  Polarimetric studies of pulsar radio emission traditionally concentrate on
how the Stokes vector (I, Q, U, V) varies with pulse longitude, with special
emphasis on the position angle (PA) swing of the linearly polarized component.
The interpretation of the PA swing in terms of the rotating vector model is
limited by the assumption of an axisymmetric magnetic field and the degeneracy
of the output with respect to the orientation and magnetic geometry of the
pulsar; different combinations of the latter two properties can produce similar
PA swings. This paper introduces Stokes phase portraits as a supplementary
diagnostic tool with which the orientation and magnetic geometry can be
inferred more accurately. The Stokes phase portraits feature unique patterns in
the I-Q, I-U, and Q-U planes, whose shapes depend sensitively on the magnetic
geometry, inclination angle, beam and polarization patterns, and emission
altitude. We construct look-up tables of Stokes phase portraits and PA swings
for pure and current-modified dipole fields, filled core and hollow cone beams,
and two empirical linear polarization models, L/I = \cos \theta_0 and L/I =
\sin \theta_0, where \theta_0 is the colatitude of the emission point. We
compare our look-up tables to the measured phase portraits of 24 pulsars in the
European Pulsar Network online database. We find evidence in 60% of the objects
that the radio emission region may depart significantly from low altitudes,
even when the PA swing is S-shaped and/or the pulse-width-period relation is
well satisfied. On the other hand, the data are explained adequately if the
emission altitude exceeds ~10% of the light cylinder radius. We conclude that
Stokes phase portraits should be analysed concurrently with the PA swing and
pulse profiles in future when interpreting radio pulsar polarization data.
