  We characterize the bulge, disk, and halo subcomponents in the Andromeda
galaxy (M31) over the radial range 4 < R_proj < 225 kpc. The cospatial nature
of these subcomponents renders them difficult to disentangle using surface
brightness (SB) information alone, especially interior to ~20 kpc. Our new
decomposition technique combines information from the luminosity function (LF)
of over 1.5 million bright (20 < m_814W < 22) stars from the Panchromatic
Hubble Andromeda Treasury (PHAT) survey, radial velocities of over 5000 red
giant branch stars in the same magnitude range from the Spectroscopic and
Photometric Landscape of Andromeda's Stellar Halo (SPLASH) survey, and
integrated I-band SB profiles from various sources. We use an affine-invariant
Markov chain Monte Carlo algorithm to fit an appropriate toy model to these
three data sets. The bulge, disk, and halo SB profiles are modeled as a Sersic,
exponential, and cored power-law, respectively, and the LFs are modeled as
broken power-laws. We present probability distributions for each of 32
parameters describing the SB profiles and LFs of the three subcomponents. We
find that the number of stars with a disk-like LF is ~5% larger than the the
number with disk-like (dynamically cold) kinematics, suggesting that some stars
born in the disk have been dynamically heated to the point that they are
kinematically indistinguishable from halo members. This is the first
kinematical evidence for a "kicked-up disk" halo population in M31. The
fraction of kicked-up disk stars is consistent with that found in simulations.
We also find evidence for a radially varying disk LF, consistent with a
negative metallicity gradient in the stellar disk.
