This paper introduces new predictive measures of association that may be used for contingency table analysis much as the simple, partial, and multiple correlation coefficients are used for regression analysis. The new measures are based on the combination of (1) the logic of the PRE (proportional reduction in error) measures of association, (2) the use of uncertainty (or maximum-likelihood-ϰ2) as indirect measures of errors in prediction, and (3) analysis strategy of log-linear models for contingency tables.
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References
1.
BAKER, R. J.
and J. A. Nelder (1978) The GLIM System, Release 3: Generalised Linear Interactive Modelling. Oxford: Numerical Algorithms Group.
2.
BEATON, A. E.
(1975) “The influence of education and ability on salary and attitudes,” pp. 365-396 in F. T. Juster (ed.) Education, Income, and Human Behavior. New York: McGraw-Hill.
3.
BERKSON, J.
(1972) “Minimum discrimination information, the no interaction' problem, and the logistic function.”Biometrics28: 443-468.
4.
BISHOP, Y.M.M.
, S. E. Fienberg, and P. W. Holland (1975) Discrete Multivariate Analysis: Theory and Practice. Cambridge, MA: MIT Press.
5.
BREIGER, R. L.
(1981) “The social class structure of occupational mobility.”Amer. J. Of Sociology87 (November): 578-611.
6.
CLOGG, C. C.
(1982) “Using association models in sociological research: Some examples.”Amer. J. of Sociology88(1): 114-134.
7.
COSTNER, H. L.
(1965) “Criteria for measures of association.”American Soc. Rev.30 (June): 341-353.
8.
DARROCH, J. N.
(1974) “Multiplicative and additive interaction in contingency tables.”Biometrika61, 2: 207-214.
9.
DAVIS, J. A.
(1976) “Analyzing contingency tables with linear flow graphs: D systems.” Pp. 111-145 in David R. Heise (ed.) Sociological Methodology 1976. San Francisco: Jossey-Bass.
10.
DAVIS, J. A.
(1974) “Hierarchical models for significance tests in multivariate contingency tables: an exegesis of Goodman's recent papers,” pp. 189-231 in H. L. Costner (ed.) Sociological Methodology 1973-1974. San Francisco: Jossey-Bass.
11.
DUNCAN, O. D.
(1979a) “Constrained parameters in a model for categorical data.”Soc. Methods and Research8 (August): 57-68.
12.
DUNCAN, O. D.
(1979b) “How destination depends on origin in the occupational mobility table.”Amer. J. of Sociology84: 793-803.
13.
ENTWISLE, D. R.
and D. KNEPP (1970) “Uncertainty analysis applied to sociological data,” pp. 200-216 in E. F. Borgatta and G. W. Bohrnstedt (eds.) Sociological Methodology 1970. San Francisco: Jossey-Bass.
14.
ERIKSON, R.
, J. H. GOLDTHORPE and L. PORTOCARERO (1979) “Intergenerational class mobility in three Western European societies: England, France and Sweden.”British J. of Sociology30 (December): 415-441.
15.
FAY, R.
and L. A. GOODMAN (1973) “ETCA: Everyman's contingency table analysis.” (unpublished; program and description available from L. A. Goodman).
16.
FIENBERG, S. E.
(1980) The Analysis of Cross-classified Categorial Data. (2nd Ed.). Cambridge, MA: MIT Press.
17.
GARNER, W. R.
(1962) Uncertainty and Structure as Psychological Concepts. New York: John Wiley.
18.
GARNER, W. R.
and W. J. McGill (1956) “The relation between information and variance analysis.”Psychometrika21: 219-228.
19.
GILLESPIE, M. W.
(1977) “Log-linear techniques and the regression analysis of dummy dependent variables: Further basis of comparison.”Sociological Methods and Research6 (August): 102-122.
20.
GOLDTHORPE, J. H.
, C. PAYNE, and C. LLEWELLYN (1978) “Trends in social mobility.”Sociology12: 441-468.
21.
GOOD, I. J.
(1963) “Maximum entropy for hypothesis formulation, especially for multidimensional contingency table.”Annals of Mathematical Statistics34: 911-943.
22.
GOODMAN, L. A.
(1981a) “Criteria for determining whether certain categories in a cross-classification table should be combined, with special reference to occupational categories in an occupational mobility table.”Amer. J. of Sociology87, 3 (November): 612-650.
23.
GOODMAN, L. A.
(1981b) “Three elementary views of log-linear models for the analysis of cross-classification having ordered categories.”Soc. Methodology1981: 193-239.
24.
GOODMAN, L. A.
(1979a) “Multiplicative models for the analysis of occupational mobility tables and other kinds of cross-classification tables.”Amer. J. of Sociology84, 4: 804-819.
25.
GOODMAN, L. A.
(1979b) “Simple models for the analysis of association in cross-classifications having ordered categories.”J. of the Amer. Stat. Assn.74: 537-552.
26.
GOODMAN, L. A.
(1976) “The relationship between modified and usual multiple-regression approaches to the analysis of dichotomous variables.” in D. R. Heise (ed.) Sociological Methodology 1976.
27.
GOODMAN, L. A.
(1972a) “A modified multiple regression approach to the analysis of dichotomous variables.”Amer. Soc. Rev.37 (February): 28-46.
28.
GOODMAN, L. A.
(1972b) “A general model for the analysis of surveys.”Amer. J. of Sociology77: 1035-1086.
29.
GOODMAN, L. A.
(1971a) “The analysis of multidimensional contingency tables: stepwise procedures and direct estimation for building models for multiple classifications.”Techometrics13 (February): 33-61.
30.
