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The Statistical Analysis of Compositional Data
Abstract
Summary: The simplex plays an important role as sample space in many practical situations where compositional data, in the form of proportions of some whole, require interpretation. It is argued that the statistical analysis of such data has proved difficult because of a lack both of concepts of independence and of rich enough parametric classes of distributions in the simplex. A variety of independence hypotheses are introduced and interrelated, and new classes of transformed-normal distributions in the simplex are provided as models within which the independence hypotheses can be tested through standard theory of parametric hypothesis testing. The new concepts and statistical methodology are illustrated by a number of applications.
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Cites
An Algorithm for Least-Squares Estimation of Nonlinear Parameters
Marquardt, D. W. (1963) · Journal of the Society for Industrial and Applied Mathematics · doi:10.1137/0111030 · Cited by 30,728
Statistical Laws of Family Expenditure
Working, H. (1943) · Journal of the American Statistical Association · doi:10.1080/01621459.1943.10501775 · Cited by 439
Research works printed but not linked: 49
- Aitchison, 1981, A new approach to null correlations of proportions, J. Math. Geol., 13, 175, 10.1007/BF01031393 · DOI
- Aitchison, 1981, Distributions on the simplex for the analysis of neutrality, 147, 10.1007/978-94-009-8549-0_11 · DOI
- Aitchison, 1981, Some distribution theory related to the analysis of subjective performance in inferential tasks, 363, 10.1007/978-94-009-8552-0_29 · DOI
- Aitchison, 1976, Statistical diagnosis when the cases are not classified with certainty, Biometrika, 63, 1, 10.1093/biomet/63.1.1 · DOI
- Aitchison, 1957, The Lognormal Distribution.
- Aitchison, 1980, Logistic-normal distributions: some properties and uses, Biometrika, 67, 261, 10.2307/2335470 · DOI · Paper page
- Andrrson, 1972, Separate sample logistic discrimination, Biometrika, 59, 19, 10.1093/biomet/59.1.19 · DOI · Paper page
- Andrews, 1973, Methods for assessing multivariate normality, 95
- Box, 1964, The analysis of transformations (with discussion), J. R. Statist. Soc. B, 26, 211, 10.1111/j.2517-6161.1964.tb00553.x · DOI · Paper page
- Brown, 1972, Models of consumer behaviour, Econ. J., 82, 177
- Chayes, 1960, On correlations between variables of constant sum, J. Geophys. Res., 65, 4185, 10.1029/JZ065i012p04185 · DOI
- Chayes, 1962, Numerical correlation and petrographic variation, J. Geol., 70, 440, 10.1086/626835 · DOI
- Chayes, 1971, Ratio Correlation.
- Chayes, 1966, An approximate statistical test for correlations between proportions, J. Geol., 74, 692, 10.1086/627204 · DOI
- Coakley, 1968, Sedimentation in an Arctic lake, J. Sedimentary Petrology, 38, 1290
- Connor, 1969, Concepts of independence for proportions with a generalization of the Dirichlet distribution, J. Amer. Statist. Assoc., 64, 194, 10.1080/01621459.1969.10500963 · DOI
- Cox, 1966, Some procedures associated with the logistic qualitative response curve, 57
- Cox, 1970, The Analysis of Binary Data.
