  In this work, we consider a conventional test of gravitational wave (GW)
propagation which is based on the phenomenological parameterized dispersion
relation to describe potential departures from General Relativity (GR) along
the propagation of GWs. But different from tests conventionally performed
previously, we vary multiple deformation coefficients simultaneously and employ
the principal component analysis (PCA) method to remedy the strong degeneracy
among deformation coefficients and obtain informative posteriors. The dominant
PCA components can be better measured and constrained, thus are expected to be
more sensitive to potential departures from the waveform model. Using this
method we analyze 10 selected events and get the result that the combined
posteriors of the dominant PCA parameters are consistent with GR within
3-$\sigma$ uncertainty. The standard deviation of the first dominant PCA
parameter is 3 times smaller than that of the original dispersion parameter of
the leading order. However, the multi-parameter test with PCA is more sensitive
to not only potential deviations from GR but also systematic errors of waveform
models. the difference in results obtained by using different waveform
templates indicates that the demands of waveform accuracy are higher to perform
the multi-parameter test with PCA.
