Constructing multiplicative measures of beliefs in the theory of planned behaviour


Correspondence should be addressed to Wendy Hardeman, Behavioural Science Group, The Primary Care Unit, Cambridge Institute of Public Health, University of Cambridge, Forvie Site, Robinson Way, Cambridge CB2 0SR, UK (e-mail:



Commonly used theories in health psychology involve multiplicative composites of measures, which have been used as predictors, mediators, and outcomes. The chosen scaling system can affect correlations with other variables. This study evaluated how best to construct composites in the context of the theory of planned behaviour (TPB), using hierarchical linear regression, a priori defined scaling systems, and optimal scaling.




At baseline, 6 and 12 months, 365 trial participants (ProActive) completed questionnaires assessing salient beliefs, which were used to construct composites (indirect measures), and direct measures of instrumental and affective attitude, subjective norm, and perceived behavioural control towards becoming more physically active over the next 12 months.


Linear regression supported a multiplicative model for indirect instrumental attitude and perceived control. Except for perceived control, associations between composites and direct measures were unaffected by different a priori scaling systems. Optimal scaling produced widely differing composites over time for subjective norm and affective attitude and a negative association between composite and direct measure for subjective norm.


We recommend that researchers who use multiplicative composites first establish clear support for a multiplicative model, before they examine a range of meaningful scaling systems on theoretical and empirical grounds. Caution is needed when using optimal scaling without checking that a multiplicative model is supported and the resulting scaling system meaningful.

Statement of contribution

What is already known on this subject? Multiplicative composites are included in commonly used theories in health psychology (e.g., theory of planned behaviour). Valid measures are needed as the choice of scaling system (e.g., unipolar or bipolar) can affect estimates of associations between composites and other variables. Ajzen has advocated the use of optimal scaling.

What does this study add? The study shows that optimal scaling can result in meaningless measures. We recommend that health psychologists use optimal scaling with great caution and we provide alternative recommendations for constructing composites.