Parametric Fractional Imputation using Adjusted Profile Likelihood for Linear Mixed Models with Nonignorable Missing Data

• Activity Number: 626
• Type: Contributed
• Date/Time: Thursday, August 2, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Survey Research Methods
• Author(s): Shu Yang*+ and Jaekwang Kim and Zhengyuan Zhu
• Companies: Iowa State University and Iowa State University and Iowa State University
• Keywords: EM algorithm ; Random effect ; Mixed effects model ; restricted maximum likelihood ; Longitudinal data

Abstract

Inference in the presence of missing data is a widely encountered and difficult problem in statistics. Imputation is often used to facilitate parameter estimation, which uses the complete sample estimators to the imputed data set. We consider the problem of parameter estimation for linear mixed models with non-ignorable missing values, which assumes the missingness depends on the missing values only through the random effects, leading to shared parameter models (Follmann and Wu,1995). We develop a parametric fractional imputation (PFI) method proposed by Kim (2011) under this non-ignorable response model, which simplifies the computation associated with the EM algorithm for maximum likelihood estimation with missing data. In the M-step, the restricted or adjusted profiled maximum likelihood method is used to reduce the bias of maximum likelihood estimation of the variance components. Results from a simulation study are presented to compare the proposed method with the existing methods, which demonstrates that imputation can significantly reduce the non-response bias and the idea of adjusted profiled maximum likelihood works nicely in PFI for the bias correction in estimating the variance components.