Profile maximal likelihood estimation for non linear mixed models with longitudinal data

In this article, the profile maximal likelihood estimate (PMLE) is proposed for non linear mixed models (NLMMs) with longitudinal data where the variance components are estimated by the expectation-maximization (EM) algorithm. Strong consistency and the asymptotic normality of the estimators are derived. A simulation study is conducted where the performance of the PLME and the Fishing scoring estimate (FSE) in literatures are compared. Moreover, a real data is also analyzed to investigate the empirical performance of the procedure.