On Obtaining Estimates of the Fraction of Missing Information From Full Information Maximum Likelihood

Fraction of missing information λ j is a useful measure of the impact of missing data on the quality of estimation of a particular parameter. This measure can be computed for all parameters in the model, and it communicates the relative loss of efficiency in the estimation of a particular parameter due to missing data. It has been recommended that researchers working with incomplete data sets routinely report this measure, as it is more informative than percent missing data (Bodner, 2008 Bodner, T. E. 2008. What improves with increasing missing data imputations?. Structural Equation Modeling, 15: 651–675. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]; Schafer, 1997 Schafer, J. L. 1997. Analysis of incomplete multivariate data. London: Chapman & Hall.. [Crossref] , [Google Scholar]). However, traditional estimates of λ j require the implementation of multiple imputation (MI). Many researchers prefer to fit structural equation models using full information maximum likelihood rather than MI. This article demonstrates how to obtain an estimate of λ j using maximum likelihood estimation routines only and argues that this estimate is superior to the estimate obtained via MI when the number of imputations is small. Interpretation of λ j is also addressed.