Nonlinear mixed-effects elliptical regression models

• Grant number: 11/18200-0
• Support Opportunities: Regular Research Grants
• Start date: January 01, 2012
• End date: December 31, 2013
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Applied Probability and Statistics
• Principal Investigator: Reiko Aoki
• Grantee: Reiko Aoki
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

The development of linear and nonlinear elliptical mixed-effects models is essential when dealing with correlated data. In particular, some problems from specific areas as pharmacokinetics, growth curves, economic or industrial data present nonlinear characteristics and may require more sophisticated regression models to an adequate fit. In this project, we propose the development and analysis of mixed-effects elliptical models, linear and nonlinear, as a form of obtaining estimates with interesting properties, as robustness against outlying observations and little sensitivity to various kinds of perturbations. This research theme includes the mean-covariance modeling, usually considered when there are heteroscedasticity patterns in the data, as well as the development of validation and diagnostic tools for the proposed models. Moreover, it is fairly appropriate to discuss the form of inclusion and interpretation of the random effects into the nonlinear models and the hypothesis testing for variance components, as well as the assessment of the estimators properties and the estimation methods comparison. Several applications with real data sets will be considered. Some appropriate references are, for instance, Russo (2009) [Russo, C. M., Paula, G. A. & Aoki, R. (2009), 'Influence diagnostics in nonlinear mixedeffectselliptical models', Computational Statistics & Data Analysis 53, 4143-4156], Russo (2010) [Russo, C. M. (2010), 'Modelos nÜao lineares elípticos para dados correlacionados', Tese de doutorado. IME USP] and Russo, C. M., Aoki, R. & Paula, G. A. (2011), 'Assessment of variance components in nonlinear mixed-effects elliptical models', TEST (Madrid) pp. DOI: 10.1007/s11749-011-0262-2. (AU)