THE LOG-MULTIPLICATIVE LAYER EFFECT MODEL FOR COMPARING MOBILITY TABLES*

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