Simple Models for the Analysis of Association in Cross-Classifications having Ordered Categories |
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| 文献名称 | Simple Models for the Analysis of Association in Cross-Classifications having Ordered Categories | ||||||
| 文献作者 | Leo A. Goodman | ||||||
| 作者所在单位 | Departments of Statistics and Sociology, University of Chicago | ||||||
| 文献分类 | 已发表文献 | ||||||
| 学科一级分类 | 统计 | ||||||
| 学科二级分类 | 统计学 | ||||||
| 文献摘要 |
A class of models is proposed for the analysis of association in a contingency table with ordered rows and ordered columns. Association is measured in terms of the odds-ratios in 2 X 2 subtables formed from adjacent rows and adjacent columns. This class includes the null association model, the uniform association model, and models that describe the possible effects of the rows and/or columns on the association. With these models, the association in the table can be analyzed in a manner analogous to the usual twoway analysis of variance, and parsimonious descriptions of this association can be obtained often. Applications are discussed here, some well-known sets of data are reanalyzed, and new insights into these data are obtained |
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| 参考文献 |
Andersen, E.B. (1979), Discrete Statistical Models With Social Science Applications, Amsterdam: North-Holland Publishing Co. Bishop, Y.M., Fienberg, S.E., and Holland, P.W. (1975). Discrete Multivariate Analysis: Theory and Practice, Cambridge, Mass.: MIT Press. Caussinus, H. (1965), "Contribution A l'analyse statistique des tableaux de corr6lation," Annales de la Facultg des Sciences de l'Universite de Toulouse, 29, 77-182. Darroch, J.N., and Ratcliff, D. (1972), "Generalized Iterative Scaling for Log-Linear Models," Annals of Mathematical Statistics, 43, 1470-1480. Duncan, O.D. (1979), "How Destination Depends on Origin in the Occupational Mobility Table," American Journal of Sociology, 84, 793-803. Edwards, A.W.F. (1963), "The Measure of Association in a 2 X 2 Table," Journal of the Royal Statistical Society, Ser. A, 126, 109- 114. Fienberg, S.E. (1968), "The Estimation of Cell Probabilities in Two-Way Contingency Tables," unpublished Ph.D. thesis, Dept. of Statistics, Harvard University. Glass, D.V. (ed.) (1954), Social Mobility in Britain, Glencoe, Ill.: Free Press. Goodman, Leo A. (1965), "On the Multivariate Analysis of Three Dichotomous Variables," American Journal of Sociology, 71, 290-301. (1968), "The Analysis of Cross-Classified Data: Independence, Quasi-Independence, and Interactions in Contingency Tables With or Without Missing Entries," Journal of the American Statistical Association, 63, 1091-1131. (1969), "How to Ransack Social Mobility Tables and Other Kinds of Cross-Classification Tables," American Journal of Sociology, 75, 1-39. (1970), "The Multivariate Analysis of Qualitative Data: Interactions among Multiple Classifications," Journal of the American Statistical Association, 65, 226-256. (1972), "Some Multiplicative Models for the Analysis of Cross-Classified Data," in Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, eds. L. Le Cam et al., Berkeley: University of California Press. (1975), "A New Model for Scaling Response Patterns: An Application of the Quasi-Independence Concept," Journal of the American Statistical Association, 70, 755-768. (1979a), "Multiplicative Models for the Analysis of Occupational Mobility Tables and Other Kinds of Cross-Classification Tables," American Journal of Sociology, 84, 804-819. (1979b), "The Analysis of Qualitative Variables IUsing More Parsimonious Quasi-Independence Models, Scaling Models, and Latent Structures that Fit the Observed Data," in Qualitative and Quantitative Social Research: Papers in Honor of Paul F. Lazarsfeld, ed. R.M. Merton, J.S. Coleman, and P.H. Rossi, New York: Free Press. Haberman, S.J. (1974a), "Log-Linear Models for Frequency Tables With Ordered Classifications," Biometrics, 30, 589-600. (1974b), The Analysis of Frequency Data, Chicago: University of Chicago Press. (1979), Analysis of Qualitative Data: Vol. 2. New Developments, New York: Academic Press. Hauser, R.M. (1980), "Some Exploratory Methods for Modeling Mobility Tables and Other Cross-Classified Data," in Sociological Methodology1 980, ed. Karl F. Schuessler, San Francisco: Jossey- Bass. McCullagh, P. (1978), "The Analysis of Matched Pairs With Qualitative Data," Technical Report No. 75, Department of Statistics, University of Chicago. Miller, S.M. (1960), "Comparative Social Mobility," Current Sociology, 9, 1-89. Rasch, G. (1966), Statistikkens Teori, Lecture notes compiled by U. Christiansen in Danish, University of Copenhagen. Simon, Gary (1974), "Alternative Analyses for the Singly-Ordered Contingency Table," Journal of the American Statistical Association, 69, 971-976. Srole, L., Langner, T.S., Michael, S.T., Opler, M.K., and Rennie, T.A.C. (1962), Mental Health in the Metropolis: The Midtown Manhattan Study, New York: McGraw-Hill Book Co. Yule, G.U., and Kendall, M.G. (1950), An Introductiont o the Theory of Statistics (14th ed.), New York: Hafner. |
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| 关键字 | Association models; Log-linear models; Partitioning chi-square; Analysis of association; Contingency tables | ||||||
| 发表所在刊物（或来源） | Journal of the American Statistical Association, Vol. 74, No. 367 (Sep., 1979), pp. 537-552 | ||||||
| 发表时间 | Sep., 1979 | ||||||
| 适用研究领域 | 统计学 | ||||||
| 评论 | |||||||
| 上传时间 | 2011-1-20 14:52 | ||||||
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