  This paper presents a factor analysis model for symbolic data, focusing on
the particular case of interval-valued variables. The proposed method describes
the correlation structure among the measured interval-valued variables in terms
of a few underlying, but unobservable, uncorrelated interval-valued variables,
called \textit{common factors}. Uniform and Triangular distributions are
considered within each observed interval. We obtain the corresponding sample
mean, variance and covariance assuming a general Triangular distribution.
  In our proposal, factors are extracted either by Principal Component or by
Principal Axis Factoring, performed on the interval-valued variables
correlation matrix. To estimate the values of the common factors, usually
called \textit{factor scores}, two approaches are considered, which are
inspired in methods for real-valued data: the Bartlett and the Anderson-Rubin
methods. In both cases, the estimated values are obtained solving an
optimization problem that minimizes a function of the weighted squared Mallows
distance between quantile functions. Explicit expressions for the quantile
function and the squared Mallows distance are derived assuming a general
Triangular distribution.
  The applicability of the method is illustrated using two sets of data:
temperature and precipitation in cities of the United States of America between
the years 1971 and 2000 and measures of car characteristics of different makes
and models. Moreover, the method is evaluated on synthetic data with predefined
correlation structures.
