In a typical adsorption experimental study, adsorbate concentration in solid phase is generally calculated by mass balance equation and rarely measured separately. This procedure causes the presence of correlated errors between adsorbate concentrations in fluid and solid phase. To determine adsorption isotherm parameters with correlated errors, the objective function of maximum likelihood estimation is derived under the framework of measurement error models. Two approximate solutions to eliminate nuisance parameters are presented following the exact expression of maximum likelihood estimation. Monte Carlo simulation is carried out to compare the accuracy and precision of proposed methods with other commonly used regression techniques for Langmuir and Freundlich isotherms. Simulation results confirm that measurement error models are most accurate and precise among all examined methods. The proposed measurement error models are especially suited for the adsorption experiment where the ratio of fluid volume to solid mass is large. (C) 2015 Elsevier B.V. All rights reserved.