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Using structural equation modelling to detect measurement bias and response shift in longitudinal data
Authors:B L King-Kallimanis  F J Oort  G J A Garst
Institution:(1) Department of Medical Psychology, Academic Medical Centre, University of Amsterdam, Amsterdam, The Netherlands;(2) Department of Education, Faculty of Social and Behavioural Sciences, University of Amsterdam, Nieuwe Prinsengracht 130, 1018 VZ Amsterdam, The Netherlands;(3) Association of Dermatological Prevention, Hamburg, Germany;(4) DeltaQuest Foundation, Concord, MA, USA;(5) Departments of Medicine and Orthopaedic Surgery, Tufts University School of Medicine, Boston, MA, USA;
Abstract:We propose a three step procedure to investigate measurement bias and response shift, a special case of measurement bias in longitudinal data. Structural equation modelling is used in each of the three steps, which can be described as (1) establishing a measurement model using confirmatory factor analysis, (2) detecting measurement bias by testing the equivalence of model parameters across measurement occasions, (3) detecting measurement bias with respect to additional exogenous variables by testing their direct effects on the indicator variables. The resulting model can be used to investigate true change in the attributes of interest, by testing changes in common factor means. Solutions for the issue of constraint interaction and for chance capitalisation in model specification searches are discussed as part of the procedure. The procedure is illustrated by applying it to longitudinal health-related quality-of-life data of HIV/AIDS patients, collected at four semi-annual measurement occasions.
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