Calibration transfer by likelihood maximization: A standard-free approach capable of handling non-overlapping wavelength ranges

Abstract

Calibration transfer is useful when modeling data collected from different, yet similar, sources. This may occur when using spectrophotometers to monitor an industrial process. The objective of this method is to compensate for differences between the instruments and reduce any biases that may arise. Calibration transfer seeks to apply a multivariate model to a validation dataset that differs in some meaningful way from the calibration set. However, making robust calibration transfer models typically requires the user to acquire many observations in both datasets and ensure that some observations are present in both the calibration and validation datasets. Our novel methodology seeks to address these issues, which are often cumbersome in an industrial context. The proposed methodology is not a typical calibration transfer method but has the same role as it estimates the observations acquired from one X2 domain into another X1 domain. We implement a bootstrapping strategy to quantify the estimates of the spectra in the new domain and the uncertainty associated with them. These results are then combined with an inverse multivariate regression to predict the y values, which is known as the likelihood maximization inverse regression (LMIR) methodology. In this paper, we first present the algorithms used for estimation and prediction. The proposed method is tested on two real datasets and the results are compared with those of three other methods that are typically used to perform direct calibration, namely, partial least squares (PLS), powered PLS and direct LMIR. A comparison to calibration methods is made here to provide a reference for the results obtained and demonstrate the benefits of using our estimation model. These results reveal that the proposed methodology outperforms the standard predictive methods. Further, it is beneficial because it does not need standard samples and is capable of handling different wavelength ranges and variables.