Modeling Aggregate Interaction Effects in Many Variable Observational Studies

Abstract

A method to examine aggregate interaction effects in high dimensional categorical data from observational studies is presented. Koch and colleagues (Koch et al. 1977) suggested using characteristics of subpopulations to model outcomes in such a situation. This technique is extended into a fuzzy partitioning of the observational space. This partitioning of the outcome space is based on representing the probabilities of response as a convex combination of archetype variables. The methodology resembles methods used to analyze samples of compounds in analytic chemistry. A grade of membership (GoM) approach is used to characterize the convex and bounded data. Subpopulations can then be defined using these grade of membership scores.

Keywords: :

• Fuzzy partitioning
• Grade of membership
• Maximum entropy
• Categorical data