  We investigate here the effect of the selection function on the metallicity
distribution function (MDF) and on the vertical metallicity gradient by
studying similar lines of sight using four different spectroscopic surveys
(APOGEE, LAMOST, RAVE, and Gaia-ESO), which have different targeting strategies
and therefore different selection functions. We use common fields between the
spectroscopic surveys of APOGEE, LAMOST, RAVE (ALR) and APOGEE, RAVE, Gaia-ESO
(AGR) and use two stellar population synthesis models, GALAXIA and TRILEGAL, to
create mock fields for each survey. We apply the selection function in the form
of colour and magnitude cuts of the respective survey to the mock fields to
replicate the observed source sample. We make a basic comparison between the
models to check which best reproduces the observed sample distribution. We
carry out a quantitative comparison between the synthetic MDF from the mock
catalogues using both models to understand the effect of the selection function
on the MDF and on the vertical metallicity gradient. Using both models, we find
a negligible effect of the selection function on the MDF for APOGEE, LAMOST,
and RAVE. We find a negligible selection function effect on the vertical
metallicity gradients as well, though GALAXIA and TRILEGAL have steeper and
shallower slopes, respectively, than the observed gradient. After applying
correction terms on the metallicities of RAVE and LAMOST with respect to our
reference APOGEE sample, our observed vertical metallicity gradients between
the four surveys are consistent within 1-sigma. We also find consistent
gradient for the combined sample of all surveys in ALR and AGR. We estimated a
mean vertical metallicity gradient of -0.241+/-0.028 dex kpc-1. There is a
significant scatter in the estimated gradients in the literature, but our
estimates are within their ranges.
