Qual Quant (2015) 49:903–915
Treating ordinal data: a comparison between rating scale
and structural equation models
Silvia Golia · Anna Simonetto
Published online: 15 August 2014
© Springer Science+Business Media Dordrecht 2014
Abstract The aim of this study is to apply rating scale model and structural equation model
to the same polytomous data in order to highlight the differences and similarities between
the two models. For this purpose a simulation study is developed. Moreover, we present a
real case regarding the analysis of the quality of work in an Italian municipality.
Keywords Ordinal data · Structural equation model · Item response theory ·
Rating scale model
The study of latent variable models has acquired an increasingly importance over the years.
The families of models focused on latent aspects are varied, but there is an important common
feature: the number of observed variables is typically greater than the number of considered
latent variables. Signiﬁcant inﬂuence on the development of these models is due to the type of
the observed data, so it is possible to distinguish between models that are based on continuous
data, ordinal data, nominal data, or a mixture of the above types. Our ﬁeld of interest is the
treatment of ordinal data, resulting from questionnaires with items developed on Likert scale.
Within this context, the two major strands of research are: the underlying variable approach
(UVA) and the item response theory approach (IRT) (Moustaki 2000; Cagnone et al. 2010).
The common feature of UVA models is to consider an ordinal observed variable (item) as a
speciﬁc realization of an underlying continuous latent variable (often normally distributed).
The IRT approach is based on the idea that the probability of response in any one of two-
or-more mutually exclusive categories of an item is a function of the subjects location on
S. Golia (
) · A. Simonetto
Department of Economics and Management, University of Brescia, C.da S.Chiara 50,
25122 Brescia, Italy