AStA Advances in Statistical Analysis

, Volume 102, Issue 4, pp 589–610 | Cite as

Varying levels of anomie in Europe: a multilevel analysis based on multidimensional IRT models

  • Lara Fontanella
  • Annalina Sarra
  • Pasquale Valentini
  • Simone Di Zio
  • Sara Fontanella
Original Paper


Recent years have seen increased attention paid to monitoring social anomie and its dependency on micro- and macro-factors. In this paper, we endorse the theorisation of social anomie as a complex, multidimensional and multilevel phenomenon. To ensure a rigorous measurement of the varying levels of social anomie in the European countries, the current study relies on a multilevel multidimensional item response theory model which explicitly accounts for the presence of a non-ignorable missing data mechanism. This unified approach makes it possible to specify an analytical model of links between anomie features and their determinants and to explore how the latent traits of interest are influenced by individual-level factors, as well as by country-level indicators. Additionally, to avoid misleading inferential conclusions, the proposed model takes into account the respondent’s omitting behaviour, assuming that the missingness mechanism is driven by a latent propensity to respond. Data used in this study have been collected in the 2010 wave of the European Social Survey. To reduce the computational complexities, a Bayesian specification of the MIRT model is provided and the parameter model estimates are obtained through MCMC algorithms.


Cross-national research Multilevel analysis Item response theory Missing data Anomie 

Supplementary material

10182_2018_320_MOESM1_ESM.pdf (17.3 mb)
Supplementary material 1 (pdf 17757 KB)


