Lasso-Type Estimators for Semiparametric Nonlinear Mixed-Effects Models Estimation

• Activity Number: 401
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): Cristian Meza*+ and Ana Arribas-Gil and Karine Bertin and Vincent Rivoirard
• Companies: Universidad de Valparaiso and Universidad Carlos III de Madrid and Universidad de Valparaiso and Université Paris Dauphine
• Keywords: Semiparametric nonlinear mixed-effects models ; LASSO ; SAEM algorithm ; REML estimation

Abstract

Parametric nonlinear mixed effects models (NLMEs) are now widely used due to the computational advances achieved during the last years. However, this kind of models may not be flexible enough for complex longitudinal data analysis. Semiparametric NLMEs (SNMMs) have been proposed by Ke and Wang (2001). These models are a good compromise and retain nice features of both parametric and nonparametric models resulting in more flexible models than standard NLMEs. However, SNMMs are complex models for which estimation still remains a challenge. The estimation procedure proposed by Ke and Wang is based on a combination of log-likelihood approximation methods for parametric estimation and smoothing splines techniques for nonparametric estimation. In this work, we propose new estimation strategies in SNMMs. On the one hand, we use the Stochastic Approximation version of EM algorithm (Delyon et al., 1999) to obtain exact ML and REML estimates of the fixed effects and variance components. On the other hand, we propose a LASSO-type method to estimate the unknown nonlinear function. We combine the two approaches in a general estimation procedure that we illustrate with simulated and real data.