Contingency table analysis: Log-linear models

SummaryThe two examples included in this section illustrate different facets of the analysis of data by means of log-linear models. The first example illustrated the classic analysis by means of unsaturated models for which there are now dozens of examples in the literature. However, as was shown by studying the sources of lack-of-fit — in other words by looking at the residuals — it was possible to identify a “rogue” cell and then to find a much simpler model. The second example explored an avenue of research which is, at present, little documented. The diagonal-crossings model presented in the previous sub-section is in fact the basis of the analysis of Swedish voting data by Upton and Särlvik (1979) where it has been found to provide new insights into the nature of voting changes. One may expect that model-building of this type will become increasingly common.Perhaps the essential message to be learnt from the two examples is that every data set presents its own problems, and that data cannot simply be analyzed by feeding it into a computer program. The log-linear model is not the end of data analysis for contingency tables but the starting point.

[1]  L. A. Goodman.  The Analysis of Cross-Classified Data: Independence, Quasi-Independence, and Interactions in Contingency Tables with or without Missing Entries , 1968 .

[2]  Murray Aitkin,et al.  The Analysis of Unbalanced Cross-classifications , 1978 .

[3]  J. Mckinlay.  Social Networks, Lay Consultation and Help-Seeking Behavior , 1973 .

[4]  J. A. Nelder,et al.  Log Linear Models for Contingency Tables: A Generalization of Classical Least Squares , 1974 .

[5]  R. D. Bock,et al.  Multivariate Statistical Methods in Behavioral Research , 1978 .

[6]  Leo A. Goodman,et al.  Causal Analysis of Data from Panel Studies and Other Kinds of Surveys , 1973, American Journal of Sociology.

[7]  Richard G. Niemi,et al.  The Persistence of Political Orientations: An Over-Time Analysis of Two Generations , 1978, British Journal of Political Science.

[8]  Stephen E. Fienberg,et al.  The Analysis of Incomplete Multi-Way Contingency Tables , 1972 .

[9]  G. J. G. Upton.  A Memory Model for Voting Transitions in British Elections , 1977 .

[10]  Leo A. Goodman,et al.  A General Model for the Analysis of Surveys , 1972, American Journal of Sociology.

[11]  D. Titterington,et al.  A comparison of iterative methods for obtaining maximum likelihood estimates in contingency tables with a missing diagonal , 1977 .

[12]  Otis Dudley Duncan,et al.  Partitioning polytomous variables in multiway contigency analysis , 1975 .

[13]  L. A. Goodman,et al.  Measures of association for cross classifications , 1979 .

[14]  F. F. Stephan,et al.  The Industrial Mobility of Labor as a Probability Process by I. Blumen, M. Kogan, Ph. J. McCarthy. Cornell Studies in Industrial and Labor Relations, Vol. VI. Ithaca, Cornell University, 1955, XII p. 163 p., $ 2.00. , 1956, Bulletin de l'Institut de recherches économiques et sociales.

[15]  L. A. Goodman.  The Multivariate Analysis of Qualitative Data: Interactions among Multiple Classifications , 1970 .

[16]  L. A. Goodman.  The Analysis of Systems of Qualitative Variables When Some of the Variables Are Unobservable. Part I-A Modified Latent Structure Approach , 1974, American Journal of Sociology.

[17]  E. H. Simpson,et al.  The Interpretation of Interaction in Contingency Tables , 1951 .

[18]  L. A. Goodman.  The Relationship between Modified and Usual Multiple-Regression Approaches to the Analysis of Dichotomous Variables , 1976 .

[19]  Leo A. Goodman,et al.  Some multiplicative models for the analysis of cross classified data , 1972 .

[20]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[21]  Leo A. Goodman,et al.  The analysis of multidimensional contingency tables when some variables are posterior to others: a modified path analysis approach , 1973 .

[22]  H. T. Reynolds,et al.  Some Comments on the Causal Analysis of Surveys with Log-Linear Models , 1977, American Journal of Sociology.

[23]  J. Lingoes.  The Multivariate Analysis Of Qualitative Data , 1968 .

[24]  Robert M. Hauser,et al.  A Structural Model of the Mobility Table , 1978 .

[25]  L. A. Goodman.  The Analysis of Multidimensional Contingency Tables: Stepwise Procedures and Direct Estimation Methods for Building Models for Multiple Classifications , 1971 .

[26]  Robin Plackett.  The analysis of categorical data , 1974 .

[27]  Morton B. Brown.  Screening Effects in Multidimensional Contingency Tables , 1976 .

[28]  V. Smith,et al.  Multivariate analysis: Theory and practice , 1974 .

[29]  Leo A. Goodman,et al.  A Modified Multiple Regression Approach to the Analysis of Dichotomous Variables , 1972 .

[30]  P. Armitage.  The Chi‐Square Test for Heterogeneity of Proportions, after Adjustment for Stratification , 1966 .

[31]  L. A. Goodman.  Exploratory latent structure analysis using both identifiable and unidentifiable models , 1974 .

[32]  Frederick Mosteller,et al.  Association and Estimation in Contingency Tables , 1968 .

[33]  Henri Caussinus,et al.  Contribution à l'analyse statistique des tableaux de corrélation , 1965 .