Partitioning of rare earth elements (REEs) between mantle minerals and basaltic melts is fundamental to understanding crystal-melt fractionation processes and can be quantitatively described by the lattice strain model. We analyzed published REE and Y partitioning data between garnet and basaltic melt and REE, Y, and Sc partitioning data between olivine and basaltic melt using the nonlinear regression method, and parameterized key partitioning parameters in the lattice strain model (D-0, r(0) and E) as functions of temperature, pressure, and mineral and melt compositions. We show that REE and Y partition coefficients between garnet and basaltic melt are inversely correlated with temperature and pressure, and that the correlation between REE partition coefficients and Ca content in garnet (X-Ca) is convoluted by the inverse relationship between D-0 and X-Ca and the positive correlation between r(0) and X-Ca. REE, Y, and Sc partition coefficients between olivine and basaltic melt are positively correlated with Al content in olivine and inversely correlated with forsterite content in olivine and pressure. To test the validity of the assumptions and simplifications used in the model development, we combined the garnet and olivine models with a recent model for REE partitioning between clinopyroxene and basaltic melt to obtain two mineral-mineral partitioning models. We found that the model-derived garnet-clinopyroxene and olivine-clinopyroxene REE partition coefficients are consistent with the measured data from well-equilibrated eclogite and peridotite xenoliths at subsolidus conditions. This demonstrates the internal consistency of our parameterized lattice strain models for REE partitioning in garnet, olivine, clinopyroxene and orthopyroxene. Taken collectively, the partitioning models for garnet, olivine, clinopyroxene and orthopyroxene all suggest the importance of crystal chemistry, temperature and pressure in determining REE partitioning between mantle minerals and basaltic melts, and that melt composition has only a secondary or indirect effect.