The advantages behind the efforts of performing higher-order calibration methods - A case study

Background: Across numerous investigations delved into second- and higher-order data, an undoubted finding emerges: models based on such data can effectively exploit the second-order advantage. However, whether further benefits can be achieved by modeling data of higher dimensions remains a subject of inquiry. In this regard, a prevailing question emerges in third-order data-based applications regarding the fundamental need to increase the data dimension and, hence, the data analysis complexity. This study aims to provide meaningful evidence to support the advantages inherent in employing third-order calibration methods despite the associated efforts, such as instrumentation and data analysis complexity. Results: This study compares the analytical performance achieved using a third-order calibration method with those obtained from most of the possible second-order calibration approaches derived from the same dataset. This work delves into the structural properties of the data, modeling limitations, and analytical characteristics associated with each model. Additionally, it includes a comprehensive statistical comparison of the models based on their recovery performance. First, the outcomes demonstrate the importance of capitalizing on all available chemical information and harnessing the full potential of data to maximize its benefits. Moreover, the results provide evidence that asserts the fact that third-order calibration methods bring the opportunity to increase the number of analytes that can be simultaneously determined, notwithstanding the need for more tedious experimental protocols, specialized instrumentation (sometimes), and quite complex data analysis. Significance: this research marks the first extensive comparison of third-order data calibration models with possible second-order calibration methods. Moreover, this work pioneers the incorporation of highly challenging non-multilinear data. The advancements detailed in this study emphasize the advantages of third-order data acquisition, notwithstanding the need for more tedious experimental protocols, specialized instrumentation (sometimes), and quite complex data analysis.