Philosophical Science, 50, 151–162.CrossRefGoogle Scholar
  19. Jerison, H. (1973). Evolution of the brain and intelligence. New York: Academic Press.Google Scholar
  20. Kendall, M. G., & Stuart, A. (1961). The advanced theory of statistics (vol. 2): Inference and relationship. New York: Hafner.Google Scholar
  21. Krauth, J. (2003). Type structures in CFA. Psychology Science, 45, 330–338.Google Scholar
  22. Langeheine, R. (1986). Log-lineare modelle. In J. van Koolwijk & M. Wieken-Mayser (Eds.), Techniken der empirischen Sozialforschung (methods of empirical social science research) (pp. 122–195). Oldenbourg Verlag: Munich.Google Scholar
  23. Lienert, G. A., & Krauth, J. (1975). Configural frequency analysis as a statistical tool for defining types. Educational and Psychological Measurement, 35, 231–238.CrossRefGoogle Scholar
  24. MacCallum, R. C., Zhang, S., Preacher, K. J., & Rucker, D. D. (2002). On the practice of dichotomization of quantitative variables. Psychological Methods, 7, 19–40.CrossRefPubMedGoogle Scholar
  25. Mair, P., & von Eye, A. (2007). Application scenarios for nonstandard log-linear models. Psychological Methods, 12, 139–156.CrossRefPubMedGoogle Scholar
  26. Muddapur, M. V. (2003). On directional dependence in a regression line. Communications in Statistics: Theory and Methods, 32, 2053–2057.CrossRefGoogle Scholar
  27. Nelder, J. A. (1974). Log linear models for contingency tables: A generalization of classical least squares. Journal of the Royal Statistical Society C, 23, 323–329.Google Scholar
  28. Nelsen, R. B. (2006). An introduction to copulas (2nd ed.). New York: Springer.Google Scholar
  29. Paul, L.A. (2009). Counterfactual theories. In H. Beebee, C. Hitchcock, & P. Menzies (eds.) (2009). The Oxford handbook of causation (pp. 158–184). New York: Oxford University Press.Google Scholar
  30. Pearson, K. (1900). On the correlation of characters not quantitatively measurable. Royal Society Philosophical Transactions, Series A, 195, 1–47.CrossRefGoogle Scholar
  31. R Core Team (2017). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. http://www.R-project.org. Accessed 10 March 2018.
  32. Rindskopf, D. (1990). Nonstandard log-linear models. Psychological Bulletin, 108(1), 150-162.  https://doi.org/10.1037/0033-2909.108.1.150.
  33. Stouffer, S.A., Suchman, E.A., DeVinney, L.C., Star, S.A., & Williams, R.M. Jr. (1949). The American soldier, Vol. 1: Adjustment during Army Life. Princeton: Princeton University Press.Google Scholar
  34. Sungur, E. A. (2005). A note on directional dependence in regression setting. Communications in Statistics: Theory and Methods, 34, 1957–1965.CrossRefGoogle Scholar
  35. Upton, G. J. G. (1978). The analysis of cross-tabulated data. Chichester: Wiley.Google Scholar
  36. von Eye, A. (2002). The odds favor antitypes - a comparison of tests for the identification of configural types and antitypes. Methods of Psychological Research - online, 7, 1–29.Google Scholar
  37. von Eye, A. (2004). Base models for configural frequency analysis. Psychology Science, 46, 150–170.Google Scholar
  38. von Eye, A., & Bergman, L. R. (2003). Research strategies in developmental psychopathology: Dimensional identity and the person-oriented approach. Development and Psychopathology, 15, 553–580.Google Scholar
  39. von Eye, A., & Brandtstädter, J. (1997). Configural frequency analysis as a searching device for possible causal relationships. Methods of Psychological Research - Online, 2(2), 1–23.Google Scholar
  40. von Eye, A., & DeShon, R.P. (2008). Characteristics of measures of directional dependence - A Monte Carlo study. http://interstat.statjournals.net/YEAR/2008/articles/0802002.pdf. Accessed 10 March 2018.
