Closed-form estimation of two randomly missing observations in non-replicated two-way factorial experiments (MultiMiss2)

This study introduced MultiMiss2, a novel closed-form methodology for estimating two randomly missing observations in non-replicated two-way factorial experiments. By minimizing the squared error loss (L2-norm), the approach provides analytic estimators that consistently demonstrated reduced bias, variance, mean absolute error (MAE), and mean squared error (MSE) as replications increased. Sensitivity analyses confirmed its robustness, with numerical optimizations converging to analytic solutions across all scenarios. Comparative benchmarking against established imputation methods (Mice, Amelia, MissForest, and Hmisc) showed that, while these approaches performed adequately in multivariate contexts, they were less suited for factorial designs. In contrast, MultiMiss2 consistently yielded smaller centered squared error loss, SSE, offering more accurate and reliable estimates. Although limited by the inability to estimate interaction effects in non-replicated designs, this methodology marks a significant step forward in factorial data analysis. Future work will extend the framework to handle more missing values, replicated designs, and higher-order factorial structures.