## Colloquium: “An unconventional approach to likelihood of correlation matrices”

Marshall University Math Colloquium

March 12, 2012

Myung Soon Song

*University of Pittsburgh*

**Abstract**

Numerical approximations are important research areas for dealing with complicated functional forms. Techniques for developing accurate and efficient calculation of combined likelihood functions in meta-analyses are studied. A multivariate numerical integration method for developing a better approximation of the likelihood of correlation matrices is studied. Analyses for (1) intercorrelations among Math, Spacial and Verbal scores in an SAT exam and (2) intercorrelations among Cognitive Anxiety, Somatic Anxiety and Self Confidence from Competitive State Anxiety Inventory (CSAI-2) are explored. Algorithms to evaluate likelihood and to find the MLE is developed. Comparison with two conventional methods (joint asymptotic weighted average and marginal asymptotic weighted average) is shown.