Quality & Quantity (2007) 41:55–72 © Springer 2007
Selection of Indicators for the Interaction Term
in Structural Equation Models with Interaction
W. E. SARIS
, J.M. BATISTA-FOGUET
and G. COENDERS
ESADE, University Ramon Llull;
Department of Economics, University of Girona
Abstract. Kenny and Judd (1984, Psychological Bulletin 96: 201–210) suggested using struc-
tural equation models to model interaction effects since they allow correction for measurement
error. They proposed using all possible products of the indicators of the two interacting vari-
ables as indicators for the interaction term. J
oreskog and Yang (1996, Advanced Structural
Equation Modeling. Mahwah, NJ: Lawrence Erlbaum, pp. 57–88.) defended that this is not
necessary; one product variable is sufﬁcient to estimate the interaction effect. However, they
did not specify which indicators should be chosen if there is more than one possibility. We
prove that the optimal choice is to select the indicators with the highest reliabilities. But this
is only true if certain assumptions hold. We go on to show that one can get very different
results depending on the indicators chosen for the interaction term if the indicators are not
congeneric which is often the case. These methodological arguments will be illustrated by a
study of the purchasing or boycotting of certain products for environmental reasons.
Kenny and Judd (1984) suggested an alternative to the regression approach
for modeling interaction effects, using structural equation models (SEMs).
This approach has the advantage that one can correct for measurement
error. Kenny and Judd proposed using all possible products of the indica-
tors of the two interacting variables as indicators for the interaction term.
oreskog and Yang (1996) subsequently defended that the use of all pos-
sible product variables is not necessary; one product variable is sufﬁcient to
estimate the interaction effect. This approach is indeed simpler but some
very restrictive assumptions are made.
In this paper we concentrate on the SEM approach of J
Yang (1995) and discuss the problem of the selection of the indicators for
We are very grateful for Albert Satorra’s comments on a previous version of the
Willem E. Saris is Full Professor in Methodology of the Social Sciences at the Uni-
versity of Amsterdam and visiting professor at the ESADE business school of Ramon Llull
University in Barcelona. Correspondence should be directed to Willem E. Saris, ESADE, Av.
de Pedralbes 60-62, 08034 Barcelona, Spain, or by email to Wsaris@planet.nl