Quantifying TiO₂ abundance of lunar soils: Partial least squares and stepwise multiple regression analysis for determining causal effect

Abstract

Partial least squares (PLS) regression was applied to the Lunar Soil Characterization Consortium (LSCC) dataset for spectral estimation of TiO₂. The LSCC dataset was split into a number of subsets including the low-Ti, high-Ti, total mare soils, total highland, Apollo 16, and Apollo 14 soils to investigate the effects of interfering minerals and nonlinearity on the PLS performance. The PLS weight loading vectors were analyzed through stepwise multiple regression analysis (SMRA) to identify mineral species driving and interfering the PLS performance. PLS exhibits high performance for estimating TiO₂ for the LSCC low-Ti and high-Ti mare samples and both groups analyzed together. The results suggest that while the dominant TiO₂-bearing minerals are few, additional PLS factors are required to compensate the effects on the important PLS factors of minerals that are not highly corrected to TiO₂, to accommodate nonlinear relationships between reflectance and TiO₂, and to correct inconsistent mineral-TiO₂ correlations between the high-Ti and low-Ti mare samples. Analysis of the LSCC highland soil samples indicates that the Apollo 16 soils are responsible for the large errors of TiO₂ estimates when the soils are modeled with other subgroups. For the LSCC Apollo 16 samples, the dominant spectral effects of plagioclase over other dark minerals are primarily responsible for large errors of estimated TiO₂. For the Apollo 14 soils, more accurate estimation for TiO₂ is attributed to the positive correlation between a major TiO₂-bearing component and TiO₂, explaining why the Apollo 14 soils follow the regression trend when analyzed with other soils groups.

Keywords

lunar soils / LSCC dataset / TiO₂ abundance / partial least squares / stepwise multiple regression

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