{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T01:25:13Z","timestamp":1773278713485,"version":"3.50.1"},"reference-count":40,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2009,4,1]],"date-time":"2009-04-01T00:00:00Z","timestamp":1238544000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Classif"],"published-print":{"date-parts":[[2009,4]]},"DOI":"10.1007\/s00357-009-9027-y","type":"journal-article","created":{"date-parts":[[2009,4,4]],"date-time":"2009-04-04T14:05:09Z","timestamp":1238853909000},"page":"29-54","source":"Crossref","is-referenced-by-count":66,"title":["Distributional Equivalence and Subcompositional Coherence in the Analysis of Compositional Data, Contingency Tables and Ratio-Scale Measurements"],"prefix":"10.1007","volume":"26","author":[{"given":"Michael","family":"Greenacre","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Paul","family":"Lewi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2009,4,5]]},"reference":[{"key":"9027_CR1","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1007\/BF00890330","volume":"22","author":"J Aitchison","year":"1980","unstructured":"AITCHISON, J. (1980), \u201cRelative Variation Diagrams for Describing Patterns of Variability in Compositional Data,\u201d Mathematical Geology, 22, 487\u2013512.","journal-title":"Mathematical Geology"},{"key":"9027_CR2","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1093\/biomet\/70.1.57","volume":"70","author":"J Aitchison","year":"1983","unstructured":"AITCHISON, J. (1983), \u201cPrincipal Component Analysis of Compositional Data\u201d, Biometrika, 70, 57\u201365.","journal-title":"Biometrika"},{"key":"9027_CR3","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-009-4109-0","volume-title":"The Statistical Analysis of Compositional Data","author":"J Aitchison","year":"1986","unstructured":"AITCHISON, J. (1986), The Statistical Analysis of Compositional Data, London: Chapman & Hall, reprinted in 2003 by Blackburn Press."},{"key":"9027_CR4","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1007\/BF00891269","volume":"24","author":"J Aitchison","year":"1992","unstructured":"AITCHISON, J.(1992), \u201cOn Criteria for Measures of Compositional Difference,\u201d Mathematical Geology, 24, 365\u201380.","journal-title":"Mathematical Geology"},{"key":"9027_CR5","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1023\/A:1007529726302","volume":"32","author":"J Aitchison","year":"2000","unstructured":"AITCHISON, J., BARCEL\u00d3-VIDAL, C., MARTIN-FERN\u00c1NDEZ, J.A., and PAWLOWSKY-GLAHN, V. (2000), \u201cLogratio Analysis and Compositional Distance,\u201d Mathematical Geology, 32, 271\u2013275.","journal-title":"Mathematical Geology"},{"key":"9027_CR6","doi-asserted-by":"crossref","first-page":"829","DOI":"10.1007\/s11004-005-7383-7","volume":"37","author":"J Aitchison","year":"2005","unstructured":"AITCHISON, J., and EGOZCUE, J.J. (2005), \u201cCompositional Data Analysis: Where Are We and Where Should We Be Heading?\u201d, Mathematical Geology, 37, 829\u2013850.","journal-title":"Mathematical Geology"},{"key":"9027_CR7","first-page":"375","volume":"51","author":"J Aitchison","year":"2002","unstructured":"AITCHISON, J., and GREENACRE, M.J. (2002), \u201cBiplots of Compositional Data,\u201d Applied Statistics, 51, 375\u2013392.","journal-title":"Applied Statistics"},{"key":"9027_CR8","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1080\/757582834","volume":"17","author":"MJ Baxter","year":"1990","unstructured":"BAXTER, M.J., COOL, H.E.M., and HEYWORTH, M.P. (1990), \u201cPrincipal Component and Correspondence Analysis of Compositional Data: Some Similarities,\u201d Journal of Applied Statistics, 17, 229\u2013235.","journal-title":"Journal of Applied Statistics"},{"key":"9027_CR9","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1007\/978-3-642-56181-8_21","volume-title":"Classification, Clustering and Data Analysis","author":"F Bavaud","year":"2002","unstructured":"BAVAUD, F. (2002), \u201cQuotient Dissimilarities, Euclidean Embeddability, and Huygens\u2019 Weak Principle,\u201d in Classification, Clustering and Data Analysis, eds. K. Jajuga, A. Sokolowski and H.