Can you trust the parametric standard errors in nonlinear least squares? Yes, with provisos.

Item request has been placed! ×
Item request cannot be made. ×
loading   Processing Request
Read More Add to Saved list
  • Author(s): Tellinghuisen J;Tellinghuisen J
  • Source:
    Biochimica et biophysica acta. General subjects [Biochim Biophys Acta Gen Subj] 2018 Apr; Vol. 1862 (4), pp. 886-894. Date of Electronic Publication: 2017 Dec 29.
  • Publication Type:
    Journal Article
  • Language:
    English
  • Additional Information
    • Source:
      Publisher: Elsevier Country of Publication: Netherlands NLM ID: 101731726 Publication Model: Print-Electronic Cited Medium: Print ISSN: 0304-4165 (Print) Linking ISSN: 03044165 NLM ISO Abbreviation: Biochim Biophys Acta Gen Subj Subsets: MEDLINE
    • Publication Information:
      Original Publication: Amsterdam : Elsevier
    • Subject Terms:
      Algorithms* ; Computer Simulation* ; Least-Squares Analysis* ; Monte Carlo Method*; Calorimetry/methods ; Enzymes/metabolism ; Humans ; Kinetics ; Reproducibility of Results
    • Abstract:
      Background: Questions about the reliability of parametric standard errors (SEs) from nonlinear least squares (LS) algorithms have led to a general mistrust of these precision estimators that is often unwarranted.
      Methods: The importance of non-Gaussian parameter distributions is illustrated by converting linear models to nonlinear by substituting e A , ln A, and 1/A for a linear parameter a. Monte Carlo (MC) simulations characterize parameter distributions in more complex cases, including when data have varying uncertainty and should be weighted, but weights are neglected. This situation leads to loss of precision and erroneous parametric SEs, as is illustrated for the Lineweaver-Burk analysis of enzyme kinetics data and the analysis of isothermal titration calorimetry data.
      Results: Non-Gaussian parameter distributions are generally asymmetric and biased. However, when the parametric SE is <10% of the magnitude of the parameter, both the bias and the asymmetry can usually be ignored. Sometimes nonlinear estimators can be redefined to give more normal distributions and better convergence properties.
      Conclusion: Variable data uncertainty, or heteroscedasticity, can sometimes be handled by data transforms but more generally requires weighted LS, which in turn require knowledge of the data variance.
      General Significance: Parametric SEs are rigorously correct in linear LS under the usual assumptions, and are a trustworthy approximation in nonlinear LS provided they are sufficiently small - a condition favored by the abundant, precise data routinely collected in many modern instrumental methods.
      (Copyright © 2018 Elsevier B.V. All rights reserved.)
    • Contributed Indexing:
      Keywords: Estimation precision; ITC; Isothermal titration calorimetry; Lineweaver-Burk; Michaelis Menten; Nonlinear least squares; Weighted least squares
    • Accession Number:
      0 (Enzymes)
    • Publication Date:
      Date Created: 20180101 Date Completed: 20180426 Latest Revision: 20180920
    • Publication Date:
      20231215
    • Accession Number:
      10.1016/j.bbagen.2017.12.016
    • Accession Number:
      29289616