Characterizing Latent Structure: Factor Analytic and Grade of Membership Models

Abstract

There are many situations in the social sciences when multiple indicators of a smaller set of latent constructs or dimensions are available and one wants to use those indicators in combination to develop valid and reliable measures of the latent constructs or dimensions. Multiple indicators are used when no single indicator is considered highly reliable and may be used in two different ways to measure latent constructs or dimensions. Techniques based upon the factor analytic model use indicators as measures of latent continuous variables which represent theoretical constructs. The second approach uses indicators as measures of latent discrete classes which are defined by combinations of indicators of multiple theoretical constructs. In this latter approach individual sample units have values on the latent variables which represent their assignment or degree of proximity to a particular class. Techniques based upon the cluster analysis model the latent class model and the grade of membership (GOM) model are of this type. The authors examine and compare the factor analytic and GOM models describing the models statistically and evaluating their usefulness under various circumstances which arise in social science research. This comparison is of particular interest because factor analysis is now used extensively in the social sciences whereas GOM is a relatively new procedure originally developed to analyze the symptoms of mental and physical disability. After discussing the generic differences between factor analysis and GOM the differences are illustrated with an empirical example focusing upon indicators of job values held by US high school seniors in 1991.