Theoretical models of radiative transfer are developed to simulate the 85 GHz brightness temperature, T85, observed by the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) radiometer as a function of rain rate. These simulations are performed separately over regions of convective and stratiform rain. For the purpose of constructing vertical profiles of hydrometeors in these regions, guidance is taken from TRMM Precipitation Radar (PR) observations, and from recent investigations of LDR and ZDR measurements made by land-based polarimetric radars. We find that for a given rain rate, the extinction in 85 GHz due to hydrometeors above the freezing level is relatively weak in convective regions compared to that in stratiform regions. The hydrometeor profile above the freezing level responsible for this weak extinction in convective regions is inferred, from LDR and ZDR observations and theoretical considerations, to contain two layers: 1) a layer of two km thickness with mixed phase particles, liquid drops and graupel, directly above the freezing level, and 2) a layer of graupel extending from the top of the mixed-phase layer to the cloud top. Strong extinction in the stratiform regions is inferred to result from slowly-falling, low-density ice aggregates (snow) above the freezing level. These theoretical results are consistent with T85 measured by TMI and the rain rate deduced from PR for convective and stratiform rain regions. On the basis of this study we infer that the accuracy of the rain rate sensed by TMI depends critically on the specification of the convective or stratiform nature of the rain.