  The physical degrees of freedom of a gravitational wave (GW) are imprints of
the nature of gravity. We can test a gravity theory by searching for
polarization modes beyond general relativity. The LIGO-Virgo collaboration
analyzed several GW events in the O1 and O2 observing runs in the pure
polarization framework, where they perform the Bayesian model selection between
general relativity and the theory allowing only scalar or vector polarization
modes. In this paper, we reanalyze the polarizations of GW170814 (binary black
hole merger) and GW170817 (binary neutron star merger) in the improved
framework of pure polarizations including the angular patterns of nontensorial
radiation. We find logarithms of the Bayes factors of 2.775 and 3.636 for
GW170814 in favor of the pure tensor polarization against pure vector and
scalar polarizations, respectively. These Bayes factors are consistent with the
previous results by the LIGO-Virgo collaboration, though the estimated
parameters of the binaries are significantly biased. For GW170817 with the
priors on the location of the binary from NGC4993, we find logarithms of the
Bayes factors of 21.078 and 44.544 in favor of the pure tensor polarization
against pure vector and scalar polarizations, respectively. These more strongly
support GR, epecially compared to the scalar polarization, than the previous
results by the LIGO-Virgo collaboration due to the location prior. In addition,
by utilizing the orientation information of the binary from a gamma-ray burst
jet, we find logarithms of the Bayes factor of 51.043 and 60.271 in favor of
the pure tensor polarization against pure vector and pure scalar polarization,
much improved from those without the jet prior.
