Cage of covariance in calibration modeling: Regressing multiple and strongly correlated response variables onto a low rank subspace of explanatory variables

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  • Carl Emil Eskildsen
  • Tormod Næs
  • Peter B. Skou
  • Lars Erik Solberg
  • Katinka R. Dankel
  • Silje A. Basmoen
  • Jens Petter Wold
  • Siri S. Horn
  • Borghild Hillestad
  • Nina A. Poulsen
  • Mette Christensen
  • Theo Pieper
  • Nils Kristian Afseth
  • Engelsen, Søren Balling

In analytical chemistry, multivariate calibration is applied when substituting a time-consuming reference measurement (based on e.g. chromatography) with a high-throughput measurement (based on e.g. vibrational spectroscopy). An average error term, of the response variable, is often used to evaluate the performance of a calibration model. However, indirect relationships, between the response and explanatory variables, may be used for calibration. In such cases, model validity cannot necessarily be determined solely by the average error term. One should also consider the use of the models, as well as the validity of the indirect relationships in future samples. If the analyte of interest is partly quantified from signals of interfering compounds, then these interfering compounds will play a hidden role in the calibration. This hidden role may affect future use of the calibration model as strong covariance relationships between analyte estimates and interfering compounds may be imposed. Hence, such model cannot detect changes in the relationship between the analyte and interfering compounds. The problem is called the cage of covariance. This paper discusses the concept cage of covariance and possible consequences of applying models exposed to this issue.

TidsskriftChemometrics and Intelligent Laboratory Systems
Antal sider7
StatusUdgivet - 2021

Bibliografisk note

Funding Information:
For funding we acknowledge the Norwegian Agricultural Food Research Foundation through the project FoodSMaCK – Spectroscopy, Modelling & Consumer knowledge, No. 262308/F40 . Furthermore, the position of the first author is currently funded via the TooCOLD project (grant number 15506 ), which is (partly) financed by the Netherlands Organization of Scientific Research (NWO) via the TTW Open Technology Programme.

Publisher Copyright:
© 2021 The Author(s)

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