Addressing Item-Level Missing Data: A Comparison of Proration and Full Information Maximum Likelihood Estimation

Abstract

Often when participants have missing scores on one or more of the items comprising a scale, researchers compute prorated scale scores by averaging the available items. Methodologists have cautioned that proration may make strict assumptions about the mean and covariance structures of the items comprising the scale (Schafer & Graham, 2002; Graham, 2009; Enders, 2010). We investigated proration empirically and found that it resulted in bias even under a missing completely at random (MCAR) mechanism. To encourage researchers to forgo proration, we describe a full information maximum likelihood (FIML) approach to item-level missing data handling that mitigates the loss in power due to missing scale scores and utilizes the available item-level data without altering the substantive analysis. Specifically, we propose treating the scale score as missing whenever one or more of the items are missing and incorporating items as auxiliary variables. Our simulations suggest that item-level missing data handling drastically increases power relative to scale-level missing data handling. These results have important practical implications, especially when recruiting more participants is prohibitively difficult or expensive. Finally, we illustrate the proposed method with data from an online chronic pain management program.

KEYWORDS:

• auxiliary variables
• full information maximum likelihood
• missing data
• proration
• questionnaires

SUPPLEMENTAL MATERIAL

Supplemental data for this article can be accessed on the publisher's website.

Notes

MSE ratios comparing FIML with items as auxiliary variables to proration are reported in Table B1 of the online appendix. Because proration resulted in non-negligible bias when either the item means or inter-item correlations varied, the MSE ratios express bias and efficiency differences between the two estimators.