  The combined fit of the measured energy spectrum and shower maximum depth
distributions of ultra-high-energy cosmic rays is known to constrain the
parameters of astrophysical models with homogeneous source distributions.
Studies of the distribution of the cosmic-ray arrival directions show a better
agreement with models in which a fraction of the flux is non-isotropic and
associated with the nearby radio galaxy Centaurus A or with catalogs such as
that of starburst galaxies. Here, we present a novel combination of both
analyses by a simultaneous fit of arrival directions, energy spectrum, and
composition data measured at the Pierre Auger Observatory.
  We find that a model containing a flux contribution from the starburst galaxy
catalog of around 20% at 40 EeV with a magnetic field blurring of around
$20^\circ$ for a rigidity of 10 EV provides a fair simultaneous description of
all three observables. The starburst galaxy model is favored with a
significance of $4.5\sigma$ (considering experimental systematic effects)
compared to a reference model with only homogeneously distributed background
sources. By investigating a scenario with Centaurus A as a single source in
combination with the homogeneous background, we confirm that this region of the
sky provides the dominant contribution to the observed anisotropy signal.
Models containing a catalog of jetted active galactic nuclei whose flux scales
with the $\gamma$-ray emission are, however, disfavored as they cannot
adequately describe the measured arrival directions.
