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Original Articles

Correspondence and canonical analysis of relational data

, &
Pages 11-64 | Received 01 May 1988, Published online: 26 Aug 2010

References

  • Agresti , A. 1983 . A survey of strategies for modelling cross‐classifications having ordinal variables . Journal of the American Statistical Association , 78 : 184 – 198 .
  • Agresti , A. 1984 . Analysis of Ordered Categorical Data , New York : Academic Press .
  • Allison , P. D. and Liker , J. K. 1982 . Analyzing sequential categorical data on dyadic interaction: a comment on Gottman . Psychological Bulletin , 91 : 393 – 403 .
  • Andersen , E. 1980 . Discrete Statistical Models with Social Science Applications , Amsterdam : North‐Holland .
  • Arabie , P. , Boorman , S. A. and Levitt , P. R. 1978 . Constructing blockmodels: how and why . Journal of Mathematical Psychology , 17 : 21 – 63 .
  • Benzecri , J.‐P. 1969 . “ Statistical analysis as a tool to make patterns emerge from data ” . In Methodologies of Pattern Recognition , Edited by: Watanabe , S. 35 – 74 . New York : Academic Press .
  • Benzecri , J‐P. 1973 . L'Analyse des Données. Tome 2: L'Analyse des Correspondances , Paris : Dunod .
  • Berkowitz , S. D. 1982 . An Introduction to Structural Analysis: The Network Approach to Social Research , Toronto : Butterworths .
  • Beum , C O. and Brundage , E G. 1950 . A method for analyzing the sociomatrix . Sociometry , 13 : 141 – 145 .
  • Blau , P. 1977 . A macrosociological theory of social structure . American Journal of Sociology , 83 : 26 – 54 .
  • Breiger , R. L. 1974 . The duality of persons and events . Social Forces , 53 : 181 – 190 .
  • Breiger , R. L. 1981 . Discussion of Holland and Leinhardt . Journal of the American Statistical Association , 76 : 51 – 53 .
  • Breiger , R. L. , Boorman , S. A. and Arabie , P. 1975 . An algorithm for clustering relational data, with applications to social network analysis and comparison with multidimensional scaling . Journal of Mathematical Psychology , 12 : 328 – 283 .
  • Budescu , D. V. 1984 . Tests of laggeed dominance in sequential dyadic interaction . Psychological Bulletin , 96 : 402 – 414 .
  • Burt , C. 1950 . The factorial analysis of qualitative data . British Journal of Psychology, Statistical Section , 3 : 166 – 185 .
  • Burt , R. S. 1980 . Models of network structure . Annual Review of Sociology , 6 : 79 – 141 .
  • Burt , R. S. and Minor , M. J. , eds. 1983 . Applied Network Analysis , Beverly Hills : Sage Publications .
  • Clogg , C. C . 1982a . Using association models in sociological research: some examples . American Journal of Sociology , 88 : 114 – 134 .
  • Clogg , C. C. 1982b . Some models for the analysis of association in multiway cross‐classifications having ordered categories . Journal of the American Statistical Association , 77 : 803 – 815 .
  • Clogg , C. C. 1986 . Statistical modelling versus singular value decomposition . Comment on Goodmaa International Statistical Review , 54 : 284 – 288 .
  • Coleman , J. S. and MacRae , D. 1960 . Electronic processing of sociometric data for groups up to 1,000 in size . American Sociological Review , 25 : 722 – 727 .
  • Davis , A. , Gardner , B. G. and Gardner , M. R. 1941 . Deep South: A Social Anthropological Study of Caste and Class , Chicago : University of Chicago Press .
  • de Leeuw , J. 1973 . Canonical Analysis of Categorical Data , Leiden : University of Leiden, Leiden, The Netherlands. (Published in 1984 by the DWSO Press . Unpublished doctoral dissertation
  • Deutsch , S. B. and Martin , J. J. 1971 . An ordering algorithm for analysis of data arrays . Operations Research , 19 : 1350 – 1362 .
  • Deville , J.‐C. and Saporta , G. 1983 . Correspondence analysis, with an extension towards nominal time series . Journal of Econometrics , 22 : 169 – 189 .
