Methods and apparatus for providing bioimpedance analysis employing alternating current at a plurality of frequencies are provided. In certain aspects, equivalent circuit frequency response models are provided which lead to improved correlations with MRI data. The frequency response models take account of body composition, including the fat component of a body segment. Data obtained by performing bioimpedance spectroscopy (BIS) and MRI on the calves of subjects illustrates the improved correlations achieved compared to single frequency analyses at 50 kilohertz and analyses performed using the conventional Cole-Cole model. Also provided is a method for determining the circumference of a portion of a body segment by applying a series of electrodes around that portion and determining the resistance between electrodes of the series by applying a low frequency current which does not substantially penetrate the skin.