Applications of Rasch modeling in chemometrics: Binary data analysis and analytical platform selection

Abstract

Often researchers make use of Principal Component Analysis and Partial Least Squares Regression, an unsupervised and a supervised method, respectively, to extract the chemical information in the shape of one or more latent variables. However, when the research question is qualitative and requires a figure of merit, these two models will primarily focus on the quantitative and continuous information present in the data. In these cases, a valid approach may be to dichotomize the data and to analyze the resulting non-linear data via Non-Linear Principal Component Analysis. However, the results of the method are not always easy to interpret due to the possible multidimensionality of the solution. Here we introduce an alternative framework, composed of Rasch modeling and Generalized Linear Mixed Effect Models, to extract information from multivariate binary chemical data with an underlying design of experiment. The model obtained by this framework provides information in a unidimensional representation that can be easily translated into one-dimensional action and control. Furthermore, we show that, through Generalized Linear Mixed Effect Models, it is possible to extend the Rasch model to its multilevel form, which enables the consideration of each random factor possibly present.