Variations on a Theme

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Abstract
This article presents an expository discussion of the use of odds, odds ratios, and functions of odds ratios as an aid to the interpretation of log-linear parameters. While there have been some previous presentations on the use of odds ratios, this method has never been fully and systematically developed for complex situations, nor have the potential problems of interpretation using odds ratios been discussed. The presentation in this article more fully elaborates the possible modes of drawing contrasts with odds ratios using any of the three common parameterizations of a log-linear model (ANOVA-like, regression-like, and logit). The sampling distribution and the calculation of standard errors for odds ratios are also discussed as are some cautions on the interpretation of odds ratios. A data analysis of unemployment using polytomous variables illustrates the application and interpretation of the odds-ratio approach.
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