A beta partial least squares regression model : diagnostics and application to mining data / Mauricio Hernán Huerta Aguiar.

Magíster en Estadística.

Partial least squares (PLS) regression is a multivariate technique developed to solve the problem of multicollinearity and/or high dimensionality related to explanatory variables in multiple linear regression. PLS regression has been widely applied assuming normality, but this assumption is often violated in different practical problems. Particularly, if the response variable follows an asymmetric distribution or it is bounded into an interval, normality should be discarded. For example, if this response variable is restricted to values between zero and one, a beta distribution is more suitable for PLS modeling than the normal distribution. We consider a beta PLS regression and its diagnostics for modeling the proportion of kaolinite, a clay mineral present in rocks which is measured by infrared spectroscopy with wavelengths. We propose a residual used in the generalized additive models for location scale and shape and the Cook and Mahalanobis distances as diagnostic tools for this model. We illustrate the proposed methodology with real-world mining data. The analyses and results provided in this study based on the beta PLS regression model and its diagnostics may be of interest for the Chilean mining sector and for the world mining industry.