The Latent Ordered Logit Model

• In Event: 1131 - Current Progress and Foundational Issues in Sociological Methodology

Abstract

This paper introduces a new regression model for a categorical dependent variable. The new model has following two distinct merits.
First, if the pattern of association between the dependent variable having ordered categories and a set of its predictors reveal latent non-equidistant spacing among categories of the dependent variable the model characterizes data more adequately than two kinds of ordered logit models, the cumulative logit model and the adjacent logit model, both of which assume equidistance spacing among categories of the dependent variable by making the proportional odds assumption.
Second, when the dependent categorical variable does not have any intrinsic order among its categories but has a major latent unidimensional hierarchy among its categories in its form of dependence on the set of predictors, the model can identify the characteristics of the latent hierarchy and can assess how the predictor variables affect that dimension of hierarchy.
The new model assumes a latent class variable as a mediator of the dependent variable and its covariates. The simplest model, which we will refer to as the latent ordered logit model, assumes that covariates affect the dependent variable only indirectly through the latent class variable. The extended model assumes that some covariates affect the dependent variable directly while others affect the dependent variable indirectly through the latent class variable. The latter model is a mixture of the latent ordered logit model and the multinomial logit model. We can select the best-fitting mixed model for a given set of covariates.
This paper introduces two applications, one for each of the two purposes of use for the new model. One focuses on the determinants of abortion attitudes, and the other focuses on the determinants of a latent occupational status. The data of General Social Surveys are employed for both applications.

Author

• Kazuo Yamaguchi, University of Chicago