Logratios and natural laws in compositional data analysis

Mathematical Geology

Volumn 31, Issue 5, 1999, Pages 563-580

  Aitchison, John ^a  

^a UNIVERSITY OF GLASGOW   (United Kingdom)

Author keywords

Logcontrast principal component analysis; Raw correlation misinterpretation; Subcompositional coherence; Subcompositional hypotheses; Variability of olivines

Indexed keywords

GEOCHEMISTRY; PRINCIPAL COMPONENT ANALYSIS; STATISTICAL ANALYSIS;

EID: 0032768141     PISSN: 08828121     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1007568008032     Document Type: Article

References (56)

1. Aitchison, J., 1981, A new approach to null correlations of proportions: Math. Geology, v. 13, no. 5, p. 175-189.
2. Aitchison, J., 1982, The statistical analysis of compositional data (with discussion): Jour. Roy Statist. Soc., v. B44, no. 2, p. 139-177.
3. Aitchison, J., 1983, Principal component analysis of compositional data: Biometrika, v. 70, no. 1, p. 57-65.
4. Aitchison, J., 1986, The statistical analysis of compositional data: Chapman and Hall, London, 416 p.
5. Aitchison, J., 1997, The one hour course in compositional data analysis, or Compositional data analysis is easy, in V. Pawlowsky-Glahn, ed., Proceedings of IAMG98, The Third Annual Conference of the International Association for Mathematical Geology: Universitat Politècnica de Catalunya, Barcelona, p. 3-35.
6. Aitchison, J., 1999, Differential perturbation processes for compositional data analysis, in preparation.
7. Aitchison, J., and Thomas, C. W., 1998, Differential perturbation processes: a tool for the study of compositional processes, in Buccianti, A., Nardi G., and Potenza, R., eds., Proceedings of IAMG98, The Fourth Annual Conference of the International Association for Mathematical Geology: De Frede, Naples, p. 499-504.
8. Anderson, B., 1997, Potential problems in the characterisation of VHMS deposits using the Zn ratio, in V. Pawlowsky-Glahn, ed., Addendum to Proceedings of IAMG97, The Third Annual Conference of the International Association for Mathematical Geology: Universitat Politècnica de Catalunya, Barcelona, p. 1-10.
9. Allan, J. F., Satiza, R., Perefit, M. R., Fornart, D. J., and Sack, R. O., 1989, Petrology of lavas from the Lamont Seamont Chain and adjacent East Pacific Rise, 10° N: Jour. Petrology, v. 30, no. 5, p. 1245-1298.
10. Barcelo, C., Pawlowsky, V., and Grunsky, E., 1996, Some aspects of transformations of compositional data and the identification of outliers: Math. Geology, v. 28, no. 4, p. 501-518.
11. Barcelo-Vidal, C., Pawlowsky-Glahn, V., and Grunsky, E. C., 1997, A critical approach to the Jensen diagram for the classification of a volcanic sequence, in V. Pawlowsky-Glahn, ed., Proceedings of IAMG97, The Third Annual Conference of the International Association for Mathematical Geology: Universitat Politècnica de Catalunya, Barcelona, p. 117-122.
12. Beard, J. S., and Day, H. W., 1988, Petrology and emplacement of reversely zoned gabbrodiorite plutons in the Smartville Complex, Northern California: Jour. Petrology, v. 29, no. 5, p. 965-995.
13. Box, G. E. P., and Cox, D. R., 1964, The analysis of transformations: Jour. Roy. Statist. Soc., v. B26, no. 2, p. 211-542.
14. Buccianti, A., 1997, Multivariate analysis to investigate Cl distribution in rocks from different settings: Math. Geology, v. 29, no. 3, p. 349-359.
15. Buccianti, A., Vaselli, G., and Szabo, Cs., 1997, Textural and chemical characterization of clinopyroxenes from ultramafic and granulaite xenoliths of the Carpathian-Pannonian region (Eastern Europe) by multivariate analysis, in V. Pawlowsky-Glahn, ed., Proceedings of IAMG97, The Third Annual Conference of the International Association for Mathematical Geology: Universitat Politècnica de Catalunya, Barcelona, p. 123-128.
