Diagnosing the cage of covariance to increase understanding and robustness of spectroscopic calibration models

When vibrational spectroscopy is used for quantification purposes, multivariate analysis is often used to extract information from covariances between the spectra and any given reference values. In complex samples, there is a high risk that the constituents covary with each other. In such scenarios many methods may confuse the analytes and use signal from several analytes, rather than just the analyte of interest. While this allows the method to use more signal, and thus have a better effective signal-to-noise ratio, it also makes them less robust to changes to the chemical composition in the samples. This effect has been termed the cage of covariance. In order to avoid cage of covariance to affect predictive performances, it is highly important to have simple diagnostic tools to analyze and review this effect. Therefore, in the present paper, a systematic overview of tools for diagnosing and quantifying the cage of covariance in spectroscopic calibration models is provided. A collection of previously published methods with some expansions is provided, as well as two completely new tools: covariance ratio and virtual spiking. Practical applications of the tools on three different datasets are also shown.