  Biplot Methods allow for the simultaneous representation of individuals and
variables of a data matrix. For Binary or Nominal data, Logistic biplots have
been recently developed to extend the classical linear representations for
continuous data. When data are ordinal, linear, binary or nominal logistic
biplots are not adequate and techniques as Categorical Principal Component
Analysis (CATPCA) or Item Response Theory (IRT) for ordinal items should be
used instead.
  In this paper we extend the Biplot to ordinal data. The resulting method is
termed Ordinal Logistic Biplot (OLB). Row scores are computed to have ordinal
logistic responses along the dimensions and column parameters produce logistic
response surfaces that, projected onto the space spanned by the row scores,
define a linear biplot. A proportional odds model is used, obtaining a
multidimensional model known as graded response model in the Item Response
Theory literature. We study the geometry of such a representation and construct
computational algorithms for the estimation of parameters and the calculation
of prediction directions. Ordinal Logistic Biplots extend both CATPCA and IRT
in the sense that gives a graphical representation for IRT similar to the
biplot for CATPCA.
  The main theoretical results are applied to the study of job satisfaction of
doctorate (PhD) holders in Spain. Holders of doctorate degrees or other
research qualifications are crucial to the creation, commercialization and
dissemination of knowledge and to innovation. The proposed methods are used to
extract useful information from the Spanish data from the international 'Survey
on the careers of doctorate holders (CDH)', jointly carried out Eurostat, the
Organisation for Economic Co-operation and Development (OECD) and UNESCO's
Institute for Statistics (UIS).
