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On elliptical multilevel models

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  • Roberto F. Manghi
  • Gilberto A. Paula
  • Francisco José A. Cysneiros

Abstract

Multilevel models have been widely applied to analyze data sets which present some hierarchical structure. In this paper we propose a generalization of the normal multilevel models, named elliptical multilevel models. This proposal suggests the use of distributions in the elliptical class, thus involving all symmetric continuous distributions, including the normal distribution as a particular case. Elliptical distributions may have lighter or heavier tails than the normal ones. In the case of normal error models with the presence of outlying observations, heavy-tailed error models may be applied to accommodate such observations. In particular, we discuss some aspects of the elliptical multilevel models, such as maximum likelihood estimation and residual analysis to assess features related to the fitting and the model assumptions. Finally, two motivating examples analyzed under normal multilevel models are reanalyzed under Student-t and power exponential multilevel models. Comparisons with the normal multilevel model are performed by using residual analysis.

Suggested Citation

  • Roberto F. Manghi & Gilberto A. Paula & Francisco José A. Cysneiros, 2016. "On elliptical multilevel models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(12), pages 2150-2171, September.
    • Handle: RePEc:taf:japsta:v:43:y:2016:i:12:p:2150-2171
    DOI: 10.1080/02664763.2015.1134445
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    References listed on IDEAS

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    1. Manuel Galea & Gilberto Paula & Miguel Uribe-Opazo, 2003. "On influence diagnostic in univariate elliptical linear regression models," Statistical Papers, Springer, vol. 44(1), pages 23-45, January.
    2. J. K. Lindsey, 1999. "Multivariate Elliptically Contoured Distributions for Repeated Measurements," Biometrics, The International Biometric Society, vol. 55(4), pages 1277-1280, December.
    3. Kloke, John D. & McKean, Joseph W. & Rashid, M. Mushfiqur, 2009. "Rank-Based Estimation and Associated Inferences for Linear Models With Cluster Correlated Errors," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 384-390.
    4. Osorio, Felipe & Paula, Gilberto A. & Galea, Manuel, 2007. "Assessment of local influence in elliptical linear models with longitudinal structure," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4354-4368, May.
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    Cited by:

    1. Ying Liu & Fang Luo & Danhui Zhang & Hongyun Liu, 2017. "Comparison and robustness of the REML, ML, MIVQUE estimators for multi-level random mediation model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(9), pages 1644-1661, July.
    2. Aline B. Tsuyuguchi & Gilberto A. Paula & Michelli Barros, 2020. "Analysis of correlated Birnbaum–Saunders data based on estimating equations," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 661-681, September.

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