A Strategy for Designing Telescoping Models for Analyzing Multiway Contingency Tables Using Mixed Parameters

Abstract

In the analysis of cross-classified data, sociologists often focus on building flexible models for the marginal distributions of a selected set of variables. One strategy for achieving flexible modeling is to design models for telescoping marginal distributions. As an illustration of telescoping distributions, consider a joint distribution of four crossclassifying variables: occupational attainment, education level, race, and gender. A set of telescoping distributions would be the univariate occupation distribution, the bivariate occupation by education, the trivariate occupation by education by race, and the entire joint distribution. A methodology that enables the telescoping modeling strategy is mixed parameterization, which has its roots in the statistics and sociology literatures. In this article, the authors develop a scheme of multilevel mixed parameterization that can be applied to a hierarchy of marginal distributions of reducing dimension. An example from the General Social Survey illustrates mixed parameters for telescoping models.