New Confidence Intervals and Bias Comparisons Show that Maximum Likelihood Can Beat Multiple Imputation in Small Samples

TL;DR

This paper introduces small-sample t-based confidence intervals for maximum likelihood estimation, demonstrating they outperform multiple imputation in terms of bias, efficiency, and coverage in small-sample analyses of incomplete data.

Contribution

The authors develop and validate small-sample t-based ML confidence intervals, showing they are superior to MI in small samples for bias, efficiency, and coverage.

Findings

ML estimates are less biased than MI in small samples.

New t-based ML confidence intervals have better coverage and are shorter than MI intervals.

ML outperforms MI in small-sample scenarios for incomplete data analysis.

Abstract

When analyzing incomplete data, is it better to use multiple imputation (MI) or full information maximum likelihood (ML)? In large samples ML is clearly better, but in small samples ML's usefulness has been limited because ML commonly uses normal test statistics and confidence intervals that require large samples. We propose small-sample t-based ML confidence intervals that have good coverage and are shorter than t-based confidence intervals under MI. We also show that ML point estimates are less biased and more efficient than MI point estimates in small samples of bivariate normal data. With our new confidence intervals, ML should be preferred over MI, even in small samples, whenever both options are available.