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 esti- mating 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 re- quired 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 incon- sistent 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 es- timates when the soils are modeled with other subgroups. For the LSCC Apollo 16 samples, the domi- nant 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 posi- tive correlation between a major TiO2-bearing component and TiO2, explaining why the Apollo 14 soils