WE-ASCA: The Weighted-Effect ASCA for Analyzing Unbalanced Multifactorial Designs-A Raman Spectra-Based Example

Analyses of multifactorial experimental designs are used as an explorative technique describing hypothesized multifactorial effects based on their variation. The procedure of analyzing multifactorial designs is well established for univariate data, and it is known as analysis of variance (ANOVA) tests, whereas only a few methods have been developed for multivariate data. In this work, we present the weighted-effect ASCA, named WE-ASCA, as an enhanced version of ANOVA-simultaneous component analysis (ASCA) to deal with multivariate data in unbalanced multifactorial designs. The core of our work is to use general linear models (GLMs) in decomposing the response matrix into a design matrix and a parameter matrix, while the main improvement in WE-ASCA is to implement the weighted-effect (WE) coding in the design matrix. This WE-coding introduces a unique solution to solve GLMs and satisfies a constrain in which the sum of all level effects of a categorical variable equal to zero. To assess the WE-ASCA performance, two applications were demonstrated using a biomedical Raman spectral data set consisting of mice colorectal tissue. The results revealed that WE-ASCA is ideally suitable for analyzing unbalanced designs. Furthermore, if WE-ASCA is applied as a preprocessing tool, the classification performance and its reproducibility can significantly improve.