  • Dillon , W. R. , Madden , T. J. and Kumar , A. 1983 . Analyzing sequential categorical data on dyadic interaction: a latent structure approach . Psychological Bulletin , 94 : 564 – 583 .
  • Faust , K. and Wasserman , S. Correspondence analysis and log linear models for relational data . Paper presented at the Sunbelt VII Social Network Conference, Clearwater . February 1987 , Florida.
  • Feick , L. F. and Novak , J. A. 1985 . Analyzing sequential categorical data on dyadic interaction: log‐linear models exploiting the order in variables . Psychological Bulletin , 98 : 600 – 611 .
  • Fienberg , S. E. 1980 . The Analysis of Cross‐Classified Categorical Data. , 2nd Ed. , Cambridge, MA : The MIT Press .
  • Fienberg , S. E. and Wasserman , S. 1981 . “ Categorical data analysis of single sociometric relations ” . In Sociological Methodology 1981 , Edited by: Leinhardt , S. San Francisco : Jossey‐Bass .
  • Fienberg , S. E. , Meyer , M. M. and Wasserman , S. 1985 . Statistical analysis of multiple sociometric relations . Journal of the American Statistical Association , 80 : 51 – 67 .
  • Fisher , R. A. 1940 . The precision of discriminant functions . Annals of Eugenics , 10 : 422 – 429 .
  • Frank , O. 1981 . “ A survey of statistical methods for graph analysis ” . In Sociological Methodology 1981 , Edited by: Leinhardt , S. and Leinhardt , S. 110 – 155 . San Francisco : Jossey‐Bass .
  • Frank , O. , Hallinan , M. and Nowicki , K. 1985 . Clustering of dyad distributions as a tool in network modeling . Journal of Mathematical Sociology , 11 : 47 – 64 .
  • Frank , O. , Komanska , H. and Widaman , K. E . 1985 . Cluster analysis of dyad distributions in networks . Journal of Classification , 2 : 219 – 238 .
  • Frank , O. , Lundquist , S. , Wellman , B. and Wilson , C. 1986 . Analysis of Composition and Structure of Social Networks Unpublished Manuscript
  • Freeman , L. C. , White , D. R. and Romney , A. K. 1989 . Research Methods in Social Network Analysis , Fairfax, VA : George Mason University Press .
  • Galaskiewicz , J. 1985 . Social Organization of an Urban Grants Economy: A Study of Business Philanthropy and Nonprofit Organizations , Orlando, FL : Academic Press .
  • Galaskiewicz , J. 1987 . “ The study of a business elite and corporate philanthropy in an United States metropolitan area ” . In Research Methods for Elite Studies , Edited by: Moyser , G. and Wagstaffe , M. 147 – 165 . London : Allen & Unwin .
  • Galaskiewicz , J. and Bielefeld , W. Organizational Non‐Profit Response to Shifting Resource Markets: 1980–1984 . Paper read at the XI World Congress of Sociology . August , New Delhi, India. pp. 18 – 22 .
  • Galaskiewicz , J. and Wasserman , S. An approach to the study of organizational change . Paper read at the 1986 Annual American Sociological Association Meeting . August 1986 , New York City.
  • Galaskiewicz , J. and Wasserman , S. 1989 . Mimetic and normative processes within an interorganizational field: An empirical test . Administrative Science Quarterly , 34 : 454 – 480 .
  • Gauch , H. G. , Whittaker , R. H. and Wentworth , T. R. 1977 . A comparative study of reciprocal averaging and other ordination techniques . Journal of Ecology , 65 : 157 – 174 .
  • Gilula , Z. 1986 . Grouping and association in contingency tables: an exploratory canonical correlation approach . Journal of the American Statistical Association , 81 : 773 – 779 .
  • Gilula , Z. and Haberman , S. J. 1986a . Canonical analysis of contingency tables by maximum likelihood . Journal of the American Statistical Association , 81 : 780 – 788 .
  • Gilula , Z. and Haberman , S. J. 1986b . Analysis of multiway contingency tables by restricted canonical and restricted association models , Technical Report No. 48 Statistics Research Center, Graduate School of Business, University of Chicago .
