  Context. Recent observations of LMC Cepheids bring new constraints on the
slope of the period-projection factor relation (hereafter Pp relation) that is
currently used in the Baade-Wesselink (hereafter BW) method of distance
determination. The discrepancy between observations and theoretical analysis is
particularly significant for short period Cepheids Aims. We investigate three
physical effects that might possibly explain this discrepancy: (1) the
spectroscopic S/N that is systematically lower for LMC Cepheids (around 10)
compared to Galactic ones (up to 300), (2) the impact of the metallicity on the
dynamical structure of LMC Cepheids, and (3) the combination of infrared
photometry/interferometry with optical spectroscopy. Methods. To study the S/N
we use a very simple toy model of Cepheids. The impact of metallicity on the
projection factor is based on the hydrodynamical model of delta Cep already
described in previous studies. This model is also used to derive the position
of the optical versus infrared photospheric layers. Results. We find no
significant effect of S/N, metallicity, and optical-versus-infrared
observations on the Pp relation. Conclusions. The Pp relation of Cepheids in
the LMC does not differ from the Galactic relation. This allows its universal
application to determine distances to extragalactic Cepheids via BW analysis.
