Likelihood-Based Inference with Missing Data Under Missing-at-Random

• Activity Number: 598
• Type: Topic Contributed
• Date/Time: Thursday, August 7, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Social Statistics Section
• Author(s): Shu Yang*+ and Jae-Kwang Kim
• Companies: Iowa State University and Iowa State University
• Keywords: Likelihood ratio ; Multiple imputation ; Profile likelihood ratio ; Wald confidence interval ; Wilk confidence interval

Abstract

Likelihood-based inference with missing data is a challenging problem because the observed likelihood is of an integral form. A naive approach is to approximate the integral by a Monte Carlo sampling, which does not necessarily lead to valid inference when the Monte Carlo samples are generated from a distribution with a fixed parameter value.

We consider an alternative approach that is based on the parametric fractional imputation of Kim (2011). In the proposed method, the observed likelihood function is correctly computed as the dependency on the parameter is properly reflected through fractional weights. We then discuss constructing the Wilk confidence interval from the profile likelihood ratio test in the presence of nuisance parameters and describe the Newton-Raphson algorithm for finding the Wilk interval end points. Two limited simulation studies show the advantage of the likelihood-based inference over the Wald-type inference in terms of power, parameter space conformity and computational efficiency. A real data example of the Salamander mating shows that our method also works well with high-dimensional missing data.