  • Goodman , L. A. 1979a . Simple models for the analysis of association in cross‐classifications having ordered categories . Journal of the American Statistical Association , 74 : 537 – 552 .
  • Goodman , L. A. 1979b . Multiplicative models for square contingency tables with ordered categories . Biometrika , 66 : 413 – 418 .
  • Goodman , L. A. 1981a . Association models and the bivariate normal for contingency tables with ordered categories . Biometrika , 68 : 347 – 355 .
  • Goodman , L. A. 1981b . Association models and canonical correlation in the analysis of cross‐classifications having ordered categories . Journal of the American Statistical Association , 76 : 320 – 334 .
  • Goodman , L. A. 1981c . “ Three elementary views of log‐linear models for the analysis of cross‐classifications having ordered categories ” . In Sociological Methodology 1981 , Edited by: Leinhardt , S. San Francisco : Jossey‐Bass .
  • Goodman , L. A. 1983 . The analysis of dependence in cross‐classifications having ordered categories, using log‐linear models for frequencies and log‐linear models for odds . Biometrics , 39 : 149 – 160 .
  • Goodman , L. A. 1984 . The Analysis of Cross‐Classified Data Having Ordered Categories , Cambridge, MA : Harvard University Press .
  • Goodman , L. A. 1985 . The 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 . Annals of Statistics , 13 : 10 – 69 .
  • Goodman , L. A. 1986 . Some useful extensions of the usual correspondence analysis approach and the usual log‐linear models approach in the analysis of contingency tables . International Statistical Review , 54 : 243 – 309 .
  • Gottman , J. 1979a . Marital Interaction: Experimental Investigations , New York : Academic Press .
  • Gottman , J. 1979b . Detecting cyclicity in social interaction . Psychological Bulletin , 86 : 338 – 348 .
  • Greenacre , M. J. 1981 . “ Practical correspondence analysis ” . In Interpreting Multivariate Data , Edited by: Barnett , Vic . New York : John Wiley and Sons .
  • Greenacre , M. J. 1984 . Theory and Application of Correspondence Analysis , New York : Academic Press .
  • Greenacre , M. J. 1986 . SIMCA: A program to perform simple correspondence analysis . Psychometrika , 51 : 172 – 173 .
  • Guttman , L. 1941 . “ The quantification of a class of attributes ” . In The Prediction of Personal Adjustment , Edited by: Horst , P. 319 – 348 . New York : Social Science Research Council .
  • Guttman , L. 1946 . An approach for quantifying paired comparisons and rank order . Annals of Mathematical Statistics , 17 : 144 – 163 .
  • Guttman , L. 1959 . Metricizing rank‐ordered and unordered data for a linear factor analysis . Sankhya: The Indian Journal of Statistics , 21 : 257 – 268 .
  • Haberman , S. J. 1974 . Log‐linear models for frequency tables with ordered classifications . Biometrics , 30 : 589 – 600 .
  • Hayashi , G. 1980 . “ Data analysis in a comparative study ” . In Data Analysis and Informatics , Edited by: Diday , E. , Lebart , L. , Pages , J. P. and Tomassone , R. 31 – 52 . Amsterdam : North Holland .
  • Heiser , W. J. and Meulman , J. 1983 . Analyzing rectangular tables by joint and constrained multidimensional scaling . Journal of Econometrics , 22 : 139 – 167 .
  • Hill , M. O. 1974 . Correspondence analysis: a neglected multivariate method . Applied Statistics , 23 : 340 – 354 .
  • Hill , M. O. 1982 . “ Correspondence analysis ” . In Encyclopedia of Statistical Sciences , Edited by: Kotz , S. and Johnson , N. L. 204 – 210 . New York : Wiley .
  • Hirschfeld , H. O. 1935 . A connection between correlation and contingency . Proceedings of the Cambridge Philosophical Society , 31 : 520 – 524 .
  • Holland , P. W. and Leinhardt , S. Notes on the statistical analysis of social network data . Presented at the Advanced Research Symposium on Stochastic Process Models of Social Structure . Pittsburgh, PA.. Carnegie‐Mellon University .