-H.Bock, New York: Springer, pp. 195\u2013202."},{"key":"9027_CR10","doi-asserted-by":"crossref","first-page":"597","DOI":"10.1007\/978-3-642-17103-1_56","volume-title":"Classification, Clustering, and Data Mining Applications","author":"F Bavaud","year":"2004","unstructured":"BAVAUD, F. (2004), \u201cGeneralized Factor Analyses for Contingency Tables,\u201d in Classification, Clustering, and Data Mining Applications, eds. D. Banks, L. House, F.R. McMorris, P. Arabie and W. Gaul, New York: Springer, pp. 597\u2013606."},{"key":"9027_CR11","unstructured":"BEARDAH, C.C., BAXTER, M.J., COOL, H.E.M., and JACKSON, C.M. (2003), \u201cCompositional Data Analysis of Archaeological Glass: Problems and Possible Solutions,\u201d in: Proceedings of the First Compositional Data Analysis Workshop, Girona, Spain, http:\/\/ima.udg.edu\/Activitats\/CoDaWork03\/paper_baxter_Beardah2.pdf"},{"key":"9027_CR12","volume-title":"L\u2019Analyse des Donn\u00e9es, T\u00f4me I: La Classification, T\u00f4me II: L\u2019Analyse des Correspondances","author":"J-P Benz\u00e9cri","year":"1973","unstructured":"BENZ\u00c9CRI, J.-P. (1973), L\u2019Analyse des Donn\u00e9es, T\u00f4me I: La Classification, T\u00f4me II: L\u2019Analyse des Correspondances, Paris : Dunod."},{"key":"9027_CR13","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1080\/03610910600591875","volume":"35","author":"C CUADRAS","year":"2006","unstructured":"CUADRAS, C., CUADRAS, D., and GREENACRE, M.J. (2006), \u201cA Comparison of Methods for Analyzing Contingency Tables,\u201d Communications in Statistics Simulation and Computation, 35, 447\u2013459.","journal-title":"Communications in Statistics \u2013 Simulation and Computation"},{"key":"9027_CR14","first-page":"112","volume-title":"Visualization of Categorical Data","author":"C Cuadras","year":"1998","unstructured":"CUADRAS, C., and FORTIANA, J. (1998), \u201cVisualizing Categorical Data with Related Metric Scaling,\u201d in Visualization of Categorical Data, eds. J. Blasius and M.J. Greenacre, San Diego: Academic Press, pp. 112\u2013129."},{"key":"9027_CR15","doi-asserted-by":"crossref","first-page":"795","DOI":"10.1007\/s11004-005-7381-9","volume":"37","author":"JJ Egozcue","year":"2005","unstructured":"EGOZCUE, J.J., and PAWLOWSKY-GLAHN, V. (2005), \u201cGroups of Parts and Their Balances in Compositional Data Analysis,\u201d Mathematical Geology, 37, 795\u2013828.","journal-title":"Mathematical Geology"},{"key":"9027_CR16","first-page":"29","volume":"26","author":"B Escofier","year":"1978","unstructured":"ESCOFIER, B. (1978), \u201cAnalyse factorielle et distances r\u00e9pondant au principe d\u2019\u00e9quivalence distributionelle,\u201d Revue de Statistique Appliqu\u00e9e, 26, 29\u201337.","journal-title":"Revue de Statistique Appliqu\u00e9e"},{"key":"9027_CR17","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1093\/biomet\/58.3.453","volume":"58","author":"KR Gabriel","year":"1971","unstructured":"GABRIEL, K.R. (1971), \u201cThe Biplot-graphical Display with Applications to Principal Component Analysis,\u201d Biometrika, 58, 453\u2013467.","journal-title":"Biometrika"},{"key":"9027_CR18","doi-asserted-by":"crossref","first-page":"1071","DOI":"10.1175\/1520-0450(1972)011<1071:AOMDBM>2.0.CO;2","volume":"11","author":"KR Gabriel","year":"1972","unstructured":"GABRIEL, K.R. (1972), \u201cAnalysis of Meteorological Data by Means of Canonical Decomposition and Biplots,\u201d Journal of Applied Meteorology, 11, 1071\u20131077.","journal-title":"Journal of Applied Meteorology"},{"key":"9027_CR19","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1093\/biomet\/89.2.423","volume":"89","author":"KR Gabriel","year":"2002","unstructured":"GABRIEL, K. R. (2002), \u201cGoodness of Fit of Biplots