On a partial least squares regression model for asymmetric data with a chemical application in mining

Abstract

In chemometrical applications, covariates in regression models are often correlated, causing a collinearity problem that can be solved by partial least squares (PLS)regression. In addition, high dimensionality in the space of covariates is also a problem with more parameters than cases, a phenomenon usually found in chemical spectral data that can also be solved by PLS regression. The Birnbaum-Saunders distribution has theoretical justifications for modeling chemical data. In this paper, a new methodology based on PLS regression models is proposed considering a reparameterized Birnbaum-Saunders (RBS)distribution for the response, which is useful for describing asymmetric data frequently found in chemical phenomena. We estimate the RBS-PLS model parameters using the maximum likelihood method. A bootstrap approach is employed to obtain the optimal number of PLS components. Quantile residuals and Cook and Mahalanobis type distances are utilized for detecting possible anomalies in the modeling. We conduct perturbation studies to assess the performance of these diagnostic tools. The proposed methodology is applied to real-world kaolinite data and compared to other competing models. This provides a useful illustration of chemical analysis in the mining industry.