  • Holland , P. W. and Leinhardt , S. 1979 . Perspectives in Social Network Research , New York : Academic Press .
  • Holland , P. W. and Leinhardt , S. 1981 . An exponential family of probability distributions for directed graphs . Journal of the American Statistical Association , 16 : 33 – 50 .
  • Holland , P. W. , Laskey , K. B. and Leinhardt , S. 1983 . Stochastic blockmodels: first steps . Social Networks , 5 : 109 – 137 .
  • Iacobucci , D. and Wasserman , S. 1987 . Dyadic social interactions . Psychological Bulletin , 102 : 293 – 306 .
  • Iacobucci , D. and Wasserman , S. 1988 . A general framework for the statistical analysis of sequential dyadic interaction data . Psychological Bulletin , 103 : 379 – 390 .
  • Iwatsubo , S. 1978 . An optimal scoring method for detecting clusters and interrelations from multi‐way qualitative data . Behaviormetrika , 5 : 1 – 22 .
  • Kadushin , C. 1966 . The friends and supporters of psychotherapy: on social circles in urban life . American Sociological Review , 31 : 786 – 802 .
  • Katz , L. 1947 . On the matric analysis of sociometric data . Sociometry , 10 : 233 – 241 .
  • Kendall , D. G. 1971 . “ Seriation from abundance matrices ” . In Mathematics in the Archaeological and Historical Sciences , Edited by: Hodson , C R. , Kendall , D. G. and Tautu , P. 215 – 222 . Edinburgh : Edinburgh Press .
  • Kendall , M. and Stuart , A. 1973 . The Advanced Theory of Statistics , 3rd Editioa , Volume 2 , London : Griffin .
  • Knoke , D. and Kuklinski , J. H. 1982 . Network Analysis , Beverly Hills, CA : Sage Publications .
  • Lancaster , H. O. 1966 . Kolmogorov's remark on the Hotelling canonical correlations . Biometrika , 53 : 585 – 588 .
  • Lebart , L. , Morineau , A. and Warwick , K. M. 1984 . Multivariate Descriptive Statistical Analysis: Correspondence Analysis and Related Techniques for Large Matrices , New York : John Wiley and Sons .
  • Levine , J. H. 1979 . Joint‐space analysis of ‘pick‐any’ data: Analysis of choices from an unconstrained set of alternatives . Psychometrika , 44 : 85 – 92 .
  • Levine , J. H. 1984 . Atlas of Corporate Interlocks , Volume I , Hanover, NH : Worldnet .
  • Lorrain , F. and White , H.C . 1971 . Structural equivalence of individuals in social networks . Journal of Mathematical Sociology , 1 : 49 – 80 .
  • Marsden , P. V. and Lin , N. 1982 . Social Structure and Network Analysis , Beverly Hills : Sage Publications .
  • Maung , K. 1941 . Measurement of association in a contingency table with special reference to the pigmentation of hair and eye colours of Scottish school children . Annals of Eugenics , 11 : 189 – 223 .
  • McCullagh , P. and Neider , J. A. 1983 . Generalized Linear Models , London : Chapman and Hall .
  • Meyer , M. M. 1981 . “ Applications and Generalizations of the Iterative Proportional Fitting Procedure ” . School of Statistics, University of Minnesota . Ph.D. Thesis
  • Meyer , M. M. 1982 . Transforming contingency tables . Annals of Statistics , 10 : 1172 – 1181 .
  • Neider , J. A. and Wedderburn , R. W. 1972 . Generalized linear models . Journal of the Royal Statistical Society, Series A , 135 : 370 – 384 .
  • Nishisato , S. 1978 . Optimal scaling of paired comparison and rank order data: an alternative to Guttman's formulatioa . Psychometrika , 43 : 263 – 271 .
  • Nishisato , S. 1980 . Analysis of Categorical Data: Dual Scaling and its Applications , Toronto : University of Toronto Press .
  • Noma , E. 1982a . Untangling citation networks . Information Processing and Management , 18 : 43 – 53 .
  • Noma , E. 1982b . The simultaneous scaling of cited and citing articles in a common space . Scientometrics , 4 : 205 – 231 .
