Large Cluster Approximation to the Finite Mixture Information Matrix with an Application to Meta-Analysis

• Activity Number: 613
• Type: Contributed
• Date/Time: Thursday, August 7, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing
• Author(s): Andrew Raim*+ and Nagaraj Neerchal
• Companies: University of Maryland Baltimore County and University of Maryland Baltimore County
• Keywords: Fisher Information ; Complete Data ; Model-Based Clustering ; Exponential Family

Abstract

Finite mixtures have been adopted in a wide range of statistical applications. Their utility comes at a computational cost and a loss of tractability for common inference techniques. The Fisher information matrix (FIM) is often used with maximum likelihood estimation but does not have a simple analytical form in the finite mixture setting. Raim, Neerchal, and Morel (2014, submitted) have recently shown that, in some finite mixture settings, a certain block-diagonal matrix becomes close to the FIM as the sample size increases. This block-diagonal matrix is the FIM of the complete data: the observed data along with a latent indicator of the subpopulation from the mixture from which an observation is drawn. The convergence requires that the sample is "grouped" so that individual observations are known to be drawn from a common subpopulation. One application where this kind of sampling can naturally be justified is meta-analysis. We consider model-based clustering of studies in a meta-analysis to explore the nature of their heterogeneity. A simulation study is presented to illustrate the closeness of the complete data FIM and actual FIM. Use of the complete data FIM is also demonstrated on an example dataset measuring selenium content in nonfat milk powder. We conclude that the complete data FIM can serve as a reasonable approximation to the actual FIM for this kind of application.