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

Traditional psychometric procedures can be inadequatefor the measurement of dynamic constructs inlongitudinal panel studies. This paper introduces an alternativebased on the longitudinal Guttman simplex(LGS) model,a measurement model developed especiallyfor dynamic constructs measured longitudinally.The LGS is a model of cumulative, unitary development.It is cumulative in the sense that as persons acquirenew skills (or abilities, or opinions), earlier obtainedskills are retained; it is unitary in the sense thatall persons progress through a sequence of skills in thesame skill order. CL, a consistency index that givesthe researcher a measure of the extent to which theLGS model axioms are obeyed in a given dataset, isintroduced. By making use of this consistency index,the researcher can develop scales uniquely sensitive tocumulative, unitary development. LGSCLUS, an exploratoryprocedure to find longitudinal Guttman scales inempirical datasets, is described. An artificial datastudy is reported, the purpose of which was to test theperformance of LGSCLUS under controlled conditions.The artificial data study showed that, in general,LGSCLUS recovers longitudinal Guttman scales with ahigh degree of accuracy. There remains a need formeasurement procedures for dynamic constructs exhibitingtypes of development other than cumulative andunitary. Index terms: Dynamic constructs, Guttmansimplex, Longitudinal panel studies, Mathematicalmodels, Measurement theory, Scaling, Three-set data.