Estimation of loss on ignition values of the magnesite minerals using robust multiple regression

Abstract

Magnesite is an ore used in the production of a wide variety of industrial minerals and compounds and magnesium metal, as well as its alloys. The main components of magnesite are MgO and CO₂. However, magnesite, which is not generally observed in nature as pure, contains certain amounts of SiO₂, CaO, and Fe₂O₃. The loss on ignition (LOI) value in magnesite minerals largely depends on the CO₂ content. This study aims to develop a model that estimates the LOI values of magnesite minerals by using SiO₂, MgO, CaO, and Fe₂O_3tot data obtained from the geochemical analysis. Measurement of the LOI can provide important information not only for calculating the amount of volatiles in magnesite, but also about the acquisition of the element magnesium. With the estimation of LOI values, samples will not need to be subjected to LOI analysis. The data used in this study were compiled from the literature and information about the study areas, deposit types, analysis methods and the laboratory/device names was presented as supplementary material. The multivariate linear regression model was applied to represent the relationship between the LOI and these major oxides. A global independent data set comprising 170 observations was used to validate the proposed model. The preliminary analysis of the data is discussed in detail to improve the quality of the analysis. In the first step, the OLS estimation method is implemented to estimate the unknown parameters. Then, model assumptions are tested. Due to the existence of outliers, violation of the assumptions can lead to the misuse of the OLS method. In such cases, obtaining reliable estimates depends on strong estimators such as robust estimators, which are resistant to the outliers. Robust M-estimation methods can be used as effective tools for this purpose. For this reason, in the final step, we consider a robust M-estimation method based on Huber, Tukey, and Hampel objective functions. The results of OLS and robust regression methods, including parameter estimates, standard errors, residual standard error, and weighted R² are presented as a comparison. The validity of the models and the importance of each explanatory variable to the relationship are also investigated. According to the residual standard error (RSE) which is a way to measure the standard deviation of the residuals in a regression model, and ${R}_W^2$ values, a robust M- estimation method based on all three considered objective functions produces more accurate results in comparison with the outcomes of the conventional OLS method. In particular, the robust estimation method based on the Tukey objective function has the smallest RSE and largest ${R}_W^2$ among the others. It is observed that deleting a few outlying points has a big impact on the regression results. In this study, a multi-linear relationship between the main oxide values and LOI was determined. As a result, an estimation model with 91% accuracy and an RSE value of 0.283 was proposed. In addition, some relationships were established between the outliers and the determination of the ranges of major oxide values in the magnesite mineral. Our results suggest that robust M-estimation can provide efficient and stable estimates when analyzing geochemical data that may contain outliers. The application of the multivariate regression analysis has been confirmed to estimate LOI by using SiO₂, MgO, CaO, and Fe₂O_3tot as a new approach. This additional field investigation has shown promising results. Also, we recommend that this study can be improved by using more data and considering different magnesite deposit types.