Obesity has become one of the major public health issues during the last three decades. A considerable number of determinants have been proposed for body mass index (BMI) by a large range of studies from multiple disciplines. In addition, it is well documented that im- pacts of these determinants are varying across demographic groups. However little is known about the relative importance of these poten- tial determinants and the varying impacts of all relatively important determinants. Using the shrinkage estimation technique, we propose a variable selection procedure for the categorical varying-coefficient model. We present a simulation study to exam performance of our method in different scenarios. We further apply the proposed method to examine the impacts of a large number of potential determinants on BMI, using data from the 2013 National Health Interview Survey in the United States. By our method, the relevant determinants of BMI are identified through the variable selection procedure; and their varying impacts across demographic groups are quantified through the post-selection estimation.