A new approach for handling missing correlation values for meta-analytic structural equation modeling: Corboundary R package

Abstract

With increased use of multivariate meta-analysis in numerous disciplines, where structural relationships among multiple variables are examined, researchers often encounter a particular challenge due to missing information. The current research concerns missing correlations (rs) in the correlation matrix of m variables (R _{m × m} ) and establish more informative and empirical prior distributions for missing rs in R _{m × m} . In particular, the method for deriving mathematically/analytically boundaries for missing rs in relation to other adjacent rs in R _{m × m} , while satisfying conditions for a valid R _{m × m} (i.e., a symmetric and positive semidefinite correlation matrix containing real numbers between -1 and 1) is first discussed. Then, a user-defined R package for constructing the empirical distributions of boundaries for rs in R _{m × m} is demonstrated with an example. Furthermore, the applicability of constructing empirical boundaries for rs in R _{m × m} beyond multivariate meta-analysis is discussed.

Keywords: boundary; meta‐analysis; missing correlation.

Figure 1

Mean square errors of estimators when number of studies included in meta‐analysis are varied

Figure 2

Mean square errors of estimators when the probabilities of missingness are varied