Department of Statistics
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Title: A Shrinkage Estimator of the Log Odds Ratio for
Comparing Mobility Tables
This paper presents a shrinkage estimator of the log odds ratio for comparing mobility tables. Based on an empirical Bayes approach, this estimator borrows information across multiple tables while placing no restrictions on the structure of association within tables. Numerical simulation shows that the shrinkage estimator outperforms the MLE in both the total squared error and the correlation with the true values. Moreover, the benefits of the shrinkage estimator relative to the MLE depend on the variation in the true log odds ratio and the variation in sample size among tables. For mobility tables with more than two categories, the shrinkage estimates of log odds ratios can be used to calculate summary measures of association that are based on aggregations of log odds ratios. Specifically, I construct an adjusted estimator of the Altham index, and, with a set of calibrated simulations, demonstrate its usefulness in both reducing the mean squared error and improving the correlation with the true values. Finally, using two real data sets, I find that in terms of gauging the overall degree of social fluidity, the adjusted estimates of the Altham index agree more closely with results from the Unidiff model than do direct estimates of the Altham index.