How many imputations are really needed? Some practical clarifications of multiple imputation theory.

Area of Science:

• Statistics
• Psychometrics
• Prevention Science

Background:

• Multiple Imputation (MI) and Full Information Maximum Likelihood (FIML) are standard methods for handling missing data.
• Theoretical equivalence between MI and FIML exists as the number of imputations (m) approaches infinity.
• Existing guidelines for sufficient m are based on relative efficiency, potentially underestimating practical needs.

Purpose of the Study:

• To determine the necessary number of imputations (m) for MI to achieve sufficient equivalence with FIML in prevention science.
• To investigate the impact of the fraction of missing information (gamma) and m on MI model results.
• To assess the relationship between m, relative efficiency, and statistical power, particularly for small effect sizes.

Main Methods:

• A Monte Carlo simulation was employed to test MI models under varying scenarios of gamma and m.
• Standard errors and p-values for regression coefficients were analyzed as a function of m.
• Statistical power was evaluated across different levels of m and effect sizes.

Main Results:

• Standard errors and p-values varied with m, but not in direct proportion to relative efficiency.
• Statistical power for small effect sizes decreased substantially as m decreased.
• The rate of power falloff with smaller m was significantly greater than predicted by relative efficiency alone.

Conclusions:

• Researchers should perform more imputations with MI than current guidelines suggest.
• Recommendations for m should consider the fraction of missing information (gamma) and the tolerance for power loss.
• Using too few imputations can lead to a preventable loss of statistical power compared to FIML.