Interpretations abound about the geological process behind the global element abundance distributions on Mars. Mineralogical insight from infrared methods can complement elemental observations, but significant differences in spatial resolution between mineralogical and elemental maps have made this comparison challenging. Here we use CRISM global mineralogical summary product maps as input for a multi-variate model to predict the chemical abundance of the elements, Fe, K, Th, Cl, Si, H2O, Al, Ca and S. Excepting Ca, the variance of chemical maps is well predicted, with explained variance typically between 30-50 %. Both the statistical importance of each of the summary products in the model, and the model accuracy in different regions, are used to interpret geological processes that influence the relation between the CRISM and geochemical data. We have concluded that models for K and Th show that acidic aqueous alteration is a likely cause of enrichment of these elements in northern Acidalia. The enrichment of Fe in the northern lowlands is found to be inversely related with the mafic summary products, possibly indicating a distinct magmatic composition. The distribution of Si is best explained by dust mantling processes, with depleted silicon content in the dust-covered regions. The enrichment of the volatile elements H2O, Cl and S, especially in the vicinity of the Medusae Fossae formation, are best explained by volcanic degassing. The low accuracy of the Ca model is likely explained by either heterogeneity in the subsurface or the non-detection of feldspars, which are featureless in the CRISM wavelength range.