Maximizing the usefulness of data obtained with planned missing value patterns: An application of maximum likelihood procedures

John W. Graham, Scott M. Hofer, David P. MacKinnon

Research output: Contribution to journalArticlepeer-review

256 Scopus citations


Researchers often face a dilemma: Should they collect little data and emphasize quality, or much data at the expense of quality? The utility of the 3-form design coupled with maximum likelihood methods for estimation of missing values was evaluated. In 3-form design surveys, four sets of items, X, A, B, and C are administered: Each third of the subjects receives X and one combination of two other item sets - AB, BC, or AC. Variances and covariances were estimated with pairwise deletion, mean replacement, single imputation, multiple imputation, raw data maximum likelihood, multiple-group covariance structure modeling, and Expectation-Maximization (EM) algorithm estimation. The simulation demonstrated that maximum likelihood estimation and multiple imputation methods produce the most efficient and least biased estimates of variances and covariances for normally distributed and slightly skewed data when data are missing completely at random (MCAR). Pairwise deletion provided equally unbiased estimates but was less efficient than ML procedures. Further simulation results demonstrated that non-maximum likelihood methods break down when data are not missing completely at random. Application of these methods with empirical drug use data resulted in similar covariance matrices for pairwise and EM estimation, however, ML estimation produced better and more efficient regression estimates. Maximum likelihood estimation or multiple imputation procedures, which are now becoming more readily available, are always recommended. In order to maximize the efficiency of the ML parameter estimates, it is recommended that scale items be split across forms rather than being left intact within forms.

Original languageEnglish (US)
Pages (from-to)197-218
Number of pages22
JournalMultivariate Behavioral Research
Issue number2
StatePublished - 1996

ASJC Scopus subject areas

  • Statistics and Probability
  • Experimental and Cognitive Psychology
  • Arts and Humanities (miscellaneous)


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