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B0717
Title: On a linear concept of association Authors:  Tamas Rudas - Hungarian Academy of Sciences Centre for Social Sciences (Hungary) [presenting]
Abstract: The deviation of a binary distribution from the uniform may be measured with the difference of the two probabilities, just as well as with their ratio. For 2x2 contingency tables, this suggests a linear contrast; its zero value indicates the lack of linear association. Higher order linear association terms may also be defined, and they constitute a parameterization of multivariate binary distributions. Higher order linear interactions may be present in a distribution, but variation independence from lower dimensional associations does not hold, in contrast with the multiplicative case. The linear association term is directionally collapsible, meaning that if in a 2x2x2 table, the two conditional associations of two variables have the same direction, then their marginal association has this direction, too. Therefore, the linear association avoids Simpsons paradox in treatment by response tables. Surprisingly, if the linear contrast is defined in terms of the row conditional distributions, the paradox appears again. It occurs for the same data as if the odds ratio was used. One interpretation of this is that the occurrence of the paradox is not a consequence of using ratios instead of differences, rather of neglecting the allocation in treatment categories.