16. Cardenas, A. A., Girty, G. H., Harison, A. D., Lahren, M. M., Knaack, C., and Johnson, D., 1986: Assessing differences in compositions between low metamorphic grade mudstones and high-grade schists using logratio techniques, Jour. Geology, v. 104, p. 279-293.
17. Chai, G., and Naldrett, A. J., 1992, The Jinchuan ultramafic intrusion: Cumulate of a high-Mg basaltic magma: Jour. Petrology, v. 33, no. 2, p. 277-303.
18. Chayes, F., 1949, On ratio correlation in petrography: Jour. Geology, v. 57, no. 3, p. 239-254.
19. Chayes, F., 1960, On correlation between variables of constant sum: Jour. Geophys. Research, v. 65, no. 12, p. 4185-4193.
20. Chayes, F., 1962, Numerical correlation and petrographic variation: Jour. Geology, v. 70, no. 4, p. 440-552.
21. Chayes, F., 1971, Ratio correlation: A manual for students of petrology and geochemistry: University of Chicago Press, Chicago, 99 p.
22. Chayes, F., and Kruskal, W., 1966, An approximate statistical test for correlation between proportions: Math. Geology, v. 74, no. 5, p. 692-702.
23. Cole, D. R., and Drummond, S. E., 1986, The effect of transport and boiling on Ag/Au ratios in hydrothermal solutions. A preliminary assessment and possible implications for the formation of epithermal precious-metal deposits: Jour. Geochemical Exploration, v. 25, no. 1, p. 45-79.
24. Davis, J. C., 1986, Statistics and data analysis in geology: Wiley, New York, 646 p.
25. Deer, W. A., Howie, R. A., and Zussman, J., 1982, Rock-forming minerals: Orthosilicates. Longman, London, 919 p.
26. Edwards, A. W. F., 1977, Foundations of mathematical genetics: Cambridge University Press, Cambridge, 119 p.
27. Eissen, J.-P., Juteau, T., Joron, J.-L., Dupre, B., Humler, E., and Al'Mukhameov, A., 1989, Petrology and geochemistry of basalts from the Red Sea Axial Drift at 18° North: Jour. Petrology, v. 30, no. 4, p. 791-839.
28. Fan, Q., and Hooper, P. R., 1989, The mineral chemistry of ultramafic xenoliths of Eastern China: Implications for upper mantle composition and the paleogeotherms: Jour. Petrology, v. 30, no. 5, p. 1117-1158.
29. Fan, Q., and Hooper, P. R., 1991. The Cenozoic basaltic rocks of Eastern China: Petrology and chemical composition: Jour. Petrology, v. 32, no. 4, p. 765-810.
30. Grunsky, E. C., Easton, R. M., Thurston, P. C., and Jensen, L. S., 1992, Characterization and statistical classification of Archean volcanic rocks of the Superior Province using major element geochemistry: Geology of Canada. Ontario Geological Survey Special Volume 4, p. 1397-1438.
31. Houthakker, H. S., 1960, Additive preferences: Econometrica, v. 2, p. 244-256.
32. Iyengar, M., and Day, D., 1997, Box-Cox transformations in Bayesian analysis of compositional data, in V. Pawlowsky-Glahn, ed., Proceedings of IAMG97, The Third Annual Conference of the International Association for Mathematical Geology: Universitat Politècnica de Catalunya, Barcelona, Addendum, p. 40-47.
33. Kamenetsky, V. S., Sobolev, A. V., Joron, J. L., and Semet, M. P., 1995, Petrology and geochemistry of cretaceous ultramafic volcanics from Eastern Kamchatka: Jour. Petrology, v. 36, no. 3, p. 637-662.
34. Krauskopf, K. B., 1979, Introduction to geochemistry: McGraw-Hill, New York, 617 p.
35. Krumbein, C., 1962, Open and closed number systems: stratigraphic mapping: Bull. Amer. Assoc. Petrol. Geologists, v. 46, p. 322-337.
36. Le Maitre, R. W., 1982, Numerical petrography: Elsevier, Amsterdam, 281 p.
37. Martin-Fernandez, J. A., Barcelo-Vidal, C., and Pawlowsky-Glahn, V., 1997, Different classifications of the Darss-Sill data set based on mixture models for compositional data, in V. Pawlowsky-Glahn, ed., Proceedings of IAMG97, The Third Annual Conference of the International Association for Mathematical Geology: Universitat Politècnica de Catalunya, Barcelona, p. 151-156.
