Mediated Models for the Analysis of Confounded Variables and Self-Selected Samples

Abstract

This paper addresses the interpretation of data that are contaminated by self-selected samples and/or lack of experimental control. Wainer (1989) reviewed different methods for treating self-selected samples and concluded that the most defensible approach is to model the process that caused the data to be missing. In concert with Wainer, the present paper emphasizes the value of specifying models; however, the theses of the present paper are that (a) any analysis should be interpreted in the context of a set of rival theoretical models, (b) these models should allow latent mediating variables that are imperfectly measured by observed variables, and (c) modeling brings clarity to the conclusion that confounded data can be misleading. Simple models clarify the limitations on conclusions one might otherwise attempt to draw from tainted data.