A new approach for the estimation of bid-rent functions for residential location choice is proposed. The method is based on the bid-auction approach and considers that the expected maximum bid of the auction is a latent variable that can be related to observed price indicators through a measurement equation. The method has the advantage of allowing for the estimation of the parameters of the bid function that explain the heterogeneous preferences of households for location while simultaneously adjusting the expected maximum bid to reproduce realistic values. The model is applied and validated for a case study on the city of Brussels. Results show that the proposed model outperforms other methods for bid-rent estimation, both in terms of real estate prices and spatial distribution of agents, especially when detailed data describing the real estate goods and their prices is not available.