Critical factors limiting the interpretation of regression vectors in multivariate calibration

It is common to see published manuscripts and presentations making interpretive comments about correct or incorrect features of the regression vector obtained from multivariate-calibration methods. While model validation is crucial, a considerable body of literature casts doubt on the value of qualitative interpretation of the regression vector. Following a review of this literature, we discuss two simple examples, which illustrate the exceptionally complex behavior of the inverse calibration methods that dominate current chemometrics practice. We show that the behavior of regression vectors in inverse calibration is too complex to be interpreted transparently unless an unusual amount of system information is available. If explicit information about sensitivity and selectivity is desired, it should be quantified using conventional figures of merit.