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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Published on: July 3, 2020

Analysis of nonlinear regression models: a cautionary note.

Shyamal D Peddada1, Joseph K Haseman

  • 1Biostatistics Branch, National Institute of Environmental Health Sciences, National Institutes of Health, Research Triangle Park, NC 27709, USA. peddada@niehs.nih.gov

Dose-Response : a Publication of International Hormesis Society
|July 24, 2008
PubMed
Summary
This summary is machine-generated.

Maximum likelihood estimators (MLE) in nonlinear regression can lead to unreliable confidence intervals. Computer simulations show that linearized standard errors for MLE may underestimate true levels, requiring caution in their application.

Keywords:
confidence intervalcoverage probabilityvariance estimation

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Area of Science:

  • Statistics
  • Applied Sciences
  • Econometrics

Background:

  • Regression models are fundamental in applied sciences for analyzing relationships between variables.
  • Statistical inference often relies on maximum likelihood estimators (MLE) for regression parameters.

Purpose of the Study:

  • To evaluate the reliability of confidence intervals derived from linearized standard errors of MLE in nonlinear regression.
  • To assess whether these intervals achieve desired confidence levels.

Main Methods:

  • Computer simulations were employed to test the performance of confidence intervals.
  • Analysis focused on nonlinear regression models and maximum likelihood estimation.

Main Results:

  • Asymptotic Wald confidence intervals derived from linearized standard errors were found to be untrustworthy.
  • These intervals can underestimate the nominal confidence level, behaving liberally.

Conclusions:

  • Caution is advised when using standard linearized errors and associated confidence intervals for MLE in nonlinear models.
  • The findings highlight potential inaccuracies in statistical inferences under common methodologies.