  41. von Eye, A., & DeShon, R.P. (2012). Directional dependency in developmental research. International Journal of Behavior Development, 36, 303–312.Google Scholar
  42. von Eye, A., & Gutiérrez Peña, E. (2004). Configural frequency analysis - the search for extreme cells. Journal of Applied Statistics, 31, 981–997.CrossRefGoogle Scholar
  43. von Eye, A., & Mun, E.-Y. (2007). A note on the analysis of difference patterns - structural zeros by design. Psychology Science, 49, 14–25.Google Scholar
  44. von Eye, A., & Mun, E.-Y. (2013). Log-linear modeling - concepts, interpretation and applications. New York: Wiley.Google Scholar
  45. von Eye, A., & Schuster, C. (1998). On the specification of models for Configural frequency analysis - sampling schemes in prediction CFA. Methods of Psychological Research - online, 3, 55–73.CrossRefGoogle Scholar
  46. von Eye, A., & Wiedermann, W. (2016). Direction of effects in categorical variables: A structural perspective. In W. Wiedermann & A. von Eye (Eds.), Statistics and causality: Methods for applied empirical research (pp. 107–130). Wiley: Hoboken.Google Scholar
  47. von Eye A.., & Wiedermann, W. (2017). Testing event-based forms of causality. Integrative Psychological & Behavioral Science (in press).Google Scholar
  48. von Eye, A., Mair, P., & Mun, E.-Y. (2010). Advances in Configural frequency analysis. New York: Guilford Press.Google Scholar
  49. von Eye, A., Wiedermann, W., & Mun, E.-Y. (2013). Granger causality - statistical analysis under a configural perspective. Integrative Psychological & Behavioral Science, 48, 79–99.Google Scholar
  50. von Eye, A., Bergman, L. R., & Hsieh, C.-A. (2015). Person-oriented methodological approaches. In W. F. Overton & P. C. M. Molenaar (Eds.), Handbook of child psychology and developmental science - theory and methods (pp. 789–841). New York: Wiley.Google Scholar
  51. von Weber, S., Lautsch, E., & von Eye, A. (2003). On the limits of Configural frequency analysis: Analyzing small tables. Psychology Science, 45, 339–354.Google Scholar
  52. von Weber, S., von Eye, A., & Lautsch, E. (2005). Combinatoric search for types and antitypes. Psychology Science, 47, 401–423.Google Scholar
  53. Wiedermann, W., & Hagmann, M. (2016). Asymmetric properties of the Pearson correlation coefficient: Correlation as the negative association between linear regression residuals. Communications in Statistics-Theory and Methods, 45, 6263–6283.CrossRefGoogle Scholar
  54. Wiedermann, W., & von Eye, A. (2015a). Direction of effects in multiple linear regression models. Multivariate Behavioral Research, 50, 23–40.CrossRefPubMedGoogle Scholar
  55. Wiedermann, W., & von Eye, A. (2015b). Direction of effects in mediation analysis. Psychological Methods, 20, 221–244.CrossRefPubMedGoogle Scholar
  56. Wiedermann, W., & von Eye, A. (2015c). Direction dependence analysis: A confirmatory approach for testing directional theories. International Journal of Behavior Development, 39, 570–580.CrossRefGoogle Scholar
  57. Wiedermann, W., & von Eye, A. (2016). Directionality of effects in causal mediation analysis. In W. Wiedermann & A. von Eye (Eds.), Statistics and causality: Methods for applied empirical research (pp. 63–106). Wiley: Hoboken.CrossRefGoogle Scholar
  58. Wiedermann, W., & von Eye (2017). Log-linear models to evaluate direction of effect in binary variables. Statistical Papers (in press).Google Scholar
  59. Wiedermann, W., Hagmann, M., & von Eye, A. (2015). Significance tests to determine the direction of effects in linear regression models. British Journal of Mathematical and Statistical Psychology, 68, 116–141.CrossRefPubMedGoogle Scholar
  60. Wiedermann, W., Artner, R., & von Eye, A. (2017). Heteroscedasticity as a basis for direction dependence in reversible linear regression models. Multivariate Behavioral Research, 52, 222–241.CrossRefPubMedGoogle Scholar
  61. Wiedermann, W., Merkle, E. C., & von Eye, A. (2018). Direction of dependence in measurement error models. British Journal of Mathematical and Statistical Psychology, 71, 117–145.CrossRefPubMedGoogle Scholar
  62. Weisberg, S. (1985). Applied Linear Regression, 2nd Ed. New York: J. Wiley & Sons.Google Scholar
  63. Wilde, M., & Williamson, J. (2016). Evidence and epistemic causality. In W. Wiedermann & A. von Eye (Eds.), Statistics and causality. Methods for applied empirical research (pp. 31–41). Wiley: Hoboken.CrossRefGoogle Scholar
  64. Wu, C. F. J., & Hamada, M. (2000). Experiments: Planning, analysis, and parameter design optimization. New York: Wiley.Google Scholar
  65. Yamaguchi, K. (2016). Log-linear causal analysis of cross-classified categorical data. In W. Wiedermann & A. Von Eye (Eds.), Statistics and causality: Methods for applied empirical research (pp. 311–331). Wiley: Hoboken.CrossRefGoogle Scholar
  66. Yan, J. (2007). Enjoy the joy of copulas: With a package copula. Journal of Statistical Software, 21(4), 1–21. http://www.jstatsoft.org/v21/i04/. Accessed 10 March 2018.

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Michigan State UniversityMontpellierFrance
  2. 2.Department of Educational, School, and Counseling Psychology; Unit of Statistics, Measurement, and Evaluation in EducationCollege of Education, University of MissouriColumbiaUSA

Personalised recommendations