Quality & Quantity 36: 93–112, 2002.
© 2002 Kluwer Academic Publishers. Printed in the Netherlands.
Nonlinear Structural Equation Models with the
Theory of Planned Behavior: Comparison of
Multiple Group and Latent Product Term Analyses
Institute of Sociology, University of Münster, Scharnhorststr. 121, 48151 Münster, Germany. E-mail:
Abstract. Nonlinear relationships in structural equation analysis became more interesting for
applied researchers since the implementation of nonlinear constraints in software programs (i.e.,
LISREL). This article provides a comprehensive application of the expectancy × value part of the
Theory of Planned Behavior (Ajzen, 1991) including interactions of latent variables. The main pur-
pose of the study is to overcome limitations of similar previous analyses of Baumgartner and Bagozzi
(1995) and Yang Jonsson (1997, 1998) with an empirical example from representative survey data.
Nonlinear relationships of the theories’ constructs (Attitude toward the behavior, subjective norm
and perceived behavioral control) are analyzed one upon another with multiple group comparisons
and latent interaction models. Results conﬁrm the strategy to use multiple group techniques for pre-
liminary analyses (i.e., detection of an interaction effect). With latent interaction models the strength
and the signiﬁcance of the interaction is estimated under control for random measurement error.
Parameters, standard errors, and goodness-of-ﬁt statistics are compared between three estimation
techniques (ML, GLS and WLS). Multiple group analyses and latent interaction modeling detect a
signiﬁcant interaction for perceived behavioral control but not for attitude toward the behavior and
subjective norm. Variations of the estimators of the perceived behavioral control submodel is proved
by bootstrapping. Further model improvements and alternative model techniques are discussed in the
Key words: Structural equation models, multiple group comparison, latent product terms, Theory of
Linear structural equation analysis became widely popular to test proposed causal
relationships between theoretical concepts. Separating structural and measurement
equations to control for random measurement error are one of the main advantages
in contrast to regression and path analysis (see e.g., Bollen, 1989). Extending and
applying linear relationships to nonlinear relationships has been of considerable in-
terest recently (Schumacker and Marcoulides, 1998). The approaches dealing with
speciﬁc forms of nonlinear equations with latent variables can be classiﬁed into
three categories: two-step procedures (Ping, 1995, 1996a, b, 1998; Bollen, 1995;