Identifiability and stability of standards in the Grade of Membership (GoM) method: methodological and practical considerations

Abstract

The Grade of Membership (GoM) method has been increasingly employed by Brazilian demographers, and has the advantage of including a parameter that measures individual heterogeneousness on the basis of non-observable correlations among the categories of responses to variables of interest. The parameter shows each individual’s degree of membership to extreme profiles. Several authors, however, have called attention to important issues in adjusting the final models that use 3.4 Version of the GoM Program, such as the problem of identifiability – multiple solutions for estimated parameters. In this article a procedure is discussed that is able to identify a final model with a single solution that describes the pure types that are the most reliable for the database, in an attempt at streamlining. To illustrate this process, a database was used with data corresponding to an economic and sociodemographic study of a population of small farmers living along the TransAmazon Highway, in the northern State of Pará, Brazil. The existence of instability in the parameters estimated by the GoM 3.4 Program was also identified and a method of stabilization of its values was proposed. With these combined procedures, users of the GoM 3.4 Program will be able to describe their databases more adequately and respond to criticisms regarding the identifiability and stability of the resulting models. These empirical solutions are significant. Not only do they affect calculations of prevalence and incidence of events of interest, they also bring about important consequences at the correct point and correct moment for interventions of public policies or of prospective planning in projection analyses.