  Using a sample of optically-selected quasars from the Sloan Digital Sky
Survey, we have determined the radio-loud fraction (RLF) of quasars as a
function of redshift and optical luminosity. The sample contains more than
30,000 objects and spans a redshift range of 0<z<5 and a luminosity range of
-30<M_i<-22. We use both the radio-to-optical flux ratio (R parameter) and
radio luminosity to define radio-loud quasars. After breaking the correlation
between redshift and luminosity due to the flux-limited nature of the sample,
we find that the RLF of quasars decreases with increasing redshift and
decreasing luminosity. The relation can be described in the form of
log(RLF/(1-RLF)) = b_0 + b_z log(1+z) + b_M (M_{2500}+26), where M_{2500} is
the absolute magnitude at rest-frame 2500A, and b_z, b_M<0. When using R>10 to
define radio-loud quasars, we find that b_0=-0.132+/-0.116, b_z=-2.052+/-0.261,
and b_M=-0.183+/-0.025. The RLF at z=0.5 declines from 24.3% to 5.6% as
luminosity decreases from M_{2500}=-26 to M_{2500}=-22, and the RLF at
M_{2500}=-26 declines from 24.3% to 4.1% as redshift increases from 0.5 to 3,
suggesting that the RLF is a strong function of both redshift and luminosity.
We also examine the impact of flux-related selection effects on the RLF
determination using a series of tests, and find that the dependence of the RLF
on redshift and luminosity is highly likely to be physical, and the selection
effects we considered are not responsible for the dependence.