  1. Albert, J.H., Chib, S.: Bayesian analysis of binary and polychotomous response data. J. Am. Stat. Assoc. 88(422), 669–679 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  2. Andrich, D.: Models for measurement, precision, and the non dichotomisation of graded responses. Psychometrika 60(1), 7–26 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  3. Andrich, D.: Understanding the response structure and process in the polytomous Rasch model. In: Nering, M.L., Ostini, R. (eds.) Handbook of Polytomous Item Response Theory Models. Routledge, New York (2010)Google Scholar
  4. Bacci, S., Bartolucci, F.: A multidimensional finite mixture structural equation model for nonignorable missing responses to test items. Struct. Equ. Model Multidiscipl. J. 22, 352–365 (2015)MathSciNetCrossRefGoogle Scholar
  5. Baumer, E.: Untangling research puzzles in Merton’s multilevel anomie theory. Theor. Criminol. 11, 63–93 (2007)CrossRefGoogle Scholar
  6. Béguin, A., Glas, C.: MCMC estimation and some model-fit analysis of multidimensional IRT models. Psychometrika 66(4), 541–561 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  7. Cao, L.: Is American society more anomic? A test of Merton’s theory with cross-national data. Int. J. Comp. Appl. Crim. Justice 28(1), 15–32 (2004)CrossRefGoogle Scholar
  8. Chalmers, R.P.: MIRT: a multidimensional item response theory package for the R environment. J. Stat. Softw. 48(6), 1–29 (2012)CrossRefGoogle Scholar
  9. de Jong, M., Steenkamp, J.: Finite mixture multilevel multidimensional ordinal IRT models for large scale cross-cultural research. Psychometrika 75(1), 3–32 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  10. de Jong, M., Steenkamp, J., Fox, J.: Relaxing measurement invariance in cross-national consumer research using a hierarchical IRT model. J. Consum. Res. 34(2), 260–278 (2007)CrossRefGoogle Scholar
  11. De Leeuw, E., Hox, J., Huisman, M.: Prevention and treatment of item nonresponse. J. Off. Stat. 19(2), 153–176 (2003)Google Scholar
  12. Deflem, M.: Anomie. In: Ritzer, G. (ed.) The Blackwell Encyclopedia of Sociology, pp. 144–146. Wiley, Oxford (2007)Google Scholar
  13. DeMars, C.: Item Response Theory. Understanding Statistics Measurement. Oxford University Press, Oxford (2010)CrossRefGoogle Scholar
  14. Durkheim, E.: The Division of Labor in Society. Free Press of Glencoe, New York (1964)Google Scholar
  15. Entink, R.H.K., Fox, J.P., van der Linden, W.: A multivariate multilevel approach to the modeling of accuracy and speed of test takers. Psychometrika 74(1), 21–48 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  16. ESS: ESS Round 5: European Social Survey Round 5 Data. Data File Edition 3.2. NSD—Norwegian Centre for Research Data, Norway Data Archive and distributor of ESS data for ESS ERIC (2010)Google Scholar
  17. Gelman, A., Meng, X.L., Stern, H.: Posterior predictive assessment of model fitness via realized discrepancies. Stat. Sin. 6, 733–807 (1996)MathSciNetzbMATHGoogle Scholar
  18. Gelman, A., Carlin, J.B., Stern, H.S., Dunson, D.B., Vehtari, A., Rubin, D.B.: Bayesian Data Analysis, 3rd edn. Chapman and Hall, Boca Raton (2013)zbMATHGoogle Scholar
  19. Holman, R., Glas, A.: Modelling non-ignorable missing-data mechanisms with item response theory models. Br. J. Math. Stat. Psychol. 58(1), 1–17 (2005)MathSciNetCrossRefGoogle Scholar
  20. Hough, M., Jackson, J., Bradford, B.: Trust in justice and the legitimacy of legal authorities: topline findings from a European comparative study. In: Body-Gendrot, S., Hough, M., Levy, R., Kerezsi, K., Snacken, S. (eds.) The Routledge Handbook of European Criminology. Routledge, London (2013)Google Scholar
  21. Jackson, J., Bradford, B., Hough, M., Kuha, J., Stares, S.R., Widdop, S., Fitzgerald, R., Yordanova, M., Galev, T.: Developing European indicators of trust in justice. Eur. J. Criminol. 8(4), 267–285 (2011)CrossRefGoogle Scholar
  22. Jackson, J., Bradford, B., Hough, M., Myhill, A., Quinton, P., Tyler, T.R.: Why do people comply with the law? Legitimacy and the influence of legal institutions. Br. J. Criminol. 52(6), 1051–1071 (2012)CrossRefGoogle Scholar
  23. Koch, A., Blohm, M.: Item nonresponse in the European Social Survey. Ask Res. Methods 18(1), 45–65 (2009)Google Scholar
  24. Lord, F.M., Novick, M.R.: Statistical Theories of Mental Test Scores. Addison-Wesley, Reading (1968)zbMATHGoogle Scholar
  25. Merton, R.: Social theory and anomie. Am. Sociol. Rev. 3, 672–682 (1938)CrossRefGoogle Scholar
  26. Merton, R.: Social Theory and Social Structure. Free Press, New York (1968)Google Scholar
  27. Passas, N.: Continuities in the anomie tradition. In: Adler, F., Laufer, W. (eds.) The Legacy of Anomie Theory: Advances in Criminological Theory. Transaction Publishers, New Brunswick (1995)Google Scholar
  28. Rose, N.: Item Nonresponses in Educational and Psychological Measurement. Thüringer Universitäts- und Landesbibliothek Jena, Jena (2013)Google Scholar
  29. Rose, N., von Davier, M., Xu, X.: Modeling Nonignorable Missing Data with IRT. Research Report RR-10-11. Educational Testing Service, Princeton, NJ (2010)Google Scholar
  30. Sampson, R.J., Bartusch, D.J.: Legal cynicism and (subcultural?) tolerance of deviance: the neighborhood context of racial differences. Law Soc. Rev. 32(4), 777–804 (1998)CrossRefGoogle Scholar
  31. Sheng, Y., Wikle, C.: Comparing multiunidimensional and unidimensional item response theory models. Educ. Psychol. Meas. 67(6), 899–919 (2007)MathSciNetCrossRefGoogle Scholar
  32. Sheng, Y., Wikle, C.: Bayesian multidimensional IRT models with a hierarchical structure. Educ. Psychol. Meas. 68(3), 413–430 (2008)MathSciNetCrossRefGoogle Scholar
  33. Tanner, M.A., Wong, W.H.: The calculation of posterior distributions by data augmentation. J. Am. Stat. Assoc. 82(398), 528–540 (1987)MathSciNetCrossRefzbMATHGoogle Scholar
  34. Thorlindsson, T., Bernburg, J.: Durkheim’s theory of social order and deviance: a multi-level test. Eur. Soc. Rev. 20(4), 271–285 (2004)CrossRefGoogle Scholar
  35. Tyler, T.R.: Why People Obey the Law, 2nd edn. Yale University Press, New Haven (2006)Google Scholar
  36. Zhao, R., Cao, L.: Social change and anomie: a cross-national study. Soc. Forces 88(3), 1209–1229 (2010)CrossRefGoogle Scholar
  37. Zhu, X., Stone, C.A.: Assessing fit of unidimensional graded response models using Bayesian methods. J. Educ. Meas. 48, 81–97 (2011)CrossRefGoogle Scholar
  38. Zhu, X., Stone, C.A.: Bayesian comparison of alternative graded response models for performance assessment applications. Educ. Psychol. Meas. 72, 774–799 (2012)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Lara Fontanella
    • 1
  • Annalina Sarra
    • 1
  • Pasquale Valentini
    • 2
  • Simone Di Zio
    • 1
  • Sara Fontanella
    • 3
  1. 1.Department of Legal and Social SciencesUniversity of Chieti-PescaraPescaraItaly
  2. 2.Department of EconomicsUniversity of Chieti-PescaraPescaraItaly
  3. 3.Imperial College LondonLondonUK

Personalised recommendations