- Darroch, 1969, Null correlations for proportions, J. Math. Geol., 3, 467
- Darroch, 1974, F-independence and null correlations of continuous, bounded-sum, positive variables, J. R. Statist. Soc. B, 36, 467, 10.1111/j.2517-6161.1974.tb01023.x · DOI
- Darroch, 1970, Null correlations for proportions II, J. Math. Geol., 2, 307, 10.1007/BF02312478 · DOI
- Darroch, 1971, A characterization of the Dirichlet distribution, J. Amer. Statist. Assoc., 66, 641, 10.1080/01621459.1971.10482324 · DOI
- Darroch, 1978, No-association of proportions, J. Math. Geol., 10, 361, 10.1007/BF01031740 · DOI
- Dawid, 1979, Conditional independence in statistical theory (with discussion), J. R. Statist. Soc. B, 41, 1, 10.1111/j.2517-6161.1979.tb01052.x · DOI · Paper page
- Day, 1967, A general maximum likelihood discriminant, Biometrics, 23, 313, 10.2307/2528164 · DOI
- Deaton, 1978, Specification and testing in applied demand analysis, Econ. J., 88, 524, 10.2307/2232051 · DOI
- Deaton, 1980, Economics and Consumer Behavior., 10.1017/CBO9780511805653 · DOI · Paper page
- Gnanadesikan, 1972, Robust estimates, residuals and outlier detection with multiresponse data, Biometrics, 28, 81, 10.2307/2528963 · DOI · Paper page
- Houthakker, 1960, Additive preferences, Econometrica, 28, 244, 10.2307/1907719 · DOI
- James, 1975, Multivariate distributions which have beta conditional distributions, J. Amer. Statist. Assoc., 70, 681
- James, 1981, Distributions associated with neutrality properties for random proportions, 125, 10.1007/978-94-009-8549-0_9 · DOI
- James, 1980, A new characterization of the Dirichlet distribution through neutrality, Ann. Statist., 8, 183, 10.1214/aos/1176344900 · DOI
- Jeffreys, 1961, Theory of Probability.
- Johnson, 1949, Systems of frequency curves generated by methods of translation, Biometrika, 36, 149, 10.1093/biomet/36.1-2.149 · DOI · Paper page
- Johnson, 1972, Distributions in Statistics. Continuous Multivariate Distributions.
- Kaiser, 1962, Composition and origin of glacial till Mexico and Kasoog quadrangles, New York, J. Sedimentary Petrology, 32, 502
- Leonard, 1973, A Bayesian method for histograms, Biometrika, 59, 581, 10.1093/biomet/59.3.581 · DOI
- Leser, 1976, Income, household size and price changes 1953-1973, Oxford Bull. Econ. Statist., 38, 1, 10.1111/j.1468-0084.1976.mp38001001.x · DOI
- McAlister, 1879, The law of the geometric mean, Proc. R. Soc., 29, 367
- Morrison, 1976, Multivariate Statistical Methods.
- Mosimann, 1962, On the compound multinomial distribution, the multivariate β-distribution and correlations among proportions, Biometrika, 49, 65
- Mosimann, 1970, Size allometry: size and shape variables with characterizations of the lognormal and generalized gamma distributions, J. Amer. Statist. Assoc., 65, 630, 10.1080/01621459.1970.10481136 · DOI · Paper page
- Mosimann, 1975, Statistical problems of size and shape. I. Biological applications and basic theorems, 187
- Mosimann, 1975, Statistical problems of size and shape. II. Characterizations of the lognormal, gamma and Dirichlet distributions, 219
- Pearson, 1897, Mathematical contributions to the theory of evolution. On a form of spurious correlations which may arise when indices are used in the measurement of organs, Proc. R. Soc., 60, 489
- Sarmanov, 1959, On the correlation of percentage values, Doklady Akad. Nauk. SSSR, 126, 22
- Stephens, 1974, EDF statistics for goodness of fit and some comparisons, J. Amer. Statist. Assoc., 69, 730, 10.1080/01621459.1974.10480196 · DOI · Paper page
- Thompson, 1972, Major element chemical variation in the Eocene lavas of the Isle of Skye, Scotland, J. Petrology, 13, 219, 10.1093/petrology/13.2.219 · DOI
- Wilks, 1938, The large-sample distribution of the likelihood ratio for testing composite hypotheses, Ann. Math. Statist., 9, 60, 10.1214/aoms/1177732360 · DOI
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Metadata
- Authors
- Aitchison, J.
- Venue
- Journal of the Royal Statistical Society Series B: Statistical Methodology
- Publisher
- Oxford University Press (OUP)
- Published
- 1982-01-01
- Volume
- 44
- Issue
- 2
- Pages
- 139-160
- ISSN
- 1369-7412 (ISSN-L)
- 1467-9868
- OpenAlex
- W2904250115
- Cited by
- 3,405
- References
- 2
- FWCI
- 8.05
- Type
- journal article
- Language
- en
- Open access
- closed
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