38. Mosimann, J. E., 1962, On the compound multinomial distribution, the multivariate β-distribution and correlations among proportions: Biometrika, v. 49, no. 1, p. 63-82.
39. Mosimann, J. E., 1963, On the compound negative binomial distribution and correlations among inversely sampled pollen counts: Biometrika, v. 50, no. 1, p. 47-54.
40. Pawlowsky, V., 1986, Räumliche Strukturanalyse and Schätzung ortsabhängiger Kompositionen mit Anwendungsbeispeilen aus der Geologie: unpublished dissertation, FB Geowissenschaften, Freie Universität Berlin, 120 p.
41. Pearson, K., 1897, Mathematical contributions to the theory of evolution: On a form of spurious correlation which may arise when indices are used in the measurements of organs: Proc. Roy. Soc., v. 60, p. 489-498.
42. Renner, R. M., 1991, An examination of the use of logratio transformations for the testing of endmember hypotheses: Math. Geology, v. 23, no. 4, p. 549-562.
43. Reyment, R. A., and Savazzi, S., 1999, A primier of multivariate statistical analysis in geology: in press.
44. Ridenour, G. S., and Giardino, J. R., 1995a, Logratio linear modelling of hydraulic geometry using indices of flow resistance as covariates: Geomorphology, v. 14, p. 65-72.
45. Ridenour, G. S., and Giardino, J. R., 1995b, Discriminant function analysis of compositional data: an example from hydraulic geometry: Physical Geography, v. 15, no. 5, p. 481-492.
46. Rock, N. M. S., 1988, Numerical petrology: Springer-Verlag, Berlin, 427 p.
47. Sarmanov, O. V., and Vistelius, A. B., 1959, On the correlation of peercentage values: Dokl. Akad. Nauk. SSSR, v. 126, p. 22-25.
48. Thomas, C. W., 1997, Closure, log-ratios and the journeyman geologist: A plea, in V. Pawlowsky-Glahn, ed., Addendum to Proceedings of IAMG97, The Third Annual Conference of the International Association for Mathematical Geology: Universitat Politècnica de Catalunya, Barcelona, p. 34-39.
49. Thomas, C. W., and Aitchison, J., 1997, Applications of logratios to the statistical analysis of the geochemistry of metamorphosed limestones from the Northern and Central Highlands of Scotland: The case for the Appin Group correlations: British Geological Survey Technical Report WA/98/03, 20 p.
50. Weltje, G. J., 1997, End-member modeling of compositional data: Numerical statistical algorithms for solving the explicit mixing problem: Math Geology, v. 29, no. 4, 503-549.
51. Woronow, A., 1987, A book review: The statistical analysis of compositional data by John Aitchison: Math. Geology, v. 19, no. 5, p. 579-581.
52. Woronow, A., 1997a, The elusive benefits of logratios, in V. Pawlowsky-Glahn, ed., Proceedings of IAMG97, The Third Annual Conference of the International Association for Mathematical Geology: Universitate Politècnica de Catalunya, Barcelona, p. 97-101.
53. Woronow, A., 1997b, Regression and discrimination analysis using raw compositional data - Is it really a problem?, in V. Pawlowsky-Glahn, ed., Proceedings of IAMG97, The Third Annual Conference of the International Association for Mathematical Geology: Universitate Politècnica de Catalunya, Barcelona, p. 157-162.
54. Woronow, A., 1997c, Calculating an equilibrium liquid-line of descent and determining a parental magma composition, in V. Pawlowsky-Glahn, ed., Proceedings of IAMG97, The Third Annual Conference of the International Association for Mathematical Geology: Universitat Politècnica de Catalunya, Barcelona, p. 129-132.
55. Woronow, A., and Love, K. M., 1990, Quantifying and testing differences among means of compositional data suites: Math. Geology, v. 22, no. 7, p. 837-852.
56. Zhou, D., 1997, Effect of logratio transformation on classifying of compositions, in V. Pawlowsky-Glahn, ed., Proceedings of IAMG97, The Third Annual Conference of the International Association for Mathematical Geology: Universitat Politècnica de Catalunya, Barcelona, p. 102-105.