GOODMAN, L. A.
(1971b) “Partitioning of chi-square, analysis of marginal contingency tables and estimation of expected frequencies in multidimensional contingency tables.”J. of the Amer. Stat. Assn.66: 339-344.
31.
GOODMAN, L. A.
(1970) “The multivariate analysis of qualitative data: interactions among multiple classifications.”J. of the Amer. Stat. Assn.65 (March): 226-257.
32.
GOODMAN, L. A.
(1969) “On partitioning chi-square and detecting partial association in three-way contingency tables.”J. of Royal Stat. Society, Series B, 31, 3: 486-498.
33.
GOODMAN, L. A.
and W. H. KRUSKAL (1954) “Measures of association for cross classifications.”Journal of the American Statistical Association49 (December): 732-764.
34.
GRIZZLE, J. E.
, C. F. STARMER, and G. G. KOCH (1969) “Analysis of categorical data by linear models.”Biometrics25: 489-504.
35.
HABERMAN, S. J.
(1979) Analysis of Qualitative Data (Vol. 2): New Developments. New York: Academic Press.
36.
HABERMAN, S. J.
(1978) Analysis of Qualitative Data (Vol. 1): Introductory Topics. New York: Academic Press.
37.
HABERMAN, S. J.
(1974) “Log-linear models for frequency tables with ordered classifications.”Biometrics30 (December): 589-600.
38.
HAUSER, R. M.
(1980) “Some exploratory methods for modeling mobility tables and other kinds of cross-classification data.”Soc. Methodology1980: 413-458.
39.
HAUSER, R. M.
(1978) “A structural model of the mobility table.”Social Forces56, 3: 919-953.
40.
HAYS, W. L.
(1963) Statistics for Psychologists. New York: Holt, Rinehart & Winston.
41.
HOELTER, J. W.
(1983) “The analysis of covariance structures: goodness-of fit-indices.”Soc. Methods and Research11 (February): 325-344.
42.
HOLT, D.
(1979) “Log-linear models for contingency table analysis.”Soc. Methods and Research7(3) (Feb.): 330-336.
43.
HOLT, D.
(1975) “Models of status inconsistency and social mobility effects.”American Sociological Review40(June): 322-343.
44.
HOPE, K.
(1982) “Vertical and nonvertical class mobility in three countries.”Amer. Soc. Rev.47 (February): 99-113.
45.
HOPE, K.
(1981) “Vertical mobility in Britain: A structured analysis.”Sociology15: 14-55.
46.
HOPE, K.
(1975) “Models of status inconsistency and social mobility effects.”Amer. Soc. Rev.40 (June): 332-343.
47.
IRELAND, C. T.
, and S. KULLBACK (1968) “Contingency tables with given marginals.”Biometrika55(1): 179-188.
48.
JORESKOG, K. G.
and D. SORBOM (1981) LISREL: Analysis of Linear Structural Relationships by Maximum Likelihood and Least Squares Methods: Users' Guide. Version V. National Education Resources, Inc.
49.
KIM, J.
(1971) “Predictive measures of ordinal association.”American Journal of Sociology76 (March): 416-434.
50.
KIM, J.
and C. W. Mueller (1978) “Predictive measures of association for contingency table analysis.” (unpublished).
51.
KNOKE, D.
(1975) “A comparison of log-linear and regression models for systems of dichotomous variables.”Soc. Methods and Research3 (May): 416-434.
52.
KNOKE, D.
and P. J. BURKE (1980) Log-Linear Models. Beverly Hills, CA: Sage.
53.
KRUSKAL, W. H.
(1958) “Ordinal measures of association.”J. of the Amer. Stat. Assn.53 (December): 814-861.
54.
KU, H. H.
and S. KULLBACK (1968) “Interaction in multidimensional contingency tables: an information theoretic approach.”J. of Research of the National Bureau of Standards-Mathematical Sciences72B: 159-199.
55.
KULLBACK, S.
(1959) Information Theory and Statistics. New York: John Wiley.
56.
LANCASTER, H. O.
(1969) The Chi-Squared Distribution. New York: John Wiley.
57.
MCGILL, W. J.
(1954) “Multivariate information transmission.”Psychometricka19: 97-116.
58.
NIEet al.
(1970) Statistical Package for the Social Sciences. New York: McGraw-Hill.
59.
REYNOLDS, H. T.
(1977) “Some comments on the causal analysis of survey with log linear models.”Amer. J. of Sociology83: 127-143.
60.
ROY, S. N.
and M. A. KASTENBAUM (1956) “On the hypothesis of `no interaction' in a multiway contingency table.”Annals of Mathematical Statistics27: 749-757.
61.
SHANNON, C. E.
(1948) “A mathematical theory of communication.”Bell System Technical J.27: 379-423; 623-656.
62.
SMITH, K. W.
(1976) “Marginal standardization and table shrinking: aids in the traditional analysis of contingency tables.”Social Forces54 (March): 669-693.
63.
SPSS—X User's Guide. (1983) New York: McGraw-Hill.
64.
SRIKANTAN, K. S.
(1970) “Canonical association between nominal measurements.”J. of the Amer. Stat. Assn.65 (March): 284-292.
65.
SWAFFORD, M.
(1980) “Three parametric techniques for contingency table analysis: a nontechnical commentary.”Amer. Soc. Rev.45 (August): 664-690.
66.
TEACHMAN, J. D.
(1980) “Analysis of population diversity: measures of qualitative variation.”Soc. Methods and Research8 (February): 341-362.
67.
THEIL, H.
(1972) Statistical Decomposition Analysis. Amsterdam: North-Holland Publishing Company.
