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Robust two-stage estimation in hierarchical nonlinear models.

Publication ,  Journal Article
Yeap, BY; Davidian, M
Published in: Biometrics
March 2001

Hierarchical models encompass two sources of variation, namely within and among individuals in the population; thus, it is important to identify outliers that may arise at each sampling level. A two-stage approach to analyzing nonlinear repeated measurements naturally allows parametric modeling of the respective variance structure for the intraindividual random errors and interindividual random effects. We propose a robust two-stage procedure based on Huber's (1981, Robust Statistics) theory of M-estimation to accommodate separately aberrant responses within an experimental unit and subjects deviating from the study population when the usual assumptions of normality are violated. A toxicology study of chronic ozone exposure in rats illustrates the impact of outliers on the population inference and hence the advantage of adopting the robust methodology. The robust weights generated by the two-stage M-estimation process also serve as diagnostics for gauging the relative influence of outliers at each level of the hierarchical model. A practical appeal of our proposal is the computational simplicity since the estimation algorithm may be implemented using standard statistical software with a nonlinear least squares routine and iterative capability.

Duke Scholars

Published In

Biometrics

DOI

ISSN

0006-341X

Publication Date

March 2001

Volume

57

Issue

1

Start / End Page

266 / 272

Location

England

Related Subject Headings

  • Statistics & Probability
  • Serotonin
  • Respiratory System
  • Rats
  • Ozone
  • Nonlinear Dynamics
  • Least-Squares Analysis
  • Biometry
  • Animals
  • Algorithms
 

Citation

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Yeap, B. Y., & Davidian, M. (2001). Robust two-stage estimation in hierarchical nonlinear models. Biometrics, 57(1), 266–272. https://doi.org/10.1111/j.0006-341x.2001.00266.x
Yeap, B. Y., and M. Davidian. “Robust two-stage estimation in hierarchical nonlinear models.Biometrics 57, no. 1 (March 2001): 266–72. https://doi.org/10.1111/j.0006-341x.2001.00266.x.
Yeap BY, Davidian M. Robust two-stage estimation in hierarchical nonlinear models. Biometrics. 2001 Mar;57(1):266–72.
Yeap, B. Y., and M. Davidian. “Robust two-stage estimation in hierarchical nonlinear models.Biometrics, vol. 57, no. 1, Mar. 2001, pp. 266–72. Pubmed, doi:10.1111/j.0006-341x.2001.00266.x.
Yeap BY, Davidian M. Robust two-stage estimation in hierarchical nonlinear models. Biometrics. 2001 Mar;57(1):266–272.
Journal cover image

Published In

Biometrics

DOI

ISSN

0006-341X

Publication Date

March 2001

Volume

57

Issue

1

Start / End Page

266 / 272

Location

England

Related Subject Headings

  • Statistics & Probability
  • Serotonin
  • Respiratory System
  • Rats
  • Ozone
  • Nonlinear Dynamics
  • Least-Squares Analysis
  • Biometry
  • Animals
  • Algorithms