  We present composite broad-line region (BLR) reverberation-mapping lag
measurements for \halpha, \hbeta, \HeII\,$\lambda4686$ and \MgII\ for a sample
of 144, $z\lesssim 1$ quasars from the Sloan Digital Sky Survey Reverberation
Mapping (SDSS-RM) project. Using only the 32-epoch spectroscopic light curves
in the first 6-month season of SDSS-RM observations, we compile
correlation-function measurements for individual objects and then coadd them to
allow the measurement of the average lags for our sample at mean redshifts of
$0.4$ (for \halpha) and $\sim 0.65$ (for the other lines). At similar quasar
luminosities and redshifts, the sample-averaged lag decreases in the order of
\MgII, \halpha, \hbeta\ and \HeII. This decrease in lags is accompanied by an
increase in the mean line width of the four lines, and is roughly consistent
with the virialized motion for BLR gas in photoionization equilibrium. These
are among the first RM measurements of stratified BLR structure at $z>0.3$.
Dividing our sample by luminosity, \halpha\ shows clear evidence of increasing
lags with luminosity, consistent with the expectation from the measured BLR
size-luminosity relation based on \hbeta. The other three lines do not show a
clear luminosity trend in their average lags due to the limited dynamic range
of luminosity probed and the poor average correlation signals in the divided
samples, a situation that will be improved with the incorporation of additional
photometric and spectroscopic data from SDSS-RM. We discuss the utility and
caveats of composite-lag measurements for large statistical quasar samples with
reverberation-mapping data.
