A Two-Step Method of Estimation for Non-Linear Mixed-Effects Models

Abstract

The main goal of this paper is to propose a two-step method for the estimation of parameters in non-linear mixed-effects models. A first-step estimate θ˜ of the vector θ of parameters is obtained by solving estimation equations, with a working covariance matrix as the identity matrix. It is shown that θ˜ is consistent. If, furthermore, we have an estimated covariance matrix, V^, by θ˜, a second-step estimator θ^ can be obtained by solving the optimal estimation equations. It is shown that θ^ maintains asymptotic optimality. We establish the consistency and asymptotic normality of the proposed estimators. Simulation results show the improvement of θ^ over θ˜. Furthermore, we provide a method to estimate the variance σ2 using the method of moments; we also assess the empirical performance. Finally, three real-data examples are considered.

Keywords

• two-step estimate
• consistency
• estimation equation
• non-linear mixed model