Home > Publications . Search All . Browse All . Country . Browse PSC Pubs . PSC Report Series

PSC In The News

RSS Feed icon

Frey comments on why sunbelt metro area economies are still struggling

Krause says having religious friends leads to gratitude, which is associated with better health

Work by Bailey and Dynarski on growing income gap in graduation rates cited in NYT


Find an innovative research Cube at the MCubed Symposium, Oct 9, register now

Martha Bailey and Nicolas Duquette win Cole Prize for article on War on Poverty

Michigan's graduate sociology program tied for 4th with Stanford in USN&WR rankings

Jeff Morenoff makes Reuters' Highly Cited Researchers list for 2014

Next Brown Bag

Monday, Oct 6
Elisha Renne (Michigan)

Xiang Zhou photo

Shrinkage Estimation of Log Odds Ratios for Comparing Mobility Tables

Publication Abstract

Zhou, Xiang. Forthcoming. "Shrinkage Estimation of Log Odds Ratios for Comparing Mobility Tables." Sociological Methodology.

Statistical analysis of mobility tables has long played a pivotal role in comparative stratification research. In this article, I propose a shrinkage estimator of the log odds ratio for comparing mobility tables. Building on an empirical Bayes framework, the shrinkage estimator improves estimation efficiency by "borrowing strength" across multiple tables while placing no restrictions on the pattern of association within tables. Numerical simulation shows that the shrinkage estimator outperforms the usual maximum likelihood estimator (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 both the variation in the true log odds ratio and the variation in sample size among mobility regimes. To illustrate the effects of shrinkage, I contrast the shrinkage estimates with the usual estimates for the mobility data assembled by Hazelrigg and Garnier for 16 countries in the 1960s and 1970s. For mobility tables with more than two categories, the shrinkage estimates of log odds ratios can also 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 enhancing both the precision of individual estimates and the accuracy of cross-table comparisons. Finally, using two real data sets, I show that in gauging the overall degree of social fluidity, the adjusted estimator of the Altham index agrees more closely with results from the Unidiff model than does the direct estimator of the Altham index.

Browse | Search : All Pubs | Next