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Multiple mediation analysis for interval-valued data

Author

Listed:
  • Antonio Calcagnì

    (University of Trento)

  • Luigi Lombardi

    (University of Trento)

  • Lorenzo Avanzi

    (University of Trento)

  • Eduardo Pascali

    (University of Salento)

Abstract

Mediation analysis is an important statistical approach to evaluate the relationships among observed variables. The most commonly used models for mediation analysis handle single-valued variables. However, there are several circumstances (e.g., dimensionality reduction of large datasets, clinical patient courses, repeated measures, masked data, uncertain data) in which the collected information can be represented more naturally by means of intervals. In these cases, standard mediation analyses can be ill-suited. Although interval-valued variables can be transformed into standard single-valued variables, such procedures may mask some relevant information provided by intervals. In this article, we present a novel and simple model (IMedA) to perform mediation analysis on interval-valued variables which is based on both the symbolic regression approach and the regression based mediation framework. We also generalize Stolzenberg’s decomposition of effects to cope with interval-valued data. We further introduce a specific variance based decomposition procedure to descriptively evaluate the sizes of such effects. Finally, to better highlight the IMedA features we apply our model to a real case study from behavioral contexts.

Suggested Citation

  • Antonio Calcagnì & Luigi Lombardi & Lorenzo Avanzi & Eduardo Pascali, 2020. "Multiple mediation analysis for interval-valued data," Statistical Papers, Springer, vol. 61(1), pages 347-369, February.
    • Handle: RePEc:spr:stpapr:v:61:y:2020:i:1:d:10.1007_s00362-017-0940-6
    DOI: 10.1007/s00362-017-0940-6
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    1. Yoshio Takane & Forrest Young & Jan Leeuw, 1977. "Nonmetric individual differences multidimensional scaling: An alternating least squares method with optimal scaling features," Psychometrika, Springer;The Psychometric Society, vol. 42(1), pages 7-67, March.
    2. Timmerman, Marieke E. & Kiers, Henk A. L., 2002. "Three-way component analysis with smoothness constraints," Computational Statistics & Data Analysis, Elsevier, vol. 40(3), pages 447-470, September.
    3. Billard L. & Diday E., 2003. "From the Statistics of Data to the Statistics of Knowledge: Symbolic Data Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 470-487, January.
    4. Guadalupe Gómez & M. Calle & Ramon Oller, 2004. "Frequentist and Bayesian approaches for interval-censored data," Statistical Papers, Springer, vol. 45(2), pages 139-173, April.
    5. Zhiyong Zhang & Lijuan Wang, 2013. "Methods for Mediation Analysis with Missing Data," Psychometrika, Springer;The Psychometric Society, vol. 78(1), pages 154-184, January.
    6. Lima Neto, Eufrasio de A. & de Carvalho, Francisco de A.T., 2008. "Centre and Range method for fitting a linear regression model to symbolic interval data," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1500-1515, January.
    7. Thomas Augustin, 2002. "Expected utility within a generalized concept of probability — a comprehensive framework for decision making under ambiguity," Statistical Papers, Springer, vol. 43(1), pages 5-22, January.
    8. Sévérien Nkurunziza & S. Ejaz Ahmed, 2011. "Estimation strategies for the regression coefficient parameter matrix in multivariate multiple regression," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 65(4), pages 387-406, November.
    9. Luo, Peng & Geng, Zhi, 2016. "Causal mediation analysis for survival outcome with unobserved mediator–outcome confounders," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 336-347.
    10. Lima Neto, Eufrásio de A. & de Carvalho, Francisco de A.T., 2010. "Constrained linear regression models for symbolic interval-valued variables," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 333-347, February.
    11. Angela Blanco-Fernández & Peter Winker, 2016. "Data generation processes and statistical management of interval data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(4), pages 475-494, October.
    12. Abbas Parchami & S. Taheri & Mashaallah Mashinchi, 2012. "Testing fuzzy hypotheses based on vague observations: a p-value approach," Statistical Papers, Springer, vol. 53(2), pages 469-484, May.
    13. M. Alkhamisi, 2010. "Simulation study of new estimators combining the SUR ridge regression and the restricted least squares methodologies," Statistical Papers, Springer, vol. 51(3), pages 651-672, September.
    14. Rosseel, Yves, 2012. "lavaan: An R Package for Structural Equation Modeling," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 48(i02).
    15. Kosuke Imai & David A. van Dyk, 2004. "Causal Inference With General Treatment Regimes: Generalizing the Propensity Score," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 854-866, January.
    16. Kiers, Henk A. L., 2002. "Setting up alternating least squares and iterative majorization algorithms for solving various matrix optimization problems," Computational Statistics & Data Analysis, Elsevier, vol. 41(1), pages 157-170, November.
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