We present composite broad-line region (BLR) reverberation-mapping lag measurements for halpha, hbeta, HeII,$lambda4686$ and MgII for a sample of 144, $zlesssim 1$ 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.
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