  • Noma , E. and Smith , D. R. 1985 . Scaling sociomatrices by optimizing an explicit function: correspondence analysis of binary single response sociomatrices . Multivariate Behavioral Research , 20 : 179 – 197 .
  • Payne , C D. 1985 . The GLIM System Release 3.77: Generalized Linear Interactive Modelling Manual , Oxford : The Numerical Algorithms Group .
  • Romney , A. K. and Boyd , J. P. Optimal dual scaling of the Sampson data . Paper presented at Sunbelt VI Social Network Conference . February 1986 , California. Santa Barbara .
  • Schriever , B.E . 1983 . Scaling of order dependent categorical variables with correspondence analysis . International Statistical Review , 51 : 225 – 238 .
  • Simmel , G. 1955 . Conflict and the Web of Group‐Affiliations , New York : Free Press .
  • Simon , G. 1974 . Alternative analyses for the singly ordered contingency table . Journal of the American Statistical Association , 69 : 971 – 976 .
  • Spath , H. 1980 . Cluster Analysis Algorithms for Data Reduction and Classification of Objects , Chichester, ENG : Ellis Harwood .
  • Tenenhaus , M. and Young , F. W. 1985 . An analysis and synthesis of multiple correspondence analysis, optimal scaling, dual scaling, homogeneity analysis and other methods for quantifying categorical multivariate data . Psychometrika , 50 : 91 – 119 .
  • Torgerson , W. S. 1958 . Theory and Methods of Scaling , New York : Wiley .
  • Tucker , L. R. 1964 . “ The extension of factor analysis to three‐dimensional matrices ” . In Contributions to Mathematical Psychology , Edited by: Frederiksen , N. and Gulliksen , H. New York : Holt, Rinehart, & Winston .
  • van der Heijden , P. G. M. and de Leeuw , J. 1985 . Correspondence analysis used complementary to loglinear analysis . Psychometrika , 50 : 429 – 447 .
  • Wampold , B. E. 1984 . Tests of dominance in sequential categorical data . Psychological Bulletin , 96 : 424 – 429 .
  • Wampold , B. F. and Margolin , G. 1982 . Nonparametric strategies to test the independence of behavioral states in sequential data . Psychological Bulletin , 92 : 755 – 765 .
  • Wang , Y. J. and Wong , G. Y. 1987 . Stochastic blockmodels for directed graphs . Journal of the American Statistical Association , 82 : 8 – 19 .
  • Wasserman , S. 1987 . Conformity of two sociometric relations . Psychometrika , 52 : 3 – 18 .
  • Wasserman , S. and Anderson , C. 1987 . Stochastic a posteriori blockmodels: Construction and assessment . Social Networks , 9 : 1 – 36 .
  • Wasserman , S. and Galaskiewicz , J. 1984 . Some generalizations of External constraints, interactions, and non‐binary relations . Social Networks , 6 : 1 177 – 192 .
  • Wasserman , S. and Iacobucci , D. 1986 . Statistical analysis of discrete relational data . British Journal of Mathematical and Statistical Psychology , 39 : 41 – 64 .
  • Wasserman , S. and Iacobucci , D. 1988 . Sequential social network data . Psychometrika , 53 : 261 – 282 .
  • Wasserman , S. and Weaver , S. O. 1985 . Statistical analysis of binary relational data: parameter estimation . Journal of Mathematical Psychology , 29 : 406 – 427 .
  • Weaver , S. and Wasserman , S. 1986 . RELTWO: interactive log linear model fitting for pairs of sociometric relations . Connections: Bulletin of the International Network for Social Network Analysis , 9 : 38 – 46 .
  • White , H. C. , Boorman , S. A. and Breiger , R. L. 1976 . Social structure from multiple networks: I. Blockmodels of roles and positions . American Journal of Sociology , 81 : 730 – 780 .
  • Whiting , J. W. M. , Romney , A. K. , White , D. R. , Burton , M. and Moore , C. Reanalysis of kinship and social structure . Paper presented at the 85th meeting of the American Anthropological Association . Philadelphia, PA..

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