Second-order bilinear calibration : the effects of vectorising the data matrices of the calibration set

N.M. Faber, J. Ferre, R. Boque, J.H. Kalivas

    Research output: Contribution to journalArticleAcademicpeer-review

    35 Citations (Scopus)

    Abstract

    In a groundbreaking paper, Linder and Sundberg [Chemometr. Intell. Lab. Syst. 42 (1998) 159] developed a statistical framework for the calibration of second-order bilinear data. Within this framework, they formulated three different predictor construction methods [J. Chemom. 16 (2002) 12], namely the so-called naïve method, the bilinear least squares (BLLS) method, and a refined version of the latter that takes account of the calibration uncertainty. Elsewhere [J. Chemom. 15 (2001) 743], a close relationship is established between the naïve method and the generalized rank annihilation method (GRAM) by comparing expressions for prediction variance. Here it is proved that the BLLS method can be interpreted to work with vectorised data matrices, which establishes an algebraic relationship with so-called unfold partial least squares (PLS) and unfold principal component regression (PCR). It is detailed how these results enable quantifying the effects of vectorising bilinear second-order data matrices on analytical figures of merit and variance inflation factors.
    Original languageEnglish
    Pages (from-to)107-116
    JournalChemometrics and Intelligent Laboratory Systems
    Volume63
    Issue number2
    DOIs
    Publication statusPublished - 2002

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