and Correspondence Analysis,\u201d Biometrika, 89, 423\u2013436.","journal-title":"Biometrika"},{"key":"9027_CR20","first-page":"1091","volume":"63","author":"LA Goodman","year":"1968","unstructured":"GOODMAN, L.A. (1968), \u201cThe Analysis of Cross-classified Data: Independence, Quasiindependence, and Interactions in Contingency Tables, With or Without Missing Entries,\u201d Journal of the American Statistical Association, 63, 1091\u20131131.","journal-title":"Journal of the American Statistical Association"},{"key":"9027_CR21","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1214\/aos\/1176346576","volume":"13","author":"LA Goodman","year":"1985","unstructured":"GOODMAN, L.A. (1985), \u201cThe Analysis of Cross-classified Data Having Ordered and\/or Unordered Categories: Association Models, Correlation Models, and Asymmetry Models for Contingency Tables With or Without Missing Entries,\u201d The Annals of Statistics, 13, 10\u201398.","journal-title":"The Annals of Statistics"},{"key":"9027_CR22","volume-title":"Theory and Applications of Correspondence Analysis","author":"MJ Greenacre","year":"1984","unstructured":"GREENACRE, M.J. (1984), Theory and Applications of Correspondence Analysis, London: Academic Press."},{"key":"9027_CR23","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1080\/02664769300000021","volume":"20","author":"MJ Greenacre","year":"1993","unstructured":"GREENACRE, M.J. (1993), \u201cBiplots in Correspondence Analysis,\u201d Journal of Applied Statistics, 20, 251\u2013269.","journal-title":"Journal of Applied Statistics"},{"key":"9027_CR24","first-page":"163","volume-title":"Proceedings in Computational Statistics","author":"MJ Greenacre","year":"2006","unstructured":"GREENACRE, M.J. (2006), \u201cTying Up the Loose Ends in Simple, Multiple and Joint Correspondence Analysis,\u201d Keynote Address, COMPSTAT 2006, in Proceedings in Computational Statistics, eds. A. Rizzi and M. Vichi, Berlin: Springer-Verlag, pp.163\u2013186."},{"key":"9027_CR25","doi-asserted-by":"crossref","DOI":"10.1201\/9781420011234","volume-title":"Correspondence Analysis in Practice","author":"MJ Greenacre","year":"2007","unstructured":"GREENACRE, M.J. (2007), Correspondence Analysis in Practice (2nd Ed.), London: Chapman & Hall \/ CRC."},{"key":"9027_CR26","unstructured":"GREENACRE, M.J. (2008), \u201cPower Transformations in Correspondence Analysis,\u201d accepted for publication in Computational Statistics and Data Analysis, downloadable at http:\/\/www.econ.upf.edu\/en\/research\/onepaper.php?id=1044"},{"key":"9027_CR27","volume-title":"Correspondence Analysis in the Social Sciences","year":"1994","unstructured":"GREENACRE, M.J., and BLASIUS, J. (eds) (1994), Correspondence Analysis in the Social Sciences, London: Academic Press."},{"key":"9027_CR28","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1177\/0049124106290316","volume":"35","author":"MJ Greenacre","year":"2006","unstructured":"GREENACRE, M.J., and PARDO, R. (2006), \u201cSubset Correspondence Analysis: Visualizing Relationships Among a Selected Set of Response Categories from a Questionnaire Survey,\u201d Sociological Methods and Research, 35, 193\u2013218.","journal-title":"Sociological Methods and Research"},{"key":"9027_CR29","first-page":"13","volume":"33","author":"JB Kazmierczak","year":"1985","unstructured":"KAZMIERCZAK, J.B. (1985), \u201cAnalyse logarithmique: deux exemples d\u2019application,\u201d Revue de Statistique Appliqu\u00e9e, 33, 13\u201324.","journal-title":"Revue de Statistique Appliqu\u00e9e"},{"key":"9027_CR30","volume-title":"Multivariate Descriptive Statistical Analysis","author":"L Lebart","year":"1984","unstructured":"LEBART, L., MORINEAU A., and WARWICK, K. (1984), Multivariate Descriptive Statistical Analysis, New York: Wiley."