A Shrinkage Estimator of the Log Odds Ratio for Comparing Mobility Tables

• In Event: 558 - Regular Session. Quantitative Methodology

Abstract

In this paper, I present a shrinkage estimator of the log odds ratio for comparing mobility tables. Building on the Jame-Stein estimation rule and an empirical Bayes derivation, this estimator borrows information across tables while placing no restrictions on the structure of association within tables. Numerical simulation indicates that the shrinkage estimator significantly outperforms the usual maximum likelihood estimator in both the mean squared error and the correlation with the true log odds ratios. To illustrate the effects of shrinkage, I apply both the usual estimator and the shrinkage estimator to the 16 mobility tables assembled by Hazelrigg and Garnier in the 1970s. For mobility tables with more than two rows (columns), 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 metric, and, with a set of calibrated simulations, show its usefulness in both reducing the mean squared error and improving the correlation with the true values. Finally, using two sets of real mobility tables, I show that in terms of gauging the overall level of social fluidity, the adjusted estimates of the Altham metric accord more closely with results from the Unidiff model than do direct estimates of the Altham metric.

Author

• Xiang Zhou, University of Michigan