The longitudinal Guttman simplex: A new methodology for measurement of dynamic constructs in longitudinal panel studies

Abstract

Traditional psychometric procedures can be inadequate for the measurement of dynamic constructs in longitudinal panel studies. This paper introduces an alternative based on the longitudinal Guttman simplex (LGS) model,a measurement model developed especially for dynamic constructs measured longitudinally. The LGS is a model of cumulative, unitary development. It is cumulative in the sense that as persons acquire new skills (or abilities, or opinions), earlier obtained skills are retained; it is unitary in the sense that all persons progress through a sequence of skills in the same skill order. CL, a consistency index that gives the researcher a measure of the extent to which the LGS model axioms are obeyed in a given dataset, is introduced. By making use of this consistency index, the researcher can develop scales uniquely sensitive to cumulative, unitary development. LGSCLUS, an exploratory procedure to find longitudinal Guttman scales in empirical datasets, is described. An artificial data study is reported, the purpose of which was to test the performance of LGSCLUS under controlled conditions. The artificial data study showed that, in general, LGSCLUS recovers longitudinal Guttman scales with a high degree of accuracy. There remains a need for measurement procedures for dynamic constructs exhibiting types of development other than cumulative and unitary. Index terms: Dynamic constructs, Guttman simplex, Longitudinal panel studies, Mathematical models, Measurement theory, Scaling, Three-set data.