  Hipparcos observations of some variable stars, and especially of long-period
(e.g. Mira) variables, reveal a motion of the photocenter correlated with the
brightness variation ({variability-induced mover -- VIM), suggesting the
presence of a binary companion. A re-analysis of the Hipparcos photometric and
astrometric data does not confirm the VIM solution for 62 among the 288 VIM
objects (21%) in the Hipparcos catalogue. Most of these 288 VIMs are
long-period (e.g. Mira) variables (LPV). The effect of a revised chromaticity
correction, which accounts for the color variations along the light cycle, was
then investigated. It is based on `instantaneous' $V-I$ color indices derived
from Hipparcos and Tycho-2 epoch photometry. Among the 188 LPVs flagged as VIM
in the Hipparcos catalogue, 89 (47%) are not confirmed as VIM after this
improved chromaticity correction is applied. This dramatic decrease in the
number of VIM solutions is not surprising, since the chromaticity correction
applied by the Hipparcos reduction consortia was based on a fixed $V-I$ color.
Astrophysical considerations lead us to adopt a more stringent criterion for
accepting a VIM solution (first-kind risk of 0.27% instead of 10% as in the
Hipparcos catalogue). With this more severe criterion, only 27 LPV stars remain
VIM, thus rejecting 161 of the 188 (86%) of the LPVs defined as VIMs in the
Hipparcos catalogue.
