Abstract
Each object of multivariate data distributed in a multidimensional space is characterised by a set of measurements corresponding to each variable. Obviously, as we have already seen (Chap. 9), if we are dealing with bivariate data corresponding to two variables, a plot on a piece of paper or computer screen can show their behaviour. Their graphical representation becomes difficult and, in fact, impossible when we want to visualise four or more dimensions. Therefore, we must learn alternate techniques for the handling of multivariate data. We describe the dimension-reducing multivariate technique of linear discriminant analysis (LDA) and illustrate it from agricultural chemistry data. One surprising result was that the isometric log-ratio transformation did not provide any improvement with respect to the use of concentration data. The chapter ends with the description of multiple linear regression exemplified from UV absorbance data.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Agrawal, S., Guevara, M., & Verma, S. P. (2008). Tectonic discrimination of basic and ultrabasic rocks through log-transformed ratios of immobile trace elements. International Geology Review, 50, 1057–1079.
Aitchison, J. (1986). The statistical analysis of compositional data. London, UK: Chapman and Hall.
Barnett, V., & Lewis, T. (1994). Outliers in statistical data. Chichester: Wiley.
Egozcue, J. J., Pawlowsky-Glahn, V., Mateu-Figueras, G., & Barceló-Vidal, C. (2003). Isometric logratio transformations for compositional data analysis. Mathematical Geology, 35, 279–300.
Miller, J. N., & Miller, J. C. (2005). Statistics and chemometrics for analytical chemistry (5th ed.). Essex, England: Pearson Prentice Hall.
Morrison, D. F. (1990). Multivariate statistical methods. New York: McGraw-Hill Publishing Co.
Phuong, T. D., Chuong, P. V., Khiem, D. T., & Kokot, S. (1999). Elemental content of Vietnamese rice. Part 1. Sampling, analysis and comparison with previous studies. Analyst, 124, 553–560.
Reyment, R. A., & Savazzi, E. (1999). Aspects of multivariate statistical analysis in geology. Amsterdam: Elsevier.
Verma, S. P. (2012). Geochemometrics. Revista Mexicana de Ciencias Geológicas, 29, 276–298.
Verma, S. P. (2015). Monte Carlo comparison of conventional ternary diagrams with new log-ratio bivariate diagrams and an example of tectonic discrimination. Geochemical Journal, 49, 393–412.
Verma, S. P., & Agrawal, S. (2011). New tectonic discrimination diagrams for basic and ultrabasic volcanic rocks through log-transformed ratios of high field strength elements and implications for petrogenetic processes. Revista Mexicana de Ciencias Geológicas, 28, 24–44.
Verma, S. P., & Armstrong-Altrin, J. S. (2013). New multi-dimensional diagrams for tectonic discrimination of siliciclastic sediments and their application to Precambrian basins. Chemical Geology, 355, 117–133.
Verma, S. P., & Díaz-González, L. (2012). Application of the discordant outlier detection and separation system in the geosciences. International Geology Review, 54, 593–614.
Verma, S. P., & Rivera-Gómez, M. A. (2017). Transformed major element based multidimensional classification of altered volcanic rocks. Episodes, 40, 295–303.
Verma, S. P., Verma, S. K., & Oliveira, E. P. (2015). Application of 55 multi-dimensional tectonomagmatic discrimination diagrams to Precambrian belts. International Geology Review, 57, 1365–1388.
Verma, S. P., Rivera-Gómez, M. A., Díaz-González, L., & Quiroz-Ruiz, A. (2016). Log-ratio transformed major-element based multidimensional classification for altered high-Mg igneous rocks. Geochemistry, Geophysics, Geosystems, 17, 4955–4972.
Verma, S. P., Verma, S. K., Rivera-Gómez, M. A., Torres-Sánchez, D., Díaz-González, L., Amezcua-Valdez, A., et al. (2018). Statistically coherent calibration of X-ray fluorescence spectrometry for major elements in rocks and minerals. Journal of Spectroscopy, 2018, 13, Article ID 5837214. https://doi.org/10.1155/2018/5837214.
Verma, S. P., Rosales-Rivera, M., Rivera-Gómez, M. A., & Verma, S. K. (2019). Comparison of matrix-effect corrections for ordinary and uncertainty weighted linear regressions and determination of major element mean concentrations and total uncertainties of 62 international geochemical reference materials from wavelength-dispersive X-ray fluorescence spectrometry. In Colloquium Spectroscopicum Internationale XLI (CSI XLI) and I Latin-American Meeting on Laser Induced Breakdown Spectroscopy (I LAMLIBS). Mexico City.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2020 Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Verma, S.P. (2020). Multivariate Data. In: Road from Geochemistry to Geochemometrics. Springer, Singapore. https://doi.org/10.1007/978-981-13-9278-8_10
Download citation
DOI: https://doi.org/10.1007/978-981-13-9278-8_10
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-13-9277-1
Online ISBN: 978-981-13-9278-8
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)