On elliptical multilevel models. Issue 12 (9th September 2016)

• Record Type: Journal Article
• Authors: Manghi, Roberto F.; Paula, Gilberto A.; Cysneiros, Francisco José A.
• Is Part Of: Journal of applied statistics. Volume 43:Issue 12(2016)
• Page Start: 2150
• Page End: 2171
• Publication Date: 2016-09-09
• Subjects: Correlated data -- elliptical models -- multilevel models -- multivariate Student-t distribution -- robust estimation; 62J05 -- 62J20; Statistics -- Periodicals; 519.5
• DOI: 10.1080/02664763.2015.1134445
• Languages: English
• ISSNs: 0266-4763

Abstract

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.