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As the exploration of Mars and other solar system bodies becomes more prevalent, the importance of accurate methods in chemical analyses has increased. The use of laser‐induced breakdown spectroscopy (LIBS) in such analyses requires that well understood and accurate statistical methods exist for appropriate interpretation of resulting spectra. Many multivariate techniques have been developed for the elemental quantification of LIBS; however, each still has its limitations. In an endeavor to improve upon existing methodologies, a new algorithm is proposed using the ChemCam preflight calibration dataset and a dataset from the characterization of a LIBS/Raman sensor prototype developed at York University. The algorithm which was developed in this work is a linear mixture model within a submodel clustering framework. The cross validation and test results of the model on both datasets were reported using various metrics for each element under consideration (root mean square error, relative standard deviation, and R2 value). The algorithm was subsequently compared with other well established chemometric models on both datasets, such as principal component regression, partial least square regression, and ordinary least squares regression. Further validation of the algorithm was achieved by comparing the results presented herein to previously published results on the ChemCam data. The samples in each dataset are highly representative of Martian geology, which, given the overwhelming success of the algorithm on both datasets, suggests that subsequent implementation of the proposed algorithm on larger databases may have significant implications for Martian geochemical analyses and for planetary exploration as a whole. One of the principle requirements as exploration to space becomes more common is the biological and geochemical analysis of planets. LIBS has been used for qualitative and quantitative elemental analyses on Mars, and is likely to continue being used. In order, however, for instruments like LIBS to reach their full potential, accurate chemometric techniques are necessary. In this work, we propose a novel framework for the elemental quantification of geological samples analyzed by LIBS. [ABSTRACT FROM AUTHOR]