In this study, we develop and estimate a censored LA/AIDS model using household-level purchase data. In addition to imposing non-negativitity constraints, we account for the endogeneity of unit value. We address the non-negativity issue using an Amemiya-Tobin approach, which imposes the adding-up condition on both observed and latent shares. We address the endogeneity of unit value by estimating share equations and unit value equations simultaneously. Given the need to evaluate high-order probability integrals, we use a simulated probability method in the model estimation. This model is applied to estimate and analyze a demand system featuring six fish and three meat commodities, using Norwegian household data.