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A Numerical Likelihood-Based Approach to Combining Correlation Matrices
Authors:Myung Soon Song  Leon J. Gleser
Affiliation:1. Department of Statistics , University of Pittsburgh , Pittsburgh , Pennsylvania , USA mys7@pitt.edu;3. Department of Statistics , University of Pittsburgh , Pittsburgh , Pennsylvania , USA
Abstract:Numerical approaches to developing accurate and efficient approximations to combined likelihoods of population correlation matrices in meta-analysis under normality assumptions for the data are studied. The likelihood is expressed as a multiple integral over the unit cube in (p ? 1)-dimensional space, where p is the row and column dimensionality of the correlation matrix. Three types of computation are proposed as ways to calculate the likelihood for any population correlation matrix P. As an application, inference is explored concerning intercorrelations among math, spatial and verbal scores in a SAT exam. Comparisons are made with conventional methods.
Keywords:Correlation matrix  Likelihood  Meta-analysis  Numerical integration
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