  Estimating dependence relationships between variables is a crucial issue in
many applied domains, such as medicine, social sciences and psychology. When
several variables are entertained, these can be organized into a network which
encodes their set of conditional dependence relations. Typically however, the
underlying network structure is completely unknown or can be partially drawn
only; accordingly it should be learned from the available data, a process known
as structure learning. In addition, data arising from social and psychological
studies are often of different types, as they can include categorical, discrete
and continuous measurements. In this paper we develop a novel Bayesian
methodology for structure learning of directed networks which applies to mixed
data, i.e. possibly containing continuous, discrete, ordinal and binary
variables simultaneously. Whenever available, our method can easily incorporate
known dependence structures among variables represented by paths or edge
directions that can be postulated in advance based on the specific problem
under consideration. We evaluate the proposed method through extensive
simulation studies, with appreciable performances in comparison with current
state-of-the-art alternative methods. Finally, we apply our methodology to
well-being data from a social survey promoted by the United Nations, and mental
health data collected from a cohort of medical students.
