The Log-Multiplicative Layer Effect Model for Comparing Mobility Tables

Abstract

I propose log-multiplicative layer effect modelfor comparing tables. The model constrains cross-table variation in origin-destination association to be log-multiplicative product of a common association pattern and a table-specific parameter. Like Yamaguchi's (1987) uniform layer effect log-multiplicative layer effect model provides one-parameter tests and thus facilitates analysis of difference in vertical mobility between two tables. Compared to uniform layer effect log-multiplicative layer effect model is far more flexible in specifying origin-destination association. Virtually all two-way models can be incorporated into log-multiplicative layer effect model while retaining their usual interpretability. All that is required is that tables being compared have a common pattern for origin-destination association. Properties of new model are demonstrated using three data sets previously analyzed in comparative research. The same methodology can be generalized to analysis of multiple twoway contingency tables if two-way association of primary interest is specified tofollow a common pattern, albeit with different levels, across tables. I n interest of testing difference in vertical mobility with a single parameter, a useful model for comparing tables has been proposed by Yamaguchi (1987). Referred to here as the uniform layer effect model, model is characterized by use of a single parameter describing uniform difference in origin and destination association between a pair of tables. The uniform layer effect model is attractive in comparative research on for its parsimony and interpretability (Wong 1990). However, there are three associated disadvantages. First, model implicitly assumes that categories of origin and destination are