Adding Covariates to Loglinear Models for the Study of Social Mobility

Abstract

Two strategies, linear regression and loglinear models, have enabled sociologists to make great progress in the study of social mobility and stratification, but each has deficiencies. Linear regression models are insensitive to the multidimensional character of stratification, while loglinear models do not easily incorporate independent variables. I propose a class of constrained multinomial logit models for the study of social mobility that bridges the gap between these two approaches. Parsimony in specifying intercepts is achieved through standard methods for parameterizing interaction terms in loglinear and related models of social mobility. Parsimony in specifying the effects of covariates is achieved by partitioning covariates into groups within which effects are constrained to be proportional. The resulting specification consists of three types ofparameters: (1) a reduced set of intercepts; (2) coefficients that convert the effect of each variable in a group into what may be thought of as a single group-specific metric; and (3) a set of scores for each group that specifies the impact of the group's covariates on outcomes. Examples are provided using data from the 1983 and 1987