Maximum likelihood estimation in meta-analytic structural equation modeling.

Meta-analytic structural equation modeling (MASEM) involves fitting models to a common population correlation matrix that is estimated on the basis of correlation coefficients that are reported by a number of independent studies. MASEM typically consist of two stages. The method that has been found to perform best in terms of statistical properties is the two-stage structural equation modeling, in which maximum likelihood analysis is used to estimate the common correlation matrix in the first stage, and weighted least squares analysis is used to fit structural equation models to the common correlation matrix in the second stage. In the present paper, we propose an alternative method, ML MASEM, that uses ML estimation throughout. In a simulation study, we use both methods and compare chi-square distributions, bias in parameter estimates, false positive rates, and true positive rates. Both methods appear to yield unbiased parameter estimates and false and true positive rates that are close to the expected values. ML MASEM parameter estimates are found to be significantly less bias than two-stage structural equation modeling estimates, but the differences are very small. The choice between the two methods may therefore be based on other fundamental or practical arguments. Copyright © 2016 John Wiley & Sons, Ltd.