Statistical Modelling 7 (2007), 3–28
A paired comparison approach for the analysis of sets of Likert-scale
responses
Regina Dittrich
Vienna University of Economics,
Department of Statistics and Mathematics,
Augasse 2–6,
A–1090 Vienna,
Austria
eMail:
regina.dittrich@wu-wien.ac.at
Brian Francis
Lancaster University,
United Kingdom
Reinhold Hatzinger and Walter Katzenbeisser
Vienna University of Economics,
Austria
Abstract:
This paper provides an alternative methodology for the analysis of
a set of Likert responses measured on a common attitudinal scale
when the primary focus of interest is on the relative importance
of items in the set. The method makes fewer assumptions about the
distribution of the responses than the more usual approaches such
as comparisons of means, MANOVA or ordinal data methods. The
approach transforms the Likert responses into paired comparison
responses between the items. The complete multivariate pattern
of responses thus produced can be analyzed by an appropriately
reformulated paired comparison model. The dependency structure
between item responses can also be modelled flexibly. The
advantage of this approach is that sets of Likert responses
can be analyzed simultaneously within the Generalized Linear
Model framework, providing standard likelihood-based inference
for model selection. This method is applied to a recent
international survey on the importance of environmental problems.
Keywords:
paired comparisons; Bradley-Terry model; response patterns;
log-linear model; generalized linear model; GLIM; R;
Likert scale
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