},{"key":"9027_CR31","first-page":"1295","volume":"26","author":"PJ Lewi","year":"1976","unstructured":"LEWI, P.J. (1976), \u201cSpectral Mapping, A Technique for Classifying Biological Activity Profiles of Chemical Compounds,\u201d Arzneimittel Forschung, 26, 1295\u20131300.","journal-title":"Arzneimittel Forschung"},{"key":"9027_CR32","first-page":"267","volume-title":"Proceedings of APL-80 Conference","author":"PJ Lewi","year":"1980","unstructured":"LEWI, P.J. (1980), \u201cMultivariate Data Analysis in APL,\u201d in Proceedings of APL-80 Conference, ed. G.A. van der Linden, Amsterdam: North-Holland, pp. 267\u2013271."},{"key":"9027_CR33","first-page":"161","volume-title":"Handbook of Chemometrics and Qualimetrics: Part B","author":"PJ Lewi","year":"1998","unstructured":"LEWI, P.J. (1998), \u201cAnalysis of Contingency Tables,\u201d in Handbook of Chemometrics and Qualimetrics: Part B, eds. B.G.M. Vandeginste, D.L. Massart, L.M.C. Buydens, S. de Jong, P.J. Lewi, and J. Smeyers-Verbeke, Amsterdam: Elsevier, pp. 161\u2013206."},{"key":"9027_CR34","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1023\/A:1023866030544","volume":"35","author":"JA Mart\u00edn-Fern\u00e1ndez","year":"2003","unstructured":"MART\u00cdN-FERN\u00c1NDEZ, J.A., BARCEL\u00d3-VIDAL, C., and PAWLOWSKY-GLAHN, V. (2003), \u201cDealing with Zeros and Missing Values in Compositional Data Sets,\u201d Mathematical Geology, 35, 253\u2013278.","journal-title":"Mathematical Geology"},{"key":"9027_CR35","doi-asserted-by":"crossref","unstructured":"NENADI\u0106, O., and GREENACRE, M.J. (2007), \u201cCorrespondence Analysis in R, with Two- and Three-dimensional Graphics: The ca Package,\u201d Journal of Statistical Software 20(3), http:\/\/www.jstatsoft.org\/v20\/i03\/ .","DOI":"10.18637\/jss.v020.i03"},{"key":"9027_CR36","unstructured":"R DEVELOPMENT CORE TEAM (2007), \u201cR: A Language and Environment for Statistical Computing,\u201d R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, http:\/\/www.R-project.org ."},{"key":"9027_CR37","unstructured":"S-PLUS, VERSION 7 (2007). Insightful Corporation, Seattle, USA, http:\/\/www.insightful.com ."},{"key":"9027_CR38","doi-asserted-by":"crossref","first-page":"859","DOI":"10.2307\/2530959","volume":"41","author":"CJF Braak Ter","year":"1985","unstructured":"TER BRAAK, C.J.F. (1985), \u201cCorrespondence Analysis of Incidence and Abundance Data: Properties in Terms of a Unimodal Response Model,\u201d Biometrics, 41, 859\u2013873.","journal-title":"Biometrics"},{"key":"9027_CR39","volume-title":"LEM: A General Program for the Analysis of Categorical Data","author":"JK Vermunt","year":"1997","unstructured":"VERMUNT, J.K. (1997), \u201cLEM: A General Program for the Analysis of Categorical Data,\u201d The Netherlands: Department of Methodology and Statistics, Tilburg University."},{"key":"9027_CR40","doi-asserted-by":"crossref","first-page":"1131","DOI":"10.1111\/j.0006-341X.2003.00130.x","volume":"59","author":"L Wouters","year":"2003","unstructured":"WOUTERS, L., G\u00d6HLMANN, H.W., BIJNENS, L., KASS, S.U., MOLENBERGHS, G., and LEWI, P.J. (2003), \u201cGraphical Exploration of Gene Expression Data: A Comparative Study of Three Multivariate Methods,\u201d Biometrics, 59, 1131\u20131139.","journal-title":"Biometrics"}],"container-title":["Journal of Classification"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00357-009-9027-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00357-009-9027-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00357-009-9027-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,28]],"date-time":"2019-05-28T14:30:10Z","timestamp":1559053810000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00357-009-9027-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,4]]},"references-count":40,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2009,4]]}},"alternative-id":["9027"],"URL":"https:\/\/doi.org\/10.1007\/s00357-009-9027-y","relation":{},"ISSN":["0176-4268","1432-1343"],"issn-type":[{"value":"0176-4268","type":"print"},{"value":"1432-